15th International Conference on Applications of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools – ICAFS-2022 3031252519, 9783031252518

Table of contents :
Preface
Organization
Keynote Speeches
Summarization of Bimodal Information from Large Data Sets
A System of Systems Framework for Intelligence in Autonomy, Big Data Analytic and Applications
Granular Knowledge Transfer and Knowledge Distillation: At the Junctions of Machine Learning and Granular Computing
Quo Vadis AI?
Contents
On Some De Novo Type Approaches to Fuzzy Decision Making, Optimization and Control: An Application to Sustainable Regional Development
The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence
Multiattribute Decision Making in Material Selection Under Z-Valued Information
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution Method
5 Conclusion
References
Maximum Dynamic Evacuation Modelling in Networks in Fuzzy Conditions with Partial Lane Reversal
1 Introduction
2 Preliminaries and Problem Statement
3 Definition of Maximum Dynamic Evacuation Flow with Lane Reversal
4 Example
5 Conclusion and Future Scope
References
Z-Number-Based Similarity Reasoning in Control Systems
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Application of Numerical Example
5 Conclusion
References
Design of Quasi-Resonant Flyback Converter Integrated by Fuzzy Controller
1 Introduction
2 Controllers Design
2.1 Design QRFBC Using Fuzzy Logic Controller
2.2 Methodology of Investigation of QRFBC Controlled by FLC
2.3 Testing the QRFBC Controlled by PI Controller
3 Results and Discussions
4 Conclusion
References
Experimental Selecting Appropriate Fuzzy Implication in Traffic IF-Then Rules
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Conclusion
References
Prediction of Cold Filter Plugging Point of Different Types of Biodiesels Using Various Empirical Models
1 Introduction
2 Material and Methods
2.1 Data
2.2 Machine Learning Models (MLMs)
2.3 QM and MLR models
3 Results and Discussion
3.1 Estimating the CFPP Using MLPNN and RBFNN
3.2 Estimating the CFPP Using QM and MLR
3.3 Performance Evaluation of Proposed Models
4 Conclusions
References
Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem
1 Introduction
2 A BLP Problem for an Industrial Symbiosis Network
3 Fuzzy Solution Approaches for the BLP Problem
3.1 Fuzzy Programming Approach – FPA
3.2 Fuzzy Goal Programming – FGP
4 Computational Results
5 Conclusion
References
Decision Making on Students’ Performance Estimation
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Application
5 Conclusion
References
A Comparative Analysis of the Different CNN Models Using Fuzzy PROMETHEE for Classification of Kidney Stone
1 Introduction
2 Materials and Methods
2.1 Dataset
2.2 Deep Learning Models
2.3 Evaluation Methods
3 Fuzzy-Based MCDM Models
4 Results
5 Conclusion
References
Developing Efficient Frontier for Investment Portfolio: A Fuzzy Model Approach
1 Introduction
2 Preliminaries
3 Problem Definition and Solution Method
4 Conclusion
References
Impact of Online Education Classes on Students’ Satisfaction: The Case of Near East University
1 Introduction
2 Research Method
2.1 Participants
2.2 Data Collection Tools
2.3 Data Analysis
2.4 Results
2.5 Discussion
3 Conclusion and Recommendation
References
Decision Making on Selection of Ferritic Stainless Steel
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Application
5 Discussion and Conclusion
References
Multicriteria Group Decision Making on Information System Project Selection Using Type-2 Fuzzy Set
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Forecasting Demand in the Commodity Market of Food Products Using Neural Networks
1 Introduction
2 Basic Definitions
3 Choosing a Neural Network Architecture for Predicting the Coefficient of Demand Elasticity
4 Conclusion
References
Introducing Uncertainty-Based Dynamics in MADM Environments
1 Introduction
2 TOPSIS
3 An Illustrative Numerical Exercise
4 Perception-Based Evaluation Intervals
4.1 Value Functions
5 Analysis
6 Conclusions
References
Analyzing the Digital Marketing Strategies Role in Post Pandemic Recovery Period
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Artificial Intelligence and Digital Economy: Development Prospects
1 Introduction
2 Artificial Intelligence: Historical Aspect
3 Contribution of AI Technologies to Economic Activity
4 Projected Gap Between Countries, Companies and Workers
5 Conclusion
References
Evaluation of Logistics Services of Airlines in the Azerbaijan Passenger Transportation Market
1 Introduction
2 Statement of the Problem
3 Estimation of Airlines Using a Fuzzy Inference System
4 Identification of Weights of Evaluation Criteria
5 Estimating Airlines Using the Fuzzy Maximin Convolution Method
6 Evaluation of Airlines by Pareto Rules and Bord Method
7 Conclusion
References
Customer Characteristics in Digital Marketing Model
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Estimation of Countries’ Economic Development by Using Z-Number Theory
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Fuzzy Approach to Explainable Artificial Intelligence
1 Introduction
2 Review of Fuzzy Rules Extraction Algorithms
3 Rule Extraction Algorithm Based on Decision Trees
3.1 Rule Extraction Algorithm
3.2 Rules Extraction from ANN Based on the Decision Trees
4 Discussion
References
Z-Numbers Based Evaluation of Expert Opinions on Agricultural Structure
1 Introduction
2 Statement of the Problem
3 The Algorithm and Solution of the Problem
4 Conclusions
References
Pareto-Optimality-Based Investigation of Quality of Fuzzy IF-THEN Rules
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem by Using Numerical Example
5 Conclusion
References
Predicting Solar Power Generated by Grid-Connected Two-Axis PV Systems Using Various Empirical Models
1 Introduction
2 Material and Methods
2.1 Study Area and Data
2.2 Adaptive-Neuro Fuzzy Inference System (ANFIS)
2.3 Response Surface Methodology
3 Results and Discussion
3.1 Modeling with ANFIS
3.2 Modeling with RSM
3.3 Performance Evaluation of ANFIS and RSM
4 Conclusions
References
Z-Preferences in Consumer Buying Behavior
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Prediction of the Power Output of a 4.5 kW Photovoltaic System Using Three Empirical Models: A Case Study in Nahr El-Bared, Lebanon
1 Introduction
2 Material and Methods
2.1 Study Area and Data
2.2 Machine Learning Models (MLMs)
2.3 Response Surface Methodology
3 Results and Discussion
3.1 Estimating the PV-Power Using MFFNN and CFNN
3.2 Estimating the PV Power Using RSM
3.3 Performance Evaluation of MFFNN, CFNN, and RSM
4 Conclusions
References
Z-Decision Making for the Selection of IT Engineers
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Optimal Implicatıon Based Fuzzy Control System for a Steam Generator
1 Introduction
2 Statement of the Problem
3 Solution of the Problem
4 Conclusion
References
Prediction of Runoff Using Artificial Neural Networks, MLR Regression, and ARIMA Model (A Case Study: Bared River, Lebanon)
1 Introduction
2 Material and Methods
2.1 Data
2.2 Machine Learning Models (MLMs)
2.3 ARIMA Model
2.4 MLR Model
3 Results and Discussion
3.1 Estimating the Runoff Using MLPNN and RBFNN
3.2 Estimating the Runoff Using ARIMA and MLR
3.3 Performance Evaluation of Proposed Models
4 Conclusions
References
Devices with Fuzzy Logic Control of Artificial Lung Ventilation
1 Methods and Models
2 Statement of the Problem and Its Solution
3 Conclusions
References
Structural Analysis of Piston Machines by Using Computer Software
1 Introduction
2 The Mechanical and Thermodynamically Analysis of the Piston Machines
3 Dynamical Parameters for the Piston Machine
4 Modeling and Meshing of the Connecting Rod
5 Conclusions
References
Using of Conventional Neural Network to Diagnose Scabies by Dermoscopy
1 Introduction
2 Materials and Method
2.1 Datasets
2.2 Data Preparation
2.3 Data Augmentation
2.4 CNN
2.5 Activation Function
2.6 Fully-Connected Layer
2.7 Optimizer Adam
2.8 Transfer Learning
3 Experiments
3.1 Experimental Results and Analysis
4 Conclusion
References
Determination of the Dynamic and Interactive Event in Exascale Computing Systems via Request Clustering
1 Introduction
2 Dynamic and Interactive Event
3 Grouping of the Requests Using Their Requirements
4 Argument
5 Conclusion
References
Evaluation of Techniques Used in Phenol Removal from Wastewater Using Fuzzy PROMETHEE Method
1 Introduction
1.1 Techniques Applied in Phenol Removal in Wastewater
2 Materials and Methodology
2.1 PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations)
3 Results and Discussion
4 Conclusion
References
Research of the Manufacturing Quality of Plastic Details with Complex Forms of Connection
1 Introduction
2 Optimal Control of Technological Regimes
3 Establishing the Mathematical Dependence Between the Quality Indicators (Shrinkage and Strength) of Details on the Pressing Temperature
4 Discussion and Conclusions
References
Tableaux Deduction System for Fuzzy Logic with Estimates of Fuzziness Values
1 Introduction. Main Definitions
2 Equivalences in the Logic of Estimates LE
3 System Σ
4 Completeness of the System Σ for Logic of Estimates LE
5 Deduction in the Logic of Estimates LE
References
Research of Bitumen-Based Asphalt Compositions Using Neural Network
1 Introduction
2 Materials Used in Practice
3 Methodology of Sample Preparation
4 Results and Discussion
5 Conclusion
References
Logical-Linguistic Model for Reactor Cleaning from Impurities
1 Introduction
2 Statement of the Problem
3 Fuzzy Control Algorithm
4 Conclusion
References
Quantitative Assessment of the Risk of Failure and Vulnerability of Oil and Gas Pipelines at Underwater Crossings
1 Introduction
2 Modeling of the Process of General Erosion
3 Application of the Model
4 Conclusions
References
Prediction of Energy Consumption in Residential Buildings Using Type-2 Fuzzy Wavelet Neural Network
1 Introduction
2 T2-FWNN Model for Energy Consumption
3 Simulations
4 Conclusions
References
Modeling the Interaction of Components of a Distributed Information and Communication Environment
1 Introduction
2 Conceptual Representation of a Behavioral Model of a Distributed Information Space
3 Conclusion
References
Fuzzy Approach to Analysis of the Temporal Variability of the Vegetation in a Specific Area
1 Introduction
2 Problem Definition
3 FTS: Initial Steps for Building a Predictive Model
4 Modeling the NDVI FTS
5 Conclusion
References
Application of Fuzzy TOPSIS in Server Selection Problem
1 Introduction
2 Fuzzy TOPSIS Method
3 Server Selection Problem Solving
4 Conclusion
References
Fuzzy Inference Based Quadcopter Flight Regulation Under Overland Monitoring
1 Introduction
2 Problem Formulation
3 Fuzzy Inference System for Quadcopter Autopilot Regulation
4 Conclusion
References
Fuzzy Logic Analysis of Parameters Affecting Students’ Satisfaction with Their Life at University
1 Introduction
2 Research Problem
3 Data Collection and Data Analysis
4 The Analysis Process of Satisfaction Values Using Fuzzy Logic
5 Conclusion
References
Investigation of Submarine Pipeline Failure Accidents in Deepwater Based on the Fuzzy Analytical Hierarchy Process
1 Introduction
2 Materials and Methods
3 Solution of the Problem
4 Conclusion
References
Healthy Weight Estimation by Using Fuzzy Concept
1 Introduction
2 Methodology
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Using Residual Learning in the Food Processing Sector: The Case of Banana Sorting
1 Introduction
1.1 Dataset
2 Transfer Learning of ResNet-50
3 Results and Discussion
4 Conclusion
References
Electre Method for Supermarket Selection Under Imperfect Information
1 Introduction
2 Methodolody
3 Numerical Example
4 Conclusion
References
Study of Gas Dynamic Processes of Drainage Zone of Oil Wells
1 Introduction
2 Conclusions
References
Appling Fuzzy Inference Logic System to Dynamic Model of Gross Domestic Product (in Case of Azerbaijan)
1 Introduction
2 The Dynamic Model of GDP with Two Controls
3 Conclusion
References
Analysis of Knee Osteoarthritis Grading Using Deep Learning
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
References
Navigation of a Mobile Robot Based on Fuzzy Images in an Uncertain Environment
1 Introduction
2 Visual Image Processing
2.1 Fuzzy Image Processing
3 Simulation of the System
4 Conclusion
References
Comparison of Oil Quality of Various Fields Based on Fuzzy Cluster Analysis
1 Introduction
2 Brief Analysis of Existing Works
3 Application of Fuzzy Clustering to Modeling Relationship Between Oil Properties and Difficulty of Oil Extraction
4 Conclusion
References
Interdisciplinary Nature of Borderline Disciplines: A Transition from Binary Logic to Fuzzy Logic
1 Introduction
2 Preliminaries
2.1 Membership Characteristic Function
2.2 Intersection of Fuzzy Sets
2.3 Fuzzy Logic Dialogical “Both-And” Approach
3 Borderline Disciplines as an Interdisciplinary Field of Research
4 Criticism of “Either/Or” Approach to Borderline Disciplines
5 Logic of Interdisciplinarity – Fuzzy Logic
6 Borderline Disciplines in the Light of Fuzzy Logic
7 Conclusion
References
Decision Making in Hepatitis B Diagnosis by Using Fuzzy Expert System: Case of Near East Hospital
1 Introduction
2 The Fuzzy Expert SYSTem’s Working Principle
3 Methodology
4 Computer Simulation
5 Conclusion
References
Application of Leointief’s Input-Output Model of Azerbaijan Economy Under Fuzzy Information
1 Introduction
2 Leontief’s Model Described by Fuzzy Linear Equations
3 Technology Matrix A"0365 A with Fuzzy Entries
4 Leontief Model of the Azerbaijani Economy Described by Fuzzy Linear Equations
5 Conclusion
References
Simulation of Fractal Kinetics of Thermooxidation of Polymer Melts Based on Fractional Differential Equations
1 Introduction
2 Analysis of Existing Works
3 Results of Experimental Studies
4 Conclusion
References
Fuzzy Models for Calculation of Oil and Gas Reserves
1 Introduction
2 Problem Statement
3 Calculation of Oil Reserves Based on the Theory of Fuzzy Sets
4 Conclusion
References
Vendor Selection by Using Ideal Solution Methodology with Fuzzy Numbers
1 Introduction
2 Preliminaries
3 Statement and Solution of the Problem
4 Conclusion
References
Selection Core Banking System by Using Fuzzy AHP and Fuzzy TOPSIS Hybrid Method
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Conclusion
References
Performance Analysis of Machine Learning Algorithms for Medical Datasets
1 Introduction
2 Materials and Methods
2.1 Datasets
2.2 Machine Learning Models
2.3 Design of Experiments and Evaluation
3 Results
3.1 Results of Binary Classification Experiments
3.2 Results of Multi-class Experiments
4 Discussions
5 Conclusion
References
Difference Between Digital Marketing and Traditional Marketing Models  
1 Introduction
2 Preliminaries
3 Difference Between Digital Marketing and Traditional Marketing Concepts
3.1 Traditional Marketing Model
3.2 Digital Marketing Model
4 Statement of the Problem
5 Solution of the Problem
6 Conclusion
References
Determination of Green Field Plants Most Suitable for Geographical Features of Places with Fuzzy Logic Methods
1 Introduction
2 Purpose of the Research
3 The Research Method
3.1 Classification by Decision Tree Method
3.2 Fuzzy Application
4 Conclusion
References
Z-Information Based MCDM Model for Assessing Green Energy Resources: A Case of Resort and Tourism Areas
1 Introduction
2 Definitions and Operations with Z-numbers
2.1 Z-Number-Based ORESTE Method
3 Results
3.1 Application of Z-numbers Based ORESTE
3.2 Application of the Z-TOPSIS
4 Discussions and Conclusion
References
Assessing the Impact of Innovations on the Volume of Production of the Final Product in a Fuzzy Information Environment
1 Introduction
2 Calculation of the Final Product of the Region Using a Production Function that Takes into Account the Innovation Factor
3 Estimation Results of Output (Y) Using the Fuzzy Cobb-douglas (Innovation) Model
4 Conclusion
References
Application of WASPAS Method to Data Platform Selection Under Z-Valued Information
1 Introduction
2 Preliminaries
3 Statement of the Problem and a Solution Method
4 Conclusion
References
Using Deep Learning Algorithm for Prediction and Detection of Covid-19
1 Introduction
2 Machine Learning Algorithm
3 Methodology of the Process
4 Result of Prediction and Detection
5 Conclusion
References
Fuzzy Logic-Based Planning of the Behavior of Autonomous Vehicles
1 Introduction
2 Models and Methods
3 Statement of the Problem and Simulation of the System
4 Conclusion
References
Digitization of Centrifugal Compressor Asset as One of Key Elements of Overall Digitized Industrial Plant
1 Introduction
2 Description of Scientific-Technical Solution
3 Conclusion
References
Investment Decision Making by Using Natural Language Processing
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Multi-attribute Decision Making Under Z-Set Valued Uncertainty
1 Introduction
2 Preliminaries
3 Statement of the Problem and a Solution Method
3.1 Hurwicz Approach
3.2 Fair Price Approach [1]
4 Numeric Example
5 Conclusion
References
Fuzzy Processing of Hydrodynamic Studies of Gas Wells Under Uncertainty
1 Introduction
2 Statement of the Problem
3 Method
4 Results
5 Discussion
6 Conclusion
References
Fuzzy Modeling for Marketing Plan Development
1 Introduction
2 Fuzzy c-means Method
3 Statement of the Problem and Solution
4 Discussion and Conclusion
References
Solving Employee Selection Problem Under Fuzzy-Valued Information
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
The Use of Fuzzy Numbers for the Rational Choice of the Structure of the Distribution Channel of Goods
1 Introduction
2 Basic Definitions
3 Method for the Rational Choice of the Structure of the Distribution Channel of Goods
4 An Example for the Rational Choice of the Structure of the Distribution Channel for the Company’s Product with Certain Characteristics
5 Conclusion
References
“Dede Korkud” Epos in Light of Fuzzy Logic
1 About Fuzzy Logic Facets [1, 2]
2 Evaluating Fuzzy Uncertainties in “Dede-korkud” Text
3 Conclusion
References
Toward Z-Number-Based Classification of Dataset
1 Introduction
2 Statement of Problem
3 Solution Approach
4 An Application
References
Application of Enterprise Solution Software for a Hotel Chain
1 Introduction
2 Materials and Methods
3 Research Findings and Results
4 Conclusion
5 Conflicts of Interest
References
Fuzzy Logic Modelling of the Relationship Between Attitudes Towards Military Services and Soldiers’ Self-esteem
1 Introduction
2 Set of Problem
3 Methodology
3.1 Design the Attitude Scale
4 Fuzzy Logic Modelling the Impact of ATMS on the Self-esteem of Soldiers
5 Conclusion
References
Applying Type-2 Fuzzy TOPSIS Method to Selection of Facility Location
1 Introduction
2 Preliminaries
3 Statement of Problem and Solution Procedures
4 Conclusion
References
Applying a Fuzzy-Set Approach to Assessing Capital Flight Management: Empirical Research from Azerbaijan
1 Introduction
2 Methodology
3 Validity of the Use of the Fuzzy Set Approach
4 Practical Calculation of a Multicriteria Problem
5 Conclusion
References
Decision Making with Z-Bounded Interval Preference
1 Introduction
2 Preliminaries
3 Statement of the Problem and Solution Methods
4 Example
5 Conclusion
References
Teacher Assessment Model with Basic Uncertain Information
1 Introduction
2 Preliminiaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Design of Receiver in Fuzzy-Chaotic Communication Systems
1 Introduction
2 Preliminaries
3 Problem Statement and Solution
4 Experimental Investigation
5 Conclusion
References
Smart Traffic Monitoring and Control System
1 Introduction
2 Literature Analysis and Problem Statement
3 Problem Solving and Basic Material
4 Conclusion
References
Extension of Delphi Method to Z-Environment
1 Introduction
2 Z-Number Related Some Preliminary Information
3 Z-Valued Delphi Steps
4 Numerical Example
5 Conclusion
References
Analysis of Intelligent Interfaces Based on Fuzzy Logic in Human-Computer Interaction
1 Introduction
2 Interface Assessment Methods
2.1 Expert Appraisals and Heuristics
3 Fuzzy Logic and Expert Systems
4 Conclusion
References
Determination of the Uncertainty of the Parameters of Oxidative-Reduction Reactions of Titanomagnetites
1 Introduction
2 Thermodynamics of Oxidative Reduction Reactions of Titanomagnetites
2.1 Determination of Reaction Conditions by Using MGA
3 Results and Discussion
4 Conclusions
References
Solving Problem of Unit Commitment by Exchange Market Algorithm and Dynamic Planning Method
1 Introduction
2 Methods
2.1 Forward Dynamic Programming Approach
2.2 Formation of the Priority Table
2.3 Exchange Market Algorithm
3 Problem Formulation
4 Applying the Proposed Method to the Unit Commitment Problem
5 Simulation and Results
6 Conclusion
References
Regular Identification Algorithms for a Special Class of Neuro-Fuzzy Models ANFIS
1 Introduction
2 Problem Definition
3 Solution
4 Conclusion
References
Author Index

Citation preview

Lecture Notes in Networks and Systems 610

R. A. Aliev · J. Kacprzyk · W. Pedrycz · Mo. Jamshidi · M. B. Babanli · F. Sadikoglu   Editors

15th International Conference on Applications of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools – ICAFS-2022

Lecture Notes in Networks and Systems

610

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

Advisory Editors Fernando Gomide, Department of Computer Engineering and Automation—DCA, School of Electrical and Computer Engineering—FEEC, University of Campinas—UNICAMP, São Paulo, Brazil Okyay Kaynak, Department of Electrical and Electronic Engineering, Bogazici University, Istanbul, Turkey Derong Liu, Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, USA Institute of Automation, Chinese Academy of Sciences, Beijing, China Witold Pedrycz, Department of Electrical and Computer Engineering, University of Alberta, Alberta, Canada Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Marios M. Polycarpou, Department of Electrical and Computer Engineering, KIOS Research Center for Intelligent Systems and Networks, University of Cyprus, Nicosia, Cyprus Imre J. Rudas, Óbuda University, Budapest, Hungary Jun Wang, Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

The series “Lecture Notes in Networks and Systems” publishes the latest developments in Networks and Systems—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNNS. Volumes published in LNNS embrace all aspects and subfields of, as well as new challenges in, Networks and Systems. The series contains proceedings and edited volumes in systems and networks, spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. The series covers the theory, applications, and perspectives on the state of the art and future developments relevant to systems and networks, decision making, control, complex processes and related areas, as embedded in the fields of interdisciplinary and applied sciences, engineering, computer science, physics, economics, social, and life sciences, as well as the paradigms and methodologies behind them. Indexed by SCOPUS, INSPEC, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science. For proposals from Asia please contact Aninda Bose ([email protected]).

R. A. Aliev · J. Kacprzyk · W. Pedrycz · Mo. Jamshidi · M. B. Babanli · F. Sadikoglu Editors

15th International Conference on Applications of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools – ICAFS-2022

Editors R. A. Aliev Azerbaijan State Oil and Industry University Baku, Azerbaijan W. Pedrycz Department of Electrical and Computer Engineering University of Alberta Edmonton, AB, Canada M. B. Babanli Azerbaijan State Oil and Industry University Baku, Azerbaijan

J. Kacprzyk System Research Institute Polish Academy of Sciences Warsaw, Poland Mo. Jamshidi Department of Electrical and Computer Engineering The University of Texas at San Antonio San Antonio, TX, USA F. Sadikoglu Department of Mechatronics Near East University Nicosia, Turkey

ISSN 2367-3370 ISSN 2367-3389 (electronic) Lecture Notes in Networks and Systems ISBN 978-3-031-25251-8 ISBN 978-3-031-25252-5 (eBook) https://doi.org/10.1007/978-3-031-25252-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The Fifteenth International Conference on Application of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools (ICAFS-2022) is the premier international conference organized by Azerbaijan Association of “Zadeh’s Legacy and Artificial Intelligence” (Azerbaijan), Azerbaijan State Oil and Industry University (Azerbaijan), University of Siegen (Siegen, Germany), BISC—Berkeley Initiative in Soft Computing (Berkeley, USA), University of Texas, San Antonio (USA), Georgia State University (Atlanta, USA), University of Alberta (Alberta, Canada), University of Toronto (Toronto, Ontario, Canada), Polish Academy of Sciences, System Research Institute (Poland) and Near East University (North Cyprus). This volume presents an edited selection of the presentations from ICAFS-2022 which was held in Budva, Montenegro, August 26–27, 2022. ICAFS-2022 is held as a meeting for the communication of research on application of fuzzy logic, uncertain computation, Z-information processing, neuro-fuzzy approaches and different constituent methodologies of soft computing applied in economics, business, industry, education, medicine, earth sciences and other fields. The conference provided an opportunity to present and discuss state-of-the-art research in this expanding domain. This volume will be a useful guide for academics, practitioners and graduates in fuzzy logic and soft computing. It will allow for increasing of interest in development and applying of soft computing and artificial intelligence methods in various real-life fields. August 2022

R. A. Aliev Chairman of ICAFS-2022

Organization

Chairman R.A. Aliev, Azerbaijan

Co-chairmen and Guest Editors J. Kacprzyk, Poland M. Jamshidi, USA W. Pedrycz, Canada M. B. Babanli, Azerbaijan F. S. Sadikoglu, North Cyprus

International Program Committee A. Averkin, Russia A. Piegat, Poland B. Fazlollahi, USA B. Kang, China B. Turksen, Canada, Turkey C. Kahraman, Turkey D. Dubois, France D. Enke, USA D. Kumar Jana, India E. Babaei, Iran F. Aminzadeh, USA G. Imanov, Azerbaijan H. Berenji, USA H. Hamdan, France, UK H. Prade, France H. Roth, Germany I. Batyrshin, Mexico I. G. Akperov, Russia I. Perfilieva, Czech Republic K. Atanassov, Bulgaria

K. Bonfig, Germany K. Takahashi, Japan L. Gardashova, Azerbaijan M. Nikravesh, USA N. Yusupbekov, Uzbekistan O. Huseynov, Azerbaijan O. Kaynak, Turkey R. R. Aliev, North Cyprus R. Abiev, North Cyprus R. O. Kabaoglu, Turkey R. Yager, USA S. Ulyanov, Russia T. Allahviranloo, Turkey T. Fukuda, Japan T. Takagi, Japan V. Kreinovich, USA V. Loia, Italy V. Niskanen, Finland V. Nourani, Iran V. Novak, Czech Republic

viii

Organization

Organizing Committee Chairman U. Eberhardt, Germany Co-chairmen L. Gardashova, Azerbaijan T. Abdullayev, Azerbaijan Members N. Adilova, Azerbaijan A. Alizadeh, Azerbaijan V. Nourani, Iran J. Lorkowski, USA K. Rizvanova, Russia H. Hamdan, France, UK H. Igamberdiev, Uzbekistan M. Karazhanova, Kazakhstan N. Mehdiyev, Germany M. Knyazeva, Russia M. M. M. Elamin, Sudan M. A. Salahli, Turkey V. Ogunbode, Nigeria Sahin Akdag, North Cyprus

Conference Organizing Secretariat Azadlig Ave. 20, AZ 1010 Baku, Azerbaijan Phone: +99 412 493 45 38, Fax: +99 412 598 45 09 E-mail: [email protected], [email protected]

Keynote Speeches

Summarization of Bimodal Information from Large Data Sets

R. A. Aliev 1

2

Georgia State University, USA Azerbaijan State Oil and Industry University, Azerbaijan, 20 Azadlig Ave., AZ1010 Baku, Azerbaijan [email protected]

Abstract. Clustering is a technique used to find groups within a data set. Complexity of data sets is characterized by large volume, imprecision and partial reliability of data. This may involve fusion of fuzzy and probabilistic information, referred to as bimodal information. Sometimes, it may be possible to describe such data by using some kind of “If-Then” rules with fuzzy probabilistic components. In this work, an approach to clustering of data sets for extraction rules that contain bimodal information is proposed. The approach is based on the fuzzy C-means objective function and an evolutionary technique to produce type-2 fuzzy clusters. Further, Z-number-based cluster descriptions are formed by using the relationship between type-2 fuzzy set and Z-number. A real-world application is considered to demonstrate the usefulness of the proposed approach.

A System of Systems Framework for Intelligence in Autonomy, Big Data Analytic and Applications

Mo Jamshidi The University of Texas, San Antonio, TX, USA [email protected] Abstract. Large data has been accumulating in all aspects of our lives for quite some time. Advances in sensor technology, the Internet, wireless communication and inexpensive memory have all contributed to an explosion of “Big Data”. System of Systems (SoS) is integration of independent operatable and non-homogeneous legacy systems to achieve a higher goal than the sum of the parts. Today’s SoS is also contributing to the existence of unmanageable “Big Data”. Recent efforts have developed promising approach, called “Data Analytics”, which uses machine learning tools from statistical and soft computing (SC) such as principal component analysis (PCA), clustering, fuzzy logic, neuro-computing, evolutionary computation, Bayesian networks, deep architectures and deep learning to reduce the size of “Big Data” to a manageable size and apply these tools to a) extract information, b) build a knowledge base using the derived data and c) eventually develop a nonparametric model for the “Big Data”. This keynote attempts to construct a bridge between SoS and Data Analytics to develop reliable models for such systems. A photovoltaic energy-forecasting problem of a microgrid SoS, traffic jams forecasting, brain disease prediction and a system of autonomous vehicles will be offered for case studies. These tools will be used to extract a nonlinear model for a SoS-generated Big Data. Videos for autonomous vehicles will be shown.

Granular Knowledge Transfer and Knowledge Distillation: At the Junctions of Machine Learning and Granular Computing

Witold Pedrycz Department of Electrical and Computer Engineering, University of Alberta, Edmonton AB T6R 2V4, Canada [email protected] Abstract. Machine Learning methods are inherently faced with masses of data leading to time-consuming learning procedures and huge black box-style architectures of classifiers and predictors (e.g., such as deep neural networks). We advocate that Granular Computing (GrC) delivers a conceptually and algorithmically sound alternative and a viable augmentation to conveniently address the challenges identified above. In particular, it is demonstrated that the notion of information granularity becomes beneficial in the formalization and knowledge-sharing essential in a slew of problems of transfer learning. Transfer learning is concerned with extraction of knowledge (expressed by some model) acquired for the previous (source) environment and its successive usage to a new (target) environment. Information granularity helps realize knowledge transfer from the source to the target domain. What becomes even more important, through GrC one can quantify the relevance of the knowledge in the new environment by constructing granular generalizations of the model existing in the source environment with the level of information granularity (viz., specificity of information granules) reflecting upon the proximity between the source and target domains. Knowledge distillation (referred to as model compression) becomes an interesting learning paradigm supporting a design of compact models (student) guided by transfer knowledge from the reference model (teacher). In this setting, the roles of granular augmentation of the learning environment of knowledge distillation are discussed. A supplementary illustrative material is focused on the design and analysis of transfer learning and knowledge distillation applied to rulebased architectures.

Quo Vadis AI?

Okyay Kaynak Bogazici University, Turkey [email protected] Abstract. During the last two decades, profound technological changes have occurred around us, supported by disruptive advances both on the software and on the hardware sides. Additionally, we have witnessed a cross-fertilization of concepts and an amalgamation of information, communication and control technology-driven approaches. This has led to what is termed as digital transformation, i.e., the integration of digital technology into all areas of business, fundamentally changing how companies operate and deliver value to customers. The most recent development is integrating artificial intelligence (AI) in digital transformation as the primary enabler and the facilitator. It is expected that the applications of AI will truly transform our world and impact all facets of society, economy, living, working, health care and technology. The study of artificial intelligence (AI) has been a continuous endeavor of scientists and engineers for over 65 years. The simple contention is that human-created machines can do more than just laborintensive work; they can develop human-like intelligence. AI has been very appealing as it aligns with the nature of human beings in terms of their never-satisfied demands for higher productivity on the one hand and, on the other hand, the curiosity of how we understand and try to change the world. Having gone through several historical stages with several winters, AI has become a leading technology today and plays novel roles like never. Therefore, it is time to discuss the past, the present and the future of both the AI tools and the AI “beings” at this juncture. In this presentation, in addition to the technical aspects of AI technology in short to mid-term, thoughts and insights are also presented regarding the symbiotic relationship of AI and humans in the long run.

Contents

On Some De Novo Type Approaches to Fuzzy Decision Making, Optimization and Control: An Application to Sustainable Regional Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Janusz Kacprzyk

1

The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexey Averkin

4

Multiattribute Decision Making in Material Selection Under Z-Valued Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. B. Babanli

6

Maximum Dynamic Evacuation Modelling in Networks in Fuzzy Conditions with Partial Lane Reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Janusz Kacprzyk, Alexander Bozhenyuk, and Evgeniya Gerasimenko

16

Z-Number-Based Similarity Reasoning in Control Systems . . . . . . . . . . . . . . . . . . Nigar E. Adilova and Aziz Nuriyev

25

Design of Quasi-Resonant Flyback Converter Integrated by Fuzzy Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fahreddin Sadikoglu, Samsam Bakhtiari, and Ebrahim Babaei

31

Experimental Selecting Appropriate Fuzzy Implication in Traffic IF-Then Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shamil A. Ahmadov

40

Prediction of Cold Filter Plugging Point of Different Types of Biodiesels Using Various Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Youssef Kassem, Hüseyin Çamur, Ahmed Hamid Mohamed Abdalla Zakwan, and Nkanga Amanam Nkanga Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bü¸sra Altınkaynak, Tolunay Göçken, Murat Ye¸silkaya, Burak Birgören, and Gülesin Sena Da¸s Decision Making on Students’ Performance Estimation . . . . . . . . . . . . . . . . . . . . . J. M. Babanli

50

58

67

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A Comparative Analysis of the Different CNN Models Using Fuzzy PROMETHEE for Classification of Kidney Stone . . . . . . . . . . . . . . . . . . . . . . . . . . Fahreddin Sadıko˘glu, Özlem Sabuncu, and Bülent Bilgehan

77

Developing Efficient Frontier for Investment Portfolio: A Fuzzy Model Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Leyla R. Hasanova

85

Impact of Online Education Classes on Students’ Satisfaction: The Case of Near East University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Saide Sadıko˘glu, S¸ ahin Akda˘g, and Murat Tezer

94

Decision Making on Selection of Ferritic Stainless Steel . . . . . . . . . . . . . . . . . . . . 101 Mustafa Babanli, Latafat Gardashova, and Tural Gojayev Multicriteria Group Decision Making on Information System Project Selection Using Type-2 Fuzzy Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Aygul Dadasheva Forecasting Demand in the Commodity Market of Food Products Using Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Mikayilova Rena Nuru Introducing Uncertainty-Based Dynamics in MADM Environments . . . . . . . . . . 130 Debora Di Caprio and Francisco J. Santos Arteaga Analyzing the Digital Marketing Strategies Role in Post Pandemic Recovery Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Khatira J. Dovlatova Artificial Intelligence and Digital Economy: Development Prospects . . . . . . . . . . 147 Ali Abbasov and Ramin Rzayev Evaluation of Logistics Services of Airlines in the Azerbaijan Passenger Transportation Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Sevil Imanova Customer Characteristics in Digital Marketing Model . . . . . . . . . . . . . . . . . . . . . . . 164 Gunay E. Imanova and Gunel Imanova Estimation of Countries’ Economic Development by Using Z-Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Rafig R. Aliyev

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Fuzzy Approach to Explainable Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . 180 Alexey Averkin and Sergey Yarushev Z-Numbers Based Evaluation of Expert Opinions on Agricultural Structure . . . . 188 G. Imanov, A. Aliyev, and R. Mikayilova Pareto-Optimality-Based Investigation of Quality of Fuzzy IF-THEN Rules . . . . 196 Nigar E. Adilova Predicting Solar Power Generated by Grid-Connected Two-Axis PV Systems Using Various Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Youssef Kassem, Hüseyin Gökçeku¸s, Marilyn Hannah Godwin, James Mulbah Saley, and Momoh Ndorbor Mason Z-Preferences in Consumer Buying Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Khatira J. Dovlatova Prediction of the Power Output of a 4.5 kW Photovoltaic System Using Three Empirical Models: A Case Study in Nahr El-Bared, Lebanon . . . . . . . . . . . 218 Hüseyin Çamur, Youssef Kassem, Mustapha Tanimu Adamu, and Takudzwa Chikowero Z-Decision Making for the Selection of IT Engineers . . . . . . . . . . . . . . . . . . . . . . . 226 Gunay A. Huseynzada Optimal Implicatıon Based Fuzzy Control System for a Steam Generator . . . . . . 234 L. A. Gardashova and K. A. Mammadova Prediction of Runoff Using Artificial Neural Networks, MLR Regression, and ARIMA Model (A Case Study: Bared River, Lebanon) . . . . . . . . . . . . . . . . . . 247 Youssef Kassem, Hüseyin Gökçeku¸s, Francis Surfia Dioh, Marcus Paye Quoigoah, and Marilyn Hannah Godwin Devices with Fuzzy Logic Control of Artificial Lung Ventilation . . . . . . . . . . . . . 256 Aynur J. Jabiyeva Structural Analysis of Piston Machines by Using Computer Software . . . . . . . . . 265 Valeh Bakhshali, Nail Mardanov, Ismayil Ismayil, and Aygun Bekirova Using of Conventional Neural Network to Diagnose Scabies by Dermoscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Husam Zendah and Kamil Dimililer

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Determination of the Dynamic and Interactive Event in Exascale Computing Systems via Request Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Nigar Ismayilova Evaluation of Techniques Used in Phenol Removal from Wastewater Using Fuzzy PROMETHEE Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Basil Bartholomew Duwa, Ay¸seGünay Kibarer, Berna Uzun, S¸ erife Kaba, and Dilber Uzun Ozsahin Research of the Manufacturing Quality of Plastic Details with Complex Forms of Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Naila A. Gasanova, Agali A. Quliyev, Aynur V. Sharifova, Tamilla U. Khankishiyeva, and Rafiga S. Shahmarova Tableaux Deduction System for Fuzzy Logic with Estimates of Fuzziness Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Gerald S. Plesniewicz and Alexey N. Aparnev Research of Bitumen-Based Asphalt Compositions Using Neural Network . . . . . 313 D. S. Mamed Hasan-zade, A. I. Babayev, and G. S. Hasanov Logical-Linguistic Model for Reactor Cleaning from Impurities . . . . . . . . . . . . . . 321 E. A. Melikov, T. M. Magerramova, and A. A. Safarova Quantitative Assessment of the Risk of Failure and Vulnerability of Oil and Gas Pipelines at Underwater Crossings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 I. A. Habibov and S. M. Abasova Prediction of Energy Consumption in Residential Buildings Using Type-2 Fuzzy Wavelet Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Rahib Abiyev and Sanan Abizada Modeling the Interaction of Components of a Distributed Information and Communication Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Nodirbek Yusupbekov, Nargiza Usmanova, and Shukhrat Gulyamov Fuzzy Approach to Analysis of the Temporal Variability of the Vegetation in a Specific Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Elchin Aliyev and Fuad Salmanov Application of Fuzzy TOPSIS in Server Selection Problem . . . . . . . . . . . . . . . . . . 364 V. H. Salimov

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Fuzzy Inference Based Quadcopter Flight Regulation Under Overland Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Tunjay Habibbayli and Murad Aliyev Fuzzy Logic Analysis of Parameters Affecting Students’ Satisfaction with Their Life at University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 M. A. Salahli, T. Gasimzade, V. Salahli, F. Alasgarova, and A. Guliyev Investigation of Submarine Pipeline Failure Accidents in Deepwater Based on the Fuzzy Analytical Hierarchy Process . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Hajar Ismayilova, Mansur Shahlarli, and Fidan Ismayilova Healthy Weight Estimation by Using Fuzzy Concept . . . . . . . . . . . . . . . . . . . . . . . 399 Farida Huseynova Using Residual Learning in the Food Processing Sector: The Case of Banana Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Khaled Almezhghwi, Wadei Algazewe, and Rabei Shwehdi Electre Method for Supermarket Selection Under Imperfect Information . . . . . . . 413 Hasan Temizkan Study of Gas Dynamic Processes of Drainage Zone of Oil Wells . . . . . . . . . . . . . 421 T. H. Ibrahimli and R. S. Gurbanov Appling Fuzzy Inference Logic System to Dynamic Model of Gross Domestic Product (in Case of Azerbaijan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Yadulla Hasanli, Shafizade Elnure, and Guliev Fariz Analysis of Knee Osteoarthritis Grading Using Deep Learning . . . . . . . . . . . . . . . 435 Serag Mohamed Akila, Elbrus Imanov, and Khaled Almezhghwi Navigation of a Mobile Robot Based on Fuzzy Images in an Uncertain Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 A. B. Sultanova Comparison of Oil Quality of Various Fields Based on Fuzzy Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 G. Efendiyev, S. Abbasova, G. Moldabayeva, and O. Kirisenko Interdisciplinary Nature of Borderline Disciplines: A Transition from Binary Logic to Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 Mehman A. Damirli

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Decision Making in Hepatitis B Diagnosis by Using Fuzzy Expert System: Case of Near East Hospital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Gunel Imanova and Arzu Gul Seyfi Application of Leointief’s Input-Output Model of Azerbaijan Economy Under Fuzzy Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 V. J. Axundov Simulation of Fractal Kinetics of Thermooxidation of Polymer Melts Based on Fractional Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Habibov Ibrahim Abulfas, Abasova Sevinc Malik, and Agamammadova Sevda Alipasha Fuzzy Models for Calculation of Oil and Gas Reserves . . . . . . . . . . . . . . . . . . . . . . 493 I. Y. Bayramov, A. N. Gurbanov, I. Z. Sardarova, G. G. Mammadova, and S. V. Abbasova Vendor Selection by Using Ideal Solution Methodology with Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 K. R. Aliyeva Selection Core Banking System by Using Fuzzy AHP and Fuzzy TOPSIS Hybrid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 Nihad Mehdiyev Performance Analysis of Machine Learning Algorithms for Medical Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Fahreddin Sadikoglu, Boran Sekeroglu, and Deborah Amaka Ewuru Difference Between Digital Marketing and Traditional Marketing Models Gunay E. Imanova

. . . . 522

Determination of Green Field Plants Most Suitable for Geographical Features of Places with Fuzzy Logic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530 Rü¸stü Ilgar, Vugar Salahli, Yagub Sardarov, Zarifa Imanova, and Zhala Jamalova Z-Information Based MCDM Model for Assessing Green Energy Resources: A Case of Resort and Tourism Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 Mahammad Nuriyev, Aziz Nuriyev, and A. N. Mahamad Assessing the Impact of Innovations on the Volume of Production of the Final Product in a Fuzzy Information Environment . . . . . . . . . . . . . . . . . . . . 549 ˙ S. Rustamov V. J. Akhundov and I.

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Application of WASPAS Method to Data Platform Selection Under Z-Valued Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 K. I. Jabbarova Using Deep Learning Algorithm for Prediction and Detection of Covid-19 . . . . . 564 Elbrus Imanov and Vidura Lakshitha Liyanagamage Fuzzy Logic-Based Planning of the Behavior of Autonomous Vehicles . . . . . . . . 572 A. B. Sultanova Digitization of Centrifugal Compressor Asset as One of Key Elements of Overall Digitized Industrial Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 Nodirbek Yusupbekov, Farukh Adilov, and I. Arsen Investment Decision Making by Using Natural Language Processing . . . . . . . . . . 588 Nigar F. Huseynova Multi-attribute Decision Making Under Z-Set Valued Uncertainty . . . . . . . . . . . . 595 Rafig R. Aliyev and Akif V. Alizadeh Fuzzy Processing of Hydrodynamic Studies of Gas Wells Under Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 Salahaddin I. Yusifov, Imran Y. Bayramov, Azar G. Mammadov, Rza S. Safarov, Rashad G. Abaszadeh, and Elmira A. Xanmammadova Fuzzy Modeling for Marketing Plan Development . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Seving R. Mustafayeva Solving Employee Selection Problem Under Fuzzy-Valued Information . . . . . . . 620 Aynur I. Jabbarova and K. I. Jabbarova The Use of Fuzzy Numbers for the Rational Choice of the Structure of the Distribution Channel of Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626 Alekperov Ramiz Balashirin “Dede Korkud” Epos in Light of Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 Kamal Abdulla and Rafik A. Aliev Toward Z-Number-Based Classification of Dataset . . . . . . . . . . . . . . . . . . . . . . . . . 637 R. R. Aliyev, O. H. Huseynov, and Babek Guirimov Application of Enterprise Solution Software for a Hotel Chain . . . . . . . . . . . . . . . 645 Serdar Oktay

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Fuzzy Logic Modelling of the Relationship Between Attitudes Towards Military Services and Soldiers’ Self-esteem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 Konul Memmedova and Banu Ertuna Applying Type-2 Fuzzy TOPSIS Method to Selection of Facility Location . . . . . 662 K. R. Aliyeva Applying a Fuzzy-Set Approach to Assessing Capital Flight Management: Empirical Research from Azerbaijan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Ulviyya Rzayeva and Rena Mikayilova Decision Making with Z-Bounded Interval Preference . . . . . . . . . . . . . . . . . . . . . . 677 Akif V. Alizadeh and Rafig R. Aliyev Teacher Assessment Model with Basic Uncertain Information . . . . . . . . . . . . . . . . 686 Farida Huseynova and Nigar F. Huseynova Design of Receiver in Fuzzy-Chaotic Communication Systems . . . . . . . . . . . . . . . 696 K. M. Babanli Smart Traffic Monitoring and Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 L. R. Bakirova and A. R. Bayramov Extension of Delphi Method to Z-Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 Rafig R. Aliyev, O. H. Huseynov, and E. R. Zeynalov Analysis of Intelligent Interfaces Based on Fuzzy Logic in Human-Computer Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 Rahib Imamguluyev and Aysel Aliyeva Determination of the Uncertainty of the Parameters of Oxidative-Reduction Reactions of Titanomagnetites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 U. N. Sharifova, A. N. Mammadov, D. B. Tagiev, and M. B. Babanly Solving Problem of Unit Commitment by Exchange Market Algorithm and Dynamic Planning Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734 Ebrahim Babaei and Sadig Mammadli Regular Identification Algorithms for a Special Class of Neuro-Fuzzy Models ANFIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747 H. Z. Igamberdiev, A. N. Yusupbekov, U. F. Mamirov, and Sh. D. Tulyaganov Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755

On Some De Novo Type Approaches to Fuzzy Decision Making, Optimization and Control: An Application to Sustainable Regional Development Janusz Kacprzyk(B) Finnish Society of Sciences and Letters Systems Research Institute, Warsaw, Poland [email protected]

Abstract. The paper is basically concerned with optimization, static and dynamic, under imprecise (fuzzy) information. Usually, the optimization problem is formulated as the maximization (or minimization) of some utility function, for instance, some financial result of an activity, subject to some constraints on, for instance, available resources, values of decision variables, etc. This general setting, which is the essence of virtually all traditional optimization problems considered, presupposes that parameter of the problem, for instance, constraints on resources devoted to particular types of activities, are given in advance.

These optimization problems have been found very useful, and over the decades many problem classes, solution methods, algorithms, software packages, etc. have been developed and have shown great usefulness for solving a multitude of practical problems. One can however readily see that all the above-mentioned optimization type problems boil down to an optimal allocation of fixed or limited resources in each problem or system considered, for instance, a transportation problem. In very many, if not all, real-world practical problems the essence is not only to find an optimal allocation of fixed, specified in advance resources in a given and specified system but rather to the (optimally) design of the particular system. For example, in the case of a large-scale transportation system, we can be interested in a proactive extension of the transportation problem, like assigning some resources for increasing total quantities at sources and destinations by building some additional facilities. Or, in the case of a regional agriculture modeling problem in which, briefly speaking, there are constraints related to the use of, for example. Fertilizers and watering (irrigation). In the traditional optimization type approach, we just have as the right-hand sides of the two respective constraints the limits (possibly financial) of the number of available fertilizers and water, which are considered separately. However, in practice it can often happen that we have some available funds for fertilizers, water, etc. which implies those limits on them because we can, for instance, purchase more (or less) fertilizering and spend more (or less) funds for the watering system. Then additionally, we should in the J. Kacprzyk---Polish Academy of Sciences Member, Academia Europaea Member, European Academy of Sciences and Arts Foreign Member, Bulgarian Academy of Sciences Foreign Member, Spanish Royal Academy of Economic and Financial Sciences (RACEF) Foreign member © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 1–3, 2023. https://doi.org/10.1007/978-3-031-25252-5_1

2

J. Kacprzyk

course of optimization, distribute these funds into parts devoted to the purchasing of fertilizers and water. This can clearly be done with respect to involving multiple objectives, too. The above philosophy of an optimal system design, termed de novo programming has been introduced by Zeleny in 1981, first for single objective problems and then extended for multi-objective problems. This approach has attracted much attention in optimization, operations research, systems analysis, etc. communities, and has been applied to solve many practical problems. In a rich literature on de novo programming, one can cite, for instance, the following developments: new general de novo programming problems with the maximization and minimization type objectives (GDNPP), cf. Li and Lee (1990a, 1990b), Chen and Hsieh (2006), Umarusman (2013), and Chakraborty& Bhattacharya (2012, 2013), to just mention a few. What concerns the applications, Miao et al. (2014) have proposed an interval-fuzzy de novo programming method for planning water resource systems under uncertainty, and Saeedi et al. (2015) have shown an application to determine the capacity in a closedloop supply chain network with a queueing system, Sarjono et al. (2015) have shown an application for production planning optimization at an Indonesian ceramics company, Chen (2014) has proposed an application in integrated circuit (IC) design, Sharah & Khalili-Damghani (2019) have proposed an application in the gas supply chain, Zhang, Huang and Zhang (2009) have proposed an application for water resources systems planning, etc. There is a long tradition of using fuzzy logic and fuzzy optimization in de novo programming. Just to mention a few, one can cite here: Chen and Hsieh (2006) who introduced a new approach to the solution of multi-stage GDNPP using fuzzy dynamic programming (cf. Kacprzyk, 1997), Chakraborty and Bhattacharya (2012, 2013) who have proposed a new method for the solution of GDNPP in one step under fuzzy environment using the Zimmermann’s (fuzzy linear programming approach, Ghorbani et al. (2014) proposed the use of a fuzzy goal programming approach, Chakraborty et al. (2014) introduced the concept of duality, Sen (2016) showed how the concept of a penalty function can be employed, Sharahi and Khalili-Damghani (2019) showed the use of type 2 fuzzy sets, etc. A good source of information is the recent paper by Banik and Bhattacharya (2020). For our purposes, an important direction is the use of the de novo programming approach in a dynamic setting in which the sustainable regional agricultural development model operates. The best-known paper is presumably here by Chen and Hsieh (2006) who introduced a new de novo type model using fuzzy dynamic programming in the sense of Bellman and Zadeh (1970) and Kacprzyk (1983, 1997). We will basically follow the line of reasoning of Chen and Hsieh (2006) but will add another important dimension related to the temporal distribution of funds over the planning horizon, which is clearly subject to the effect of discounting, that is, the funds to be determined for earlier development planning stages are more valuable than those for the later stages. This is both in the sense of the face value, that is, expressed directly in monetary terms, and indirectly, in terms of some value to various stakeholders, for

On Some De Novo Type Approaches

3

instance, the inhabitants whose preference is possibly fast attainment of some socioeconomic objectives, and it is obvious that more funds at earlier stages can have a positive effect on the attainment of these objectives. Moreover, we add to the traditional de novo fuzzy dynamic programming model the condition of the so-called stability which boils down to a limitation on the variability of crucial agricultural regional development indicators and funds to be spent over the planning horizon. The above synergistic combination of both traditional de novo programming approaches and new elements, mostly in the context of dynamic optimization, related to discounting and stability, maybe a powerful tool for solving a multitude of problems. In the paper, an application for sustainable regional agriculture planning is shown.

The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence Alexey Averkin1,2(B) 1 Federal Research Centre of Informatics and Computer Science of RAS, Vavilova Street, 42,

Moscow, Russia [email protected] 2 Russia Educational and Scientific Laboratory of Artificial Intelligence, Neuro-Technologies and Business Analytics, Plekhanov Russian University of Economics, Stremyanny Lane, 36, Moscow, Russia

Abstract. Every decade technology makes revolutionary shifts that become the new platforms on which application technology is built. Artificial intelligence (AI) is no different. AI has moved from 1st Generation shallow learning and handcrafted features to 2nd Generation deep learning, which has been effective at learning patterns. We have now entered the 3rd Generation of AI which is machine reasoning-driven – where the machine can interpret decision making algorithm, even if it has the black-box nature. Explainable artificial intelligence and augmented intelligence are the main part of the 3rd Generation of AI. The role of Professor Lotfi Zadeh and Professor Rafik Aliev in these AI generations are tremendous. Professor L. Zadeh was the founder of the theory of fuzzy sets and linguistic variables, the “father” of fuzzy logic and approximate reasoning, the author of the theory of possibility and general theory of uncertainty, the creator of Z-numbers theory and generalized restrictions, the ancestor of granular and soft computing. His ideas and theories not only opened a new epoch in the development of scientific thought, free from the limitations of narrow scientific directions and contributing to their synergy. They made a significant contribution to the development of new information and cognitive technologies, led to the creation of effective industrial technologies, such as fuzzy computers and processors, fuzzy regulators, fuzzy clustering and recognition systems, and many others. Professor L. Zadeh has been deservedly included in the IEEE Computer Society’s gallery of fame scientists who have made pioneering contributions to the field of artificial intelligence and intelligent systems. The role of L. Zadeh in AI is also hard to overestimate especially in the l focus on the concept of soft computing, originally combining hybrid models based on fuzzy sets, neural networks, and soft computing. The emergent properties of these models were one of the foundations of the current hype in artificial intelligence and machine learning. For many years L. Zadeh fruitfully cooperated with Professor Rafik Aliev. The result of their research was fundamental scientific achievements published in several joint monographs. The generalized theory of stability created by L. Zadeh and R. Aliev jointly has been recognized as a major contribution to the development of mathematics, management theory, dynamic economics and a number of other © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 4–5, 2023. https://doi.org/10.1007/978-3-031-25252-5_3

The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence sciences. The main scientific directions of Professor Rafik Aliev’s research are the theory of decision-making in terms of high uncertainty, the theory of coordination in complex social, economic, and technical systems, fuzzy logic, and neurocomputing. Applied fields of his scientific results are economics, conflictology, space objects and technical systems. These areas of modern artificial intelligence are referred to augmented intelligence (intelligence decision-making). Augmented intelligence is a design pattern for a human-centered partnership model where humans and artificial intelligence work together to improve cognitive functions, including learning, decision-making, and new experiences. The business value forecast for augmented intelligence in 2025 will be 44 percent of all AI business applications. Explainable artificial intelligence now represents a key area of research in artificial intelligence and an unusually promising one in which many fuzzy logics could become crucial. Research in the of area of explainable artificial intelligence can be divided into three stages, which correlates with the 3 generation of AI: in the first stage (starting from 1970) expert systems were developed; in the second stage (mid-1980s), the transition was made from expert systems to knowledgebased systems; and in the third phase (since 2010), deep architectures of artificial neural networks, which required new global research on the construction of explainable systems, have been studied. On each stage the ideas of L. Zadeh and R. Aliev played the important roles. They were the first ones in explainable artificial intelligence field with neuro-fuzzy systems – a synergistic combination of fuzzy logic and neural networks, providing the first interpretable AI system based on neural network learning. Since 2011 L. Zadeh had been involved in Z Advanced Computing, Inc. (ZAC), the pioneer Cognitive Explainable Artificial Intelligence (Cognitive XAI). The Cognitive Explainable-AI approach also use the results of Prof. Rafik Aliev, Prof. Ronald Yager, Prof. Mo Jamshidi. Nowadays, explainable and augmented intelligence are prominent and fruitful research fields where many of Zadeh’s and R. Aliev’s contributions can become crucial if they are carefully considered and thoroughly developed. It is worth noting that about 30% of publications in Scopus related to XAI, dated back to 2017 or earlier, came from authors well recognized in the fuzzy logic field. This is mainly due to the commitment of the fuzzy community to produce interpretable intelligent systems since interpretability is deeply rooted in the fundamentals of fuzzy logic.

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Multiattribute Decision Making in Material Selection Under Z-Valued Information M. B. Babanli(B) Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]

Abstract. Material selection is a complex problem that involves analysis of a series of factors. One of the issues is imperfect decision relevant-information stemming from incomplete theoretical knowledge and experimental data. Often, fuzzy logic and soft-computing-based approaches are used to deal with this complexity. However, works devoted to account for both fuzziness and partial reliability of information in material selection are scarce. To account for such kind of information, Zadeh introduced the concept of a Z-number. In view of this, a problem of an optimal alloy selection for pressure vessel under Z-number-valued information is considered in this paper. Degrees of relative importance of attributes and values of attributes for alternatives are described by Z-numbers. Differential evolution optimization technique is used to reduce inconsistency of degrees of relative importance provided by an expert. An ideal solution idea is used to determine an optimal alternative (alloy). The applied solution procedures are characterized by relatively low computational complexity. Keywords: Alloy selection · Decision making · Z-number · Pairwise comparison matrix · Differential evolution

1 Introduction Material selection is a complex task that requires analysis of four groups of factors [1]: material properties, material processing requirements, availability of materials, cost of materials [2]. Decision making in material selection includes three stages: initial screening, development and comparison of alternatives, and determination of best solution [3]. Thus, theoretical knowledge and experimental data are sources for decisionrelevant information in material selection. Often, multiattribute decision making methods (MADM) are used to solve problems of decision making in material selection. Let us shortly overview existing works on this topic. A series of works is devoted to the use of AHP method in selection of Al/SiC composite materials [4], semiconductor switching devices [5], minimization of environmental impact while choosing of aluminum alloy in screw manufacturing [6]. In [7] it is proposed not to deal with material selection decision matrices but to determine the most important criterion for whole selection process. In the article, five material selection problems are examined from different point of views. VIKOR, TOPSIS and PROMETHEE methods are used. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 6–15, 2023. https://doi.org/10.1007/978-3-031-25252-5_7

Multiattribute Decision Making

7

Systematic analysis of the field may be found in [3, 7–10]. [8] is devoted to selection problems in the mechanic field. Classical optimization techniques-based approaches and several case studies are considered. Both analytical and computer-aided approaches are considered in [9]. In [10], authors analyze existing methods of material screening and selection based on their advantages, drawbacks and potential applications. A wide overview of existing works on material selection is also given in [11]. To deal with imperfect decision relevant information and other complexities in material selection problems, they considered the use of soft-computing-based approaches [8, 12]. The related works includes application of MADM methods under fuzzy information, genetic algorithms, fuzzy expert systems and other approaches. For the first time, MADM problem of material selection under Z-number valued information is considered in [13]. Selection of titanium alloys based on their properties is considered. Z-numbers were used to describe attributes values (describe alloy properties) and attributes weights. The solution approach is based on simple additive weighting of Z-numbers. Further, a series of problems of material selection under fuzzy and Z-number-valued information was considered in book [14]. For solving the problems, VIKOR and AHP methods, If-Then rules and other approaches are used. The existing works on material selection under fuzzy and Z-valued information are characterized by problems of consistency and information aggregation. Often, simplified assumptions are used. For example, it is assumed that importance weights of decision attributes are initially given in form of fuzzy or Z-numbers. Usually, some information about comparative importance of attributes can be provided. In this case, a problem of consistency of pairwise comparisons arises, whereas initially consistent information is assumed to be given. From the other side, aggregation of attribute values leads to loss of information (especially in case of dependence of attributes). This paper is devoted to material selection under Z-valued information for pressure vessel. Information about relative importance of attributes is described in form of userderived Z-number-valued pairwise comparison matrix (PCM). Based on consistency requirements, a consistent Z-number-valued PCM is obtained by solving optimization problem. Next, Z-number-valued attributes importance weights are found by computing the 1st eigenpair of this matrix. Finally, the optimal alternative is determined as one closest to the ideal alternative (to reduce loss of information that arise due to aggregation of attribute values).

2 Preliminaries Definition 1. A continuous Z-number [15]. A continuous Z-number is an ordered pair Z(A, B). A is a continuous fuzzy number playing a role of a fuzzy restriction on a value that a random variable X may take: Value of X is A.

(1)

In other words, A is used to describe imprecise information about a value of X. A degree of reliability of A is described as a value of probability measure P(A) =

8



M. B. Babanli

μA (x)p(x)dx, where p is probability distribution of X and μA (x) is membership func-

R

tion of A. If p is precisely known, then P(A) is a crisp number. However, in real-world problems an actual p may not be precisely known, and one considers a set of distributions. This requires dealing with fuzzy restriction on a value of P(A). Thus, a fuzzy number B with a membership function μB : [0, 1] → [0, 1] [0, 1] is used as a fuzzy restriction: The value of P(A) is B

(2)

This implies that fuzzy uncertainty related to p induces fuzziness of a value of P(A). Thus, a value of a random variable X can be described as a Z-number Z(A, B): A is a fuzzy estimation of a value, and B is a fuzzy reliability of this estimation. Definition 2. A Z-number-valued pairwise comparison matrix [16]. A Z-numbervalued pairwise comparison matrix (PCM) (Zij ) is a square matrix of Z-numbers: ⎛

⎞ Z11 = (A11 , B11 ) ... Z1n = (A1n , B1n ) ⎠. (Zij = (Aij , Bij )) = ⎝ . ... . Zn1 = (An1 , Bn1 ) ... Znn = (Ann , Bnn )

(3)

A Z-number Zij = (Aij , Bij ), i, j = 1, ..., n describes partially reliable information on degree of preference for i-th criterion against j-th one. Definition 3. A Distance between Z-numbers [17]. A Z-number Z = (A, B) is characterized by fuzzy number A, fuzzy number B and an underlying set of probability distributions G. We propose to define distance between Z-numbers D(Z1 , Z2 ) as follows. Distance between A1 and A2 is computed as D(A1 , A2 ) = supα∈(0,1] D(Aα1 , Aα2 ), D(Aα1 , Aα2 )

(4)

  α  A11 + Aα12 Aα21 + Aα22   − = . 2 2

Aα1 and Aα2 denote α-cuts of A1 and A2 respectively, Aα11 , Aα12 denote lower and upper bounds of Aα1 (Aα21 , Aα22 are those of Aα2 ). Distance between B1 and B2 is computed analogously. A distance between sets G1 and G2 of probability distributions p1 and p2 can be expressed as 

1 1 2 D(G1 , G2 ) = inf p1 ∈G1 ,p2 ∈G2 (1 − (p1 p2 ) 2 dx) , R

where the expression in figure brackets is the Hellinger distance between two probability distributions p1 and p2 . The use of inf operator implies that among all the possible pairs of distributions, the pair of the closest p1 ∈ G1 and p2 ∈ G2 is found to define distance D(G1 , G2 ).

Multiattribute Decision Making

9

Given D(A1 , A2 ), D(B1 , B2 ) and D(G1 , G2 ), the distance for Z-numbers is defined as D(Z1 , Z2 ) = βD(A1 , A2 ) + (1 − β)Dtotal (B1 , B2 )

(5)

Here Dtotal (B1 , B2 ) is a distance for reliability restrictions which is computed as: Dtotal (B1 , B2 ) = wD(B1 , B2 ) + (1 − w)D(G1 , G2 ),

(6)

β, w ∈ [0, 1] are DM’s assigned importance degrees. Definition 4. An inconsistency index for Z-number-valued PCM [17]. An inconsistency index K for Z-number-valued PCM (Zij ) is defined as follows: 





 Zij Zjk Zik D Z(1), , (7) K Zij = max min D Z(1), i 0˜ is satisfied, the residual arc capacity of the opposite arc is equal to u˜ μr (j, i, v, t) = ξ˜ μ (i, j, t, v). μ

2.2. Implement the breadth-first search that seeks for the shortest trails p˜ e from the   source s to the sink r . μ 2.2.1. Transition to the Step 2.3 if p˜ e is detected. 2.2.2. The value of fuzzy maximum flow and corresponding flow partition is detected ˜ eμr , transition to the Step 3. if there isn’t any augmenting path in the network G ∼μ 2.3.  Transmit the given flow according to residual capacity σ e = min[˜uμr xi , xj , t, v ]. 2.4. Update the flow using the rule:   ∼μ μr 1) decrease ξ˜ μ xi , xj , t, v by value σ e for arcs between vertex (xj , v) and vertex μr (xi , t). Go to 2.1.   ∼μ μr μr 2) increase ξ˜ μ xi , xj , t, v by σ e for arcs between vertex (xi , t) and vertex (xj , v). Go to 2.1. Step 3. Arc reversal

∼μ

3.1. For ∀t ∈ T reverse the arc between (j, v) and (i, t) up to ξ (i, j, t, v)−u˜ (i, j, t, v), ∼μ if ξ (i, j, t, v) > u˜ (i, j, t, v) with replacing u˜ (i, j, t, v) by 0˜ if the arc (i, t) (j, v) ∈ / A. 3.2. For ∀t ∈ T and the arc joining (i, t) with (j, v) if the arc connecting (i, t) with (j, v) should be reversed, and the value of saved arc capacity s˜(i, j, t, v) = ˜ s˜ (i, j, t, v) = u˜ (i, j, t, v) − ξ˜ (i, j, t, v) if u˜ μr (i, j, t, v) − ξ˜ (j, i, v, t) and s˜ (j, i, v, t) = 0. both arcs connecting (i, t) with (j, v) alongside (j, v) with (i, t) are not reversed. 3.3. Remove super vertices and artificial arcs connecting them. A path in the timeexpanded network connecting vertices (s, t) and (r, γ = t + τst (t)) with ξ˜ (s, r, t, γ ) corresponds to ξ˜sr (t). Thus, the time-spaced network transits to the original dynamic one.

4 Example We consider the evacuation scenario to convey the evacuees from endangered node s to the destination d in the evacuation network with fuzzy arguments and the partial lane reversal within T = 5 considering dynamic nature of evacuation. Network for modelling is represented by fuzzy dynamic graph (Fig. 1). Transit arc capacities are given in Tables 1 and 2. Transition to the modified network with the new values of the arc capacities is implemented by the step 1, as shown in Fig. 2. The figure represents modified arc capacities in Table 2. The modified version of the graph is represented in Fig. 3.

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J. Kacprzyk et al.

Fig. 1. Example of fuzzy dynamic network with the arguments in Tables 1 and 2.

Table 1. Transit arc capacities u˜ ij (t) at time periods t. Arcs (s, 1) (1, s) (s, 2) (2, s) (1, 2) (2, 1) (1, 3) (3, 1) (2, 3) (3, 2) (2, r) (r, 2) (3, 4) (4, 3) (4, r) (r, 4)

Periods 0

1

2

3

4

5

 20  18

 22  18

 23  20

 19  17

 19  17

 23  20

 18  15

 23  17

 17  16

 10  17

 18  15

 15  18

 22  18

 22  18

 30  20

 30  20

 20  20

 20  20

 22  18

 22  23

 18  22

 22  23

 22  23

 18  22

 11 9˜

 11 9˜

 12  11

6˜ 9˜

6˜ 9˜

 12  11

 15  11

 15  11

 15  11

 20  15

 22  16

 22  16

 19  21

 19  21

 24  22

 24  22

 22  18

 21  15

 20  18

 20  18

 13  17

 18  14

 18  14

 20  18

The maximum flow finding algorithm is implemented by finding augmenting paths and conveying the flow among them in order to define the evacuation flow of the maximum value in the fuzzy network in Fig. 3. Fuzzy maximum dynamic flow distribution after partial lane reversal is presented in Table 3. We can conclude that modified outbound arc capacities by the lane reversal procedure units. Let us evaluate the saved allow us to increase the total fuzzy flow value up to 131 dynamic arc capacities by the step 3 of the algorithm. The final network is shown in Fig. 4.

Maximum Dynamic Evacuation Modelling in Networks μ

Table 2. Modified transit arc capacities u˜ ij (t) at time periods t. Arcs (s, 1) (s, 2) (1, 2) (1, 3) (2, 3) (2, 5) (3, 4) (4, 5)

Periods 0

1

2

3

4

5

 1 38,  2 33,

 2 40,  2 40,

 2 43,  2 33,

 1 36,  1 27,

 1 36,  1 33,

 1 43,  2 33,

 1 40,  2 40,

 2 40,  45, 2

 2 50,  2 40,

 3 50,  3 45,

 3 40,  45, 3

 3 40,  3 40,

 2 20,  26, 2

 1 20,  26, 3

 1 23,  3 26,

 1 15,  2 35,

 1 15,  1 38,

 2 23,  1 38,

 2 40,  2 38,

 2 40,  1 38,

 1 46,  1 30,

 1 46,  1 32,

 1 40,  1 32,

 2 36,  1 38,

Fig. 2. Modified network in fuzzy terms

Fig. 3. The time-expanded version of the modified fuzzy network

21

22

J. Kacprzyk et al. Table 3. Fuzzy maximum dynamic flow distribution after partial lane reversal.

The path

Departure time (T)

Arrival time (T)

Flow value

s0 → 22 → r5

0

5

s0 → 22 → 33 → 44 → r5 s0 → 11 → 33 → 44 → r5 s0 → 11 → 23 → r5

0

5

 26 7˜

0

5

0

5

s1 → 23 → r5 s1 → 13 → 24 → r5

1

5

1

5

 25  13  22  38 1 31

Total flow

Fig. 4. The time-expanded network with the saved arc capacities.

5 Conclusion and Future Scope This work presents the method for macroscopic evacuation of the maximum possible amount of aggrieved as a model with the partial lane reversal in fuzzy conditions. Implementing the pattern of the partial lane reversal enables us to redirect the traffic by increasing the outbound modified capacities and optimizing the routes of the vehicles in such a way that revers the movement direction along the roads with low traffic, thereby enhancing the traffic along the overloaded road sections. A lack of the initial information on the values of the arc capacities of the road segments, traversal times, the number of aggrieved etc. leads to the fuzzy evacuation modelling. The novelty of the method is in fuzzy nature of evacuation due to the concept of partial lane reversal

Maximum Dynamic Evacuation Modelling in Networks

23

in the network with time-varying arc capacities and traversal times. A case study was carried out to illustrate the proposed algorithm. Generalized evacuation models in fuzzy modified networks allowing partial lane reversal will be examined as a series for future studies. Acknowledgments. The research was funded by the Russian Science Foundation (project No. 22-71-10121, implemented by the Southern Federal University).

References 1. Chalmet, L.G., Francis, R.L., Saunders, P.B.: Network models for building evacuation. Manage. Sci. 28, 86–105 (1982). https://doi.org/10.1287/mnsc.28.1.86 2. Fahy, R.F.: An evacuation model for high rise buildings. In: Proceedings of the Third International Symposium on Fire Safety Science, pp. 815–823. Elsevier, London (1991) 3. Choi, W., Hamacher, H.W., Tufekci, S.: Modeling of building evacuation problems by network flows with side constraints. Eur. J. Oper. Res. 35(1), 98–110 (1984). https://doi.org/10.1016/ 0377-2217(88)90382-7 4. Benjaafar, S., Dooley, K., Setyawan, W.: Cellular Automata for Traffic Flow Modeling. University of Minnesota, Mineapolis (1997) 5. Gipps, P.G., Marksjö, B.: A micro-simulation model for pedestrian flows. Math. Comput. Simul. 27(2–3), 95–105 (1985). https://doi.org/10.1016/0378-4754(85)90027-8 6. Ford, L.R., Fulkerson, D.R.: Flows in Networks, 212 p.. Princeton University Press, Princeton (1962) 7. Minieka, E.: Maximal, lexicographic, and dynamic network flows. Oper. Res. 21, 517–527 (1973) 8. Megiddo, N.: Optimal flows in networks with multiple sources and sinks. Math. Program. 7, 97–107 (1974) 9. Hamacher, H.W., Tufekci, S.: On the use of lexicographic min cost flows in evacuation modeling. Nav. Res. Log. 34(4), 487–503 (1987). https://doi.org/10.1002/1520-6750(198708 )34:4%3c487::AID-NAV3220340404%3e3.0.CO;2-9 10. Kalinic, M., Krisp, J.M.: Fuzzy inference approach in traffic congestion detection. Ann. GIS 25(4), 329–336 (2019). https://doi.org/10.1080/19475683.2019.1675760 11. Caudill, R.J., Kuo, N.M.: Development of an interactive planning model for contraflow lane evaluation. Transp. Res. Record, 47–54 (1983) 12. Jha, M., Moore, K., Pashaie, B.: Emergency evacuation planning with microscopic traffic simulation. Transp. Res. Record 1886, 40–48 (2004). https://doi.org/10.3141/1886-06 13. Theodoulou, G., Wolshon, B.: Alternative methods to increase the effectiveness of freeway contraflow evacuation. Transp. Res. Record 1865, 48–56 (2004). https://doi.org/10.3141/186 5-08 14. Kim, S., Shekhar, S., Min, M.: Contraflow transportation network reconfiguration for evacuation route planning. IEEE T. Knowl. Data En. 20(8), 1115–1129 (2008). https://doi.org/10. 1109/TKDE.2007.190722 15. Rebennack, S., Arulselvan, A., Elefteriadou, L., Pardalos, P.M.: Complexity analysis of maximum flow problem with arc reversal. J. Comb. Optim. 19(2), 200–216 (2010). https://doi. org/10.1007/s10878-008-9175-8 16. Pyakurel, U., Dhamala, T.N.: Models and algorithms on contraflow evacuation planning network problems. Int. J. Oper. Res. 12(2), 36–46 (2015). https://doi.org/10.21307/ijor-201 5-005

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17. Pyakurel, U., Nath, H.N., Dempe, S., Dhamala, T.N.: Efficient dynamic flow algorithms for evacuation planning problems with partial lane reversal. Mathematics 7(10), 993 (2019). https://doi.org/10.3390/MATH7100993 18. Bozhenyuk, A., Gerasimenko, E., Kacprzyk, J., Rozenberg, I.: Flows in Networks Under Fuzzy Conditions. Studies in Fuzziness and Soft Computing, vol. 346, Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-319-41618-2 19. Bozhenyuk, A., Gerasimenko, E., Rozenberg, I.: Method of maximum two-commodity flow search in a fuzzy temporal graph. In: Kacprzyk, J., Szmidt, E., Zadro˙zny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT - 2017. AISC, vol. 641, pp. 249–260. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66830-7_23

Z-Number-Based Similarity Reasoning in Control Systems Nigar E. Adilova(B)

and Aziz Nuriyev

Azerbaijan State Oil and Industry University, 34 Azadlyg Ave., Baku AZ1010, Azerbaijan [email protected], [email protected]

Abstract. The application of Z-based If-Then rules is a contemporary direction in the research of uncertain decision-making environment. Stemming from necessity, the ranking fuzzy and Z-numbers has become a prerequisite procedure for decision-making problems. Numerous techniques including similarity-based methods have been proposed to deal with fuzzy ranking problems. However practically there is no analysis of similarity reasoning in a Z-based control system. This paper provides to investigate Z-based similarity reasoning in the control system. The suggested approach is illustrated with a numerical example. Keywords: Z-number · Z-based control system · Reasoning · Similarity measure · IF-THEN rules

1 Introduction Similarity measure can be used to detect and group fuzzy numbers. In more general terms, similarity can also be applied to comparing alternatives. Up to now, many authors have suggested different types of fuzzy ranking methods, and some of them are related to similarity measure which was first presented by [1] considering compatibility between fuzzy numbers. In [2] ranking fuzzy numbers using distance method was discussed and presented based on 3 numerical examples. Various similarity measure techniques have been developed in time. Afterward, Jaccard similarity measure has been suggested and applied in ranking fuzzy numbers. Despite the popularity of standard Jaccard index, it has successfully been replaced by FUJI (Fuzzy Jaccard Index). The extension of Jaccard index in different types of fuzzy numbers has been introduced in [3]. Apart from that, the authors investigated a functional approach based on a fuzzy Jaccard index with a degree of optimism [4]. Broadly developed theories in the field of Jaccard similarity measures are also available in the literature [5–10]. In [11] fuzzy Jaccard index has been demonstrated by showing the limitations of other similarity measures, and the authors compared FUJI with different proposed scores. Although the author in [12] offered investigations on the consistency of fuzzy If-Then rules regarding similarity for rule premise (antecedent) and rule consequent, unfortunately, research on similarity reasoning of Z-based rules is still scarce. In this paper, we address Z-number-based similarity reasoning in control systems. The motivation of the study is on the analysis of the Jaccard similarity measure for rule © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 25–30, 2023. https://doi.org/10.1007/978-3-031-25252-5_9

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premise in a Z-based control system. For a comprehensive review of the matter, the proposed work is characterized as follows: Section 2 interprets the basic concept of Jaccard similarity measure, we also briefly review the definitions of Z-numbers and Jaccard similarity index. Section 3 demonstrates the problem description and its solutional approach. In Sect. 4, a practical example is illustrated as an application of the method. Eventually, Sect. 5 is related to the concluding marks.

2 Preliminaries For convenience, a Z-number can be characterized as below: Definition 1: Z-numbers [13–15]. A discrete Z-number is an ordered pair Z = (A, B) of discrete fuzzy numbers (A,B). Here A has the same meaning as it has in a continuous Z-number. B is a discrete fuzzy number with a membership function µB : {b1 , ..., bn } → [0, 1], {b1 , ..., bn } ⊂ [0, 1] [0, 1]. Definition 2. Z-based If-Then rules [16, 17]: Z-based IF-THEN rules comprehensively identify conditional statements as fuzzy If-Then rules. In contrast to the fuzzy If-Then rules, Z-based If-Then rules are defined as below: IF X is Z1 = (A1 , B1 ) THEN Y is Zy1 = (Ay1 , By1 ) ... IF X is Zn = (An , Bn ) THEN Y is Zyn = (Ayn , Byn ) Definition 3. Jaccard similarity measure [6, 18–20]. The Jaccard similarity measure between two Z-numbers Z1 and Z2 , in which parts A and B are expressed with triangular fuzzy numbers, is calculated by the given formula: 3 1 i=1 aA1i aA2i J = 3 3 3 2 2 − 2 i=1 aA1 + i=1 aA2 i=1 aA1i aA2i i i 3 1 i=1 bB1i bB2i + 3   2 i=1 b2B1 + 3i=1 b2B2 − 3i=1 bB1i bB2i i

(1)

i

where aA1 , aA2 bB1 , bB2 and are the components of the first and second Z-numbers respectively.

3 Statement of the Problem Consider that Z-based control system [21] consists of n of rules given below: IF X is Zx1 = (A1 , B1 ), THEN Y is Zy1 = (Ay1 , By1 ) IF X is Zx2 = (A2 , B2 ), THEN Y is Zy2 = (Ay2 , By2 ) . . . .. IF X is Zxn = (An , Bn ), THEN Y is Zyn = (Ayn , Byn )

(2)

Z-Number-Based Similarity Reasoning in Control Systems

27

Each of the components in the control system is characterized by Z-numbers. The problem is to analyze similarity reasoning in a Z-based control system. In the first step, the solution of the problem will be realized by defining Jaccard’s similarity measure between the new antecedent and current inputs of the control system. After the calculation of similarity indexes, some of the antecedents of the rules must be selected regarding to the threshold. In the end, the new consequent has to be formalized based on Z-number similarity reasoning. A numerical example illustrates the application of the described methodology.

4 Application of Numerical Example For overcoming the above-mentioned problem, let us take a look at the Z-based control system. Parts A and B of Z-numbers are expressed by triangular fuzzy numbers. 1. IF X is Z1A = [(−10, −10, −7), sure] THEN Y is Z1B = [(−1, −0.9, −0.7), sure]   2. IF X is Z2A = (−10, −7, −3), very sure THEN Y is Z2B = [(−0.7, −0.6, −0.4), sure]   3. IF X is Z3A = (−7, −4, −1), very sure THEN Y is   Z3B = (−0.4, −0.25, −0.1), very sure 4. IF X is Z4A = [(−3, 0, 3), less sure]THEN Y is Z4B = [(0, 0.1, 0.3), less sure] 5. IF X is Z5A = [(0, 3.5, 7), sure]THEN Y is

(3)

Z5B = [(0.25, 0.4, 0.55), less sure]   6. IF X is Z6A = (3, 5, 8), very sure THEN Y is Z6B = [(0.6, 0.8, 0.85), sure] 7. IF X is Z7A = [(7, 10, 10), less sure]THEN Y is Z7B = [(0.85, 0.9, 1), less sure] where less sure, sure, very sure are B part of Z-number which defines the degree of belief. The values for B components are as follows: less sure = [0.4; 0.5; 0.6], sure = [0.7; 0.8; 0.9], very sure = [0.8; 0.9; 1] Regarding to the control system in (2) the graphical representation of Z-numbers is shown in Figs. 1, 2 and 3. For solving the problem, assume that the antecedent of the new rule is in the form of Z-number Znew = [(−8, 2, 6), (0.1, 0.8, 0.9)]. We suggest applying formula (1) to separately calculate the similarity between new and current promises of Z-based rules. For this purpose, firstly, membership functions must be evaluated for the given 7 rules. By using the values of membership functions Jaccard similarity measure will be defined as below:

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Z1

Z2

1Z4 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

Z5

Z3

1

2

3

Z6

4

5

Z7

6

7

8

9 10

Fig. 1. A part of promises of Z-based rules

Z1

Z2

Z3

1

Z4

Z5

Z6 Z7

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -1 -0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fig. 2. A part of consequents of Z-based rules 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.3

0.4

0.5

0.6

0.7

Fig. 3. B part of Z-based rules

0.8

0.9

1

Z-Number-Based Similarity Reasoning in Control Systems

29

Table 1. Jaccard similarity measure Matches

Similarity index

J(R1 - R-new)

0.431

J(R2 - R-new)

0.497

J(R3 - R-new)

0.549

J(R4 - R-new)

0.655

J(R5 - R-new)

0.615

J(R6 - R-new)

0.486

J(R7 - R-new)

0.428

Then we define the threshold as the value of 0.5 (as a sample). Corresponding to the threshold we will take only the promises which are greater than the determined value. As seen in Table 1 fourth and fifth rules must be chosen in the next process of similarity reasoning. After that weights for the antecedent parts of the selected rules will compute using the following formula: J1 J2 J3 , w2 = , w3 = J1 + J2 + J3 J1 + J2 + J3 J1 + J2 + J3 After calculations we have w1 = 0.3, w2 = 0.36, w3 = 0.34. The result of similarity reasoning will be found by considering the following expression on the consequent parts of the selected rules (Rule-3, Rule-4, and Rule-5). w1 =

Z3B ∗ w1 + Z4B ∗ w2 + Z5B ∗ w3 Thus, new consequent will be formalized as Z3B ∗ w1 + Z4B ∗ w2 + Z5B ∗ w3 = (−0.035, 0.097, 0.265) (0.128, 0.225, 0.36) As a result, we get a new rule IF X is Zxnew = (−8, 2, 6)(0.1, 0.8, 0.9) THEN Y is Zynew = (−0.035, 0.097, 0.265)(0.128, 0.225, 0.36).

5 Conclusion In this study the applicability of jaccard similarity measure for Z-based reasoning in the control system was analyzed. The developed apparatus and the axiomatics of Z-numbers potentiate the determining of similarity measures and usage of them for decision-making. The suggested approach to determination of similarity measures makes it possible to select appropriate rules during the Z-based reasoning. In this research the Z-numberbased similarity reasoning has been solved in the example of a control system. We showcased the validity of suggested approach on the experimental analysis. The experimental analysis has revealed new consequent for the control system on the new premise (antecedent).

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References 1. Setnes, M., Cross, V.: Compatibility-based ranking of fuzzy numbers. Proc. Fuzzy Information Processing Society, NAFIPS-97, 305–310 (1997) 2. Cheng, C.-H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy sets syst. 95, 307–317 (1998) 3. Ramli, N., Mohamad, D.: On the Jaccard index similarity measure in ranking fuzzy numbers. Matematika 25(2), 157–165 (2009) 4. Ramli, N., Mohamad, D.: Fuzzy Jaccard with degree of optimism ranking index based on function principle approach. J. Electr. Eng. 4(4), 9–15 (2010). https://doi.org/10.1234/mjee. v4i4.305 5. Niwattanakul, S., Singthongchai, J., Naenudorn, E., Wanapu, S.: Using of Jaccard coefficient for keywords similarity. In: Proceedings of the International Multi Conference of Engineers and Computer Scientists, vol. 1, p. 5 (2013) 6. Aliyev, R.R.: Similarity-based multi-attribute decision making under Z-information. bQuadrat Verlag, Germany, 33–38 (2015) 7. Hwang, Ch.-M., Yang, M.-Sh., Hung, W.-L.: New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. Int. J. Intell. Syst. 1–17 (2018). https://doi.org/10.1002/int.21990 8. Mahmood, T., Rehman, U.U., Ali, Z., Chinram R.: Jaccard and dice similarity measures based on novel complex dual hesitant fuzzy sets and their applications. Comput. Intell. Complex Decision Making, p. 25(2020). https://doi.org/10.1155/2020/5920432 9. Aliyev, R.R.: Fuzzy logic’s Z-extension-based decision tools and their applications. Dissertation work for the degree of Doctor of Philosophy, p. 104. Baku, Azerbaijan (2021) 10. Poruthukaren, K.: An attempt to estimate the noises in homeopathic pathogenetic trials by employing the jaccard similarity index and noise index. Homeopathy 111(3), 176–183 (2021). https://doi.org/10.1055/s-0041-1735983 11. Petkovic, M., Skrlj, B., Kocev, D., Simidjievski, N.: Fuzzy Jaccard index: A robust comparison of ordered lists. Appl. Soft Comput. 113 (2021). https://doi.org/10.1016/j.asoc.2021.107849 12. Adilova, N.E.: Consistency of Fuzzy IF-THEN rules for control system. Adv. Intell. Syst., Springer 1095, 137–143 (2019) 13. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inform. Sci. 290, 134–155 (2015) 14. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers: Theory and Applications. World Scientific, Singapore (2015) 15. Aliev, R.A.: Uncertain computation-based decision theory, p. 521. World Scientific, Singapore (2017) 16. Aliev, R.A., Pedrycz, W., Huseynov, O.H., Eyupoglu, S.: Approximate reasoning on a basis of Z-Number-valued if-then rules. IEEE T. Fuzzy Syst. 25(6), 1589–1600 (2017) 17. Aliev, R.A., Huseynov, O.H., Zulfugarova, R.Kh.: Z-Distance based if-then rules. Sci. World J. 2016, 9 (2016). https://doi.org/10.1155/2016/1673537 18. Zhang, L., Xu, X., Tao, L.: Some similarity measures for triangular fuzzy number and their applications in multiple criteria group decision-making. J. Appl. Math. 2013(3), 7 (2013). https://doi.org/10.1155/2013/538261 19. Ye, J., Jiang, W.: Multicriteria decision-making method based on a cosine similarity measure between trapezoidal fuzzy numbers, IEEE Int. Conf. Intell. Syst. Knowl. Eng. 3(1), 95–97 (2011). https://doi.org/10.1109/ISKE.2010.5680802 20. Ye, J.: Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int. J. Fuzzy Syst. 16(2), 204–211 (2014) 21. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: ICAFS2020, Adv. Intell. Syst. Comput. 1306, 10-21 (2021). https://doi.org/10.1007/978-3-030-640 58-3_2

Design of Quasi-Resonant Flyback Converter Integrated by Fuzzy Controller Fahreddin Sadikoglu1,2

, Samsam Bakhtiari1(B)

, and Ebrahim Babaei3

1 Engineering Faculty, Near East University, Mersin 10, 99138 Nicosia, North Cyprus, Turkey

{fahreddin.sadikoglu,samsam.bakhtiari}@neu.edu.tr

2 Odlar Yurdu University, Koroglu Rahimov Street, 13, 1072 Baku, Azerbaijan

[email protected]

3 Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran

[email protected]

Abstract. One of the disadvantages of on-off switching of the Flyback Converter (FBC) at a fixed frequency is the power switching losses that negatively affect the efficiency of the switching process. This problem can be met in switching modes: Discontinuous Conduction Mode (DCM) and Continuous Conduction Mode (CCM). Development of the Quasi Resonant Flyback Converter (QRFBC) operating with variable frequency decreases the loss of switching and improves its efficiency. This study considers the development of QRFBC converter using MATLAB Simulink controlled by fuzzy logic controllers (FLC). The performance analysis of the FLC is compared with traditional PI-controller using the different values of the input, reference voltages and loads. The results show that FLC provides efficiency control to the output voltage of QRFBC, the efficient switching of zero voltage, reducing switching losses, and increasing switching speed and precision. Keywords: Flyback converter · Fuzzy logic controller · PI controller · Quasi-resonant

1 Introduction The Quasi Resonance Flyback Converter (QRFBC) are used in mobile systems, laptops, notebooks, Liquid-Crystal Display (LCD), etc. These converters are used in switchedmode power supply (SMPS) applications. The QRFBC is simpler than other topologies in SMPS applications, so this converter is popular in industries. The power efficiency of QRFBC is enhanced using different methods such as soft-switching and synchronous rectification [1–5]. They achieved cost-effective power conversion with less power losses. In [6], the authors proposed a divided resonant capacitor to enhance the voltage spikes and the power conversion efficiency of QRFBC The both negative and positive sides of using high switching frequency in resonant mode are discussed in [7]. A resonant mode based flyback converter is introduced with the aim of soft switching, decreased loss and reduced electromagnetic interference using a high switching frequency. The results © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 31–39, 2023. https://doi.org/10.1007/978-3-031-25252-5_10

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of their experimental reveal that quasi-peak and harmonics are decreased compared to conventional discontinuous-conduction mode based converters. This converter can be used in low-power isolated – limited voltage converters. In [8], a single switched QRFBC with a high switching frequency is applied by using a resonant inductor and capacitor in primary and secondary, respectively. The proposed converter improves leakage energy along with zero current and valley switching. A result, switching losses and noises decreased remarkably. A zero voltage multi-output QRFBC is applied in [9]. The two most significant achievements of the model are proper voltage regulation for load changing and supply disturbance with minimum settling time. In [10], an adaptive frequency reduction model is proposed for QRFBC. The control system skips some valleys switching to decrease the frequency for lighter load and power loss. A resistor measures the primary current and sets the sensor output, which is shifted and compared with the feedback voltage value. In [11], the dynamic behaviour of QRFBC is analyzed, and the efficiency is enhanced by using a digital control method. The continuous conduction modulation mode controls the input power for the voltages less than a certain value. If the voltage is more than the specific value, a proportional iterative of switching period is applied to detect the stable control parameters of the changed load. The control parameters are applied by setting the output voltage to the reference value. A Quasi-resonant and fixed time control-based method for a flyback converter is proposed in [12]. The control system can select 2 statues in operation as changing input voltage and load amount and optimized the efficiency and losses simultaneously. Fixed off time control acts in low input voltage and high load, while QR acts at high voltage and low load. Also, the valley skipping ability is discussed as one of the advantages of the proposed method. In [13], self-calibrated valley switching and voltage regulation in QRFBC using a simple analogue method and perturbs and observes method is presented. The model is simulated in SPICE and applied to 5–40 high-voltage CMOS process. The results show the efficiency of the control model to regulate the output voltage to 0.8 percent by 10% to full and 127 to 375 V changes in load and input voltage, respectively. A PID controller is applied in [14] to control the performance of a flyback converter. In the respond model, different operation modes, including on and off statues of switching, overshoot, settling and rise time parameters, are improved by optimizing the controlling parameters. Also, a minimum overshoot is achieved using a PI controller. In [15], the authors applied a feed-forward Artificial Neural Network (ANN) to control a multi-output flyback zero voltage of a quasi-resonant converter. The results show the method’s efficiency in controlling changes in the set point and load values. A single output fuzzy logic model is used in [16] to control a zero voltage switching QRFBC. The main idea of using fuzzy model is to overcome the nonlinearity and complexity of the control process. The paper’s objective is to regulate the output voltage of the variable load. ISE value, rise time, settling time and offset are performance measurement parameters compared with a single input fuzzy logic controller. The results show that single fuzzy logic performs better in the case of ISE and offset values.

Design of Quasi-Resonant Flyback Converter

33

2 Controllers Design 2.1 Design QRFBC Using Fuzzy Logic Controller Figure 1 shows the QRFB converter associated with the fuzzy logic controller (FLC). The system consists of a QRFBC, a comparator that defines the differences U = Uo − Ur between the output voltage Uo of QRFBC and the reference voltage Ur , FLC and voltage-controlled oscillator (VCO). The FLC is based on Mamdani inference model. Ui

Uo +

QRFBC

-

Ur

ΔU VCO

FLC

Fig. 1. Quasi-resonant flyback converter controlled by fuzzy logic

Input and output of FLC is represented by nine linguistic variables (membership functions): TL = Too Low, NL = Negative Large, NM = Negative Medium, NS = Negative Small Z = Zero, PS = Positive Small, PM = Positive Medium, PL = Positive Large, TH = Too High. The rule base consists of the following nine rules (Table 1): Table 1. IF-Then rules Rules

1

2

3

4

5

6

7

8

9

IF Input

TL

NL

MM

NS

Z

PS

PM

PL

TH

Then Output

PS

Z

Z

NM

Z

TL

PS

PS

PM

Example rule 1: If Input is TL then Output is PS The output frequency of VCO varies according to the output of FLC. Output of VCO is applied to the Metal Oxide Semiconductor Field Effect Transistor (MOSFET) to switch the QRFBC. Figure 2 presents QRFBC circuit with FLC and VCO. Circuit was developed using MATLAB Simulink.

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2.2 Methodology of Investigation of QRFBC Controlled by FLC The three different tests are performed for the study: 1. For the input of QRFBC was used two different voltages: Ui = 190 V and Ui = 280 V; reference voltage Ur and output load R are fixed (Ur = 28.5 V; R = 15.7 ) 2. For the reference voltages are used two different values, Ur = 25 V and Ur = 37 V; input voltage and output load R are fixed (Ui = 240 V; R = 15.7 ) 3. The two different loads are used (R = 12  and R = 17 ); the input and reference voltages are fixed (Ui = 240 V, Ur = 28.5 V). The simulation results are presented in Fig. 3, 4, 5, and 6. In each case overshoot, the values of peaks, rise, and settling times are recorded (see Table 2).

Fig. 2. QRFBC circuit with FLC and VCO generated MATLAB Simulink

Fig. 3. Output scope of circuit in Ui = 190 V (a) and in Ui = 280 V (b)

Design of Quasi-Resonant Flyback Converter

35

Fig. 4. Voltage and current of MOSFET Ui = 190 V (a) and in Ui = 280 V (b)

Fig. 5. Voltage and current of MOSFET Ur = 25 V (a) and Ur = 37 V (b)

By looking the Fig. 3, it can understand that the output voltage is controlled very well around the reference voltage. Also, by looking at Fig. 4–Fig. 5 it can easily find out that the MOSFET switched to zero voltage. By comparing figures, it can be concluded that MOSFET current and voltage are increased by increasing the reference voltage. Also, by increasing the load value (Fig. 6) the current of MOSFET is decreased.

Fig. 6. Voltage and Current of MOSFET in R = 12  (a) and R = 17  (b)

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2.3 Testing the QRFBC Controlled by PI Controller In this case, FLC is replaced by the PI-controller, and VCO is needed like the previous circuit. As with FLC, the three tests are performed with PI-controller. The results are represented in Fig. 7, 8 and 9.

Fig. 7. Voltage and current of MOSFET in 190 V(a) and 280 V (b)

By simple glance to the Fig. 7, 8 and 9, it can understand that the behaviour of the PI-controller is the same as the fuzzy logic controller, but the values of the specifications are different (see Table 2). Like FLC, in PI-controller output voltage are controlled very well around the reference voltage, and MOSFET is switched at zero voltage, so in this way, the efficiency increased. Also, by comparing figures in each experiment, it is clear that by increasing the input voltage and load MOSFET current decreased.

Fig. 8. Voltage and current of MOSFET Ur = 25 V (a) and Ur = 37 V(b)

Design of Quasi-Resonant Flyback Converter

37

Fig. 9. Voltage and current of MOSFET in R = 12  (a) and R = 17  (b)

3 Results and Discussions With a simple glance at Table 2, it is evident in fuzzy logic and PI controller by increasing the input voltage and value of the load, the amount of overshoot is increased (especially when the input voltage is increased), but the rise time of both controllers are decreased by changing input voltage, and does not change by changing load. Table 2. QRFBC circuit specification by using FLC and PI Controller Parameters Overshoot Peak value Peak time Rise time Settling time Fuzzy controller Vi = 190 Vi = 280

PI-controller

134.8809

67.2628

0.0013

0.00038

0.0204

245.3225

99.1892

0.0019

0.00026

0.0173

Vref = 25

246.3747

87.0530

0.0014

0.00026

0.0175

Vref = 37

129.2971

84.8951

0.0019

0.00039

0.0166

Load = 12 195.1413

84.7773

0.0013

0.00030

0.0186

Load = 17 196.1259

85.2974

0.0019

0.00030

0.0167

Vi = 190

25.9138

35.8726

0.0103

0.0020

0.0729

Vi = 280

57.8641

45.2444

0.0055

0.00078

0.0574

Vref = 25

57.0299

39.5799

0.0061

0.00078

0.0607

Vref = 37

22.1385

45.5439

0.0095

0.0021

0.0428

Load = 12

36.7397

39.3773

0.0073

0.0011

0.0508

Load = 17

45.2919

41.5382

0.0070

0.0011

0.0615

By increasing the reference voltage in both controller’s overshoot is decreased and rise time is increased. The value of peak voltage increases with increasing the input voltage, reference voltage, and load, when the PI controller controls the circuit. The

38

F. Sadikoglu et al.

peak voltage has a lower value by changing reference voltage, and by changing the load value almost does not change when the circuit is controlled with FLC. In all conditions, by using FLC we faced increasing the value of peak time, but by using the PI controller, peak time decreased (except when the reference voltage is changed). Finally, it is obvious that using FLC, settling time in all conditions is decreased,also this is valid for PI controller (except when the load value is increased).

4 Conclusion Results of the study show that both controllers could control the output voltage of the QRFBC efficiently. Both controllers provide zero voltage switching and the reduction of power switching losses. Comparing these two controllers shows that both had good efficiency in controlling the output parameters of QRFBC, but the fuzzy controller had a quick response. The rise time for FLC is approximately 3–5, setting time 2.6–3.7 and peak time 3–8 times is less than PI controller. However, the amount of overshoot and peak voltage in the PIcontroller is less than by comparison with the fuzzy controller. Generally, the overshoot in the fuzzy logic controller is greater than the PI controller (4.2–5.8 times), and this range is around 1.9–2.2 times for the peak value.

References 1. Watson, R., Lee, F.C., Hua, G.C.: Utilization of an active-clamp circuit to achieve soft switching in flyback converters. IEEE Trans. Power Electron. 11(1), 162–169 (1996). https://doi. org/10.1109/63.484429 2. Dong, H., Xie, X., Zhang, L.: A new primary PWM control strategy for CCM synchronous rectification flyback converter. IEEE Trans. Power Electron. 35(5), 4457–4461 (2020). https:// doi.org/10.1109/TPEL.2019.2944492 3. Dong, H., Xie, X., Zhang, L.: A new CCM/DCM hybrid-mode synchronous rectification flyback converter. IEEE Trans. Ind. Electron. 67(5), 3629–3639 (2020). https://doi.org/10. 1109/TIE.2019.2920474 4. Wang, J., Lin, C., Huang, K., Wong, J.: The novel quasi-resonant flyback converter with the auto regulated structure for parallel/serial input. IEEE Trans. Ind. Electron. 67(2), 992–1004 (2020). https://doi.org/10.1109/TIE.2019.2902827 5. Li, M., Ouyang, Z., Andersen, M.A.E.: Analysis and optimal design of high frequency and high efficiency asymmetrical half-bridge flyback converters. IEEE Trans. Ind. Electron. 67(10), 8312–8321 (2020). https://doi.org/10.1109/TIE.2019.2950845 6. Park, H.P., Jung, J.H.: Design methodology of quasi-resonant flyback converter with a divided resonant capacitor. IEEE Trans. Ind. Electron. 68(11), 10796–10805 (2021). https://doi.org/ 10.1109/TIE.2020.3029481 7. Li, J., van Horck, F.B.M., Daniel, B.J., Bergveld, H.J.: A high-switching-frequency flyback converter in resonant mode. IEEE Trans. Power Electr. 32(11), 8582–8592 (2017). https:// doi.org/10.1109/TPEL.2016.2642044 8. Xu, S., Wang, C., Qian, Q., Zhu, J., Sun, W., Li, H.: A single-switched high-switchingfrequency quasi-resonant flyback converter with zero-current-switching and valley-switching. In: 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 2123– 2127. Anaheim, CA, USA (2019). https://doi.org/10.1109/APEC.2019.8721815

Design of Quasi-Resonant Flyback Converter

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9. Arulselvi, S., Deepa, K., Uma, G.: Design, analysis and control of a new multi-output flyback CF-ZVS-QRC. In: 2005 IEEE International Conference on Industrial Technology, pp. 413– 418. Hong Kong, China (2005). https://doi.org/10.1109/ICIT.2005.1600673 10. Park, J., et al.: Quasi-resonant (QR) controller with adaptive switching frequency reduction scheme for flyback converter. IEEE T. Ind. Electr. 63(6), 3571–3581 (2016). https://doi.org/ 10.1109/TIE.2016.2523931 11. Wang, C., et al.: New digital control method for improving dynamic performance of a quasi-resonant flyback converter. In: Applied Power Electronics Conference and Exposition (APEC), pp. 1788–1793. IEEE Press, Anaheim (2019). https://doi.org/10.1109/APEC. 2019.8721873 12. Stracquadaini, R.D.: Mixed mode control (fixed off time & quasi resonant) for flyback converter. In: 36th Annual Conference IEEE Industrial Electronic Society, pp. 556–561. IEEE Press, Glendale (2010). https://doi.org/10.1109/IECON.2010.5675222 13. Hsieh, P.C., Chang, C.H., Chen, C.L.: A primary-side-control quasi-resonant flyback converter with tight output voltage regulation and self-calibrated valley switching. In: IEEE Energy Conversion Congress and Exposition, pp. 3406–3412. IEEE Press Denver (2013). https://doi. org/10.1109/ECCE.2013.6647148 14. Modak, S., Panda, G.K., Saha, P.K., Das, S.: Design of novel fly-back converter using PID controller. Int. J. Adv. Res. Electr., Electron. Instrum. Eng. 04(01), 289–297 (2015). https:// doi.org/10.15662/ijareeie.2015.0401046 15. Arulselvi, S., Uma, G., Kalaranjini, B.: Design and Simulation of Model-Based Controllers for Quasi-Resonant Converters using Neural Networks. In: Proceedings of India International Conference Power Electronics, pp. 197–202. IEEE Press, Chennai (2006). https://doi.org/10. 1109/IICPE.2006.4685367 16. Anitha, T., Arulselvi, S.: Design of single-input fuzzy logic control of flyback multi-output quasi-resonant converter. Int. J. Develop. Res. 4(3), 672–677 (2014)

Experimental Selecting Appropriate Fuzzy Implication in Traffic IF-Then Rules Shamil A. Ahmadov1,2(B) 1 Azerbaijan State Oil and Industry University, 34 Azadliq Avenue, Az 1010, Baku, Azerbaijan

[email protected]

2 French-Azerbaijani University, 183 Nizami Street, Baku, Azerbaijan

[email protected]

Abstract. Nowadays, implications are widely used in Fuzzy Logic and decision making. Implication is the basic operation of fuzzy reasoning. Choosing the right fuzzy implication for each specific application is a complex task. In the scientific literature, there are methods that take into account the compatibility of fuzzy implication with theoretical recommendations. The theoretical results of these methods, which include generalized inference rules, are not always correct for every situation. In spite of that, existing methods are based on theoretical idea of fuzzy statement. In reality the expert’s opinion regarding the suitability of the resulting appropriate implications for interpreting the application data is not taken into account by these approaches. This paper include the method for selecting the best fuzzy implication. Used if-then rules for selecting appropriate fuzzy implication covers linguistic model of traffic problem. Experimenting several fuzzy implications can be used for number of problems, however traffic congestion problem is one of the global problem for most of the countries and for this reason named problem is selected. Keywords: Fuzzy implication · Fuzzy aggregation · Fuzzy set · Traffic problem · Efficiency index · Fuzzy logic

1 Introduction Fuzzy logic is the leading tool for describing subjective information and fuzzy sets are a universal approximator in modelling unknown objects. Implications in Fuzzy logic are one of the main logical operations. In scientific literature a number of works are devoted to application of fuzzy implications. Professor Zadeh is denoted the following in study [1]: “The problem is that the term ‘fuzzy logic’ has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw, is almost synonymous with the theory of Fuzzy Sets. In this context, what is important to recognize is that: a) FLw is much broader than FLn and subsumes FLn as one of its branches; © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 40–49, 2023. https://doi.org/10.1007/978-3-031-25252-5_11

Experimental Selecting Appropriate Fuzzy Implication

41

b) the agenda of FLn is very different from the agendas of classical multivalued logics; and c) at this juncture, the term fuzzy logic is usually used in its wide rather than the narrow sense, effectively equating Fuzzy Logic with FLw.” It has been proven in the scientific literature that fuzzy implication is an extension crisp implication to the [0, 1] interval. Authors of book [2] have analyzed algebraical, analytical and experimental aspects of fuzzy implications. Selection method of fuzzy implication based on the distance is described in [3]. Authors of study [4] discussed selection method of fuzzy implication based on Statistical Data. Obtained theoretical and practical results of selection metod for fuzzy implication are not supported for each situation. Fuzzy implications play an important role in fuzzy reasoning and information about them is given in[5]. In study [6], authors examine the statistical characteristics of the fuzzy implication. They have determined that truth values of an fuzzy implication depend on truth values of the input(antecedent) and the output(consequent). Aggregating fuzzy implications is discussed in [7]. In [8] author described a framework for simultaneously learning first order fuzzy rules and the corresponding implication operator. It has been determined that the use of finite dimensional representations of implication is a good compromise between expressivity and prediction ability. In paper [9] is given an approach for selecting implication based on truth value of the rule consequent. A method of inference based on fuzzy implication is described in [10]. It is based on the theorem of decomposition fuzzy implication and depend on a truth value. Discussed method is possible to implement for modeling large-dimensional MISO-structure systems. Also, authors have analyzed set of implications sush as: Goguen, Godel, Rescher, Ali-1, Ali-2, Ali-3, Yager, Kleene-Dienes, Reichenbach, Fodor, etc. implications. Also in this paper properties of Lukasiewicz, Ali-3, Yager and Reichenbach implications are graphically demonstrated. Experimental selection of fuzzy implication and analysis set of implications are discussed in [11]. Basic characteristics of fuzzy implication are discussed in [12] and shown that fuzzy implications can give the evidence for belief or disbelief in the result. There are serious works of researches based on application of fuzzy implication, such as Aliev, Weber, Dubois and Prade, Baldwin, Willmot, etc. Application of Fuzzy Logic to Control Traffic Signals is discussed in [14]. It is reality that implication based reasoning approaches has a number of shortcomings, since the index of efficiency is often not considered. It is clear that, the index of efficiency [11] gives possibility to select the best implication. The aim of the paper is experimental selecting appropriate fuzzy implication. The structure of the paper is as follows. The preliminaries is given in Sect. 2. Statement of the problem and its solution is discussed in next Section. Last part of the paper concludes the work.

42

S. A. Ahmadov

2 Preliminaries Definition 1 [2] . A binary operation I on [0; 1] is called a fuzzy implication if (i) I is decreasing in the first variable, (ii) I is increasing in the second variable, (iii) I(0; 0) = I(1; 1) = 1 and I(1; 0) = 0. The set of all fuzzy implications is defined on [0; 1]. Definition 2 [11–13] . Fuzzy implications and connectives: Lukasiewicz implication: I (x,⎧y) = min(1, 1 − x + y), ⎧ T = max(x + y−1, 0). ⎨ 1 − x, if x < y ⎨ x, if x + y < 1 AL˙I-1 implication: I (x, y) = 1, if x = y , T = 0, if x + y = 1 ⎩ ⎩ b, if x > y y, if x + y > 1   1, if x ≤ y 0, if x + y ≤ 1 T= Ali-2 implication: I (x, y) = (1 − x)ˆy, if x > y max(a,b), if x + y > 1  1, if x ≤ y  Ali-3 implication: I (a, b) = , T = y/ x + (1 − y) , otherwise  0, if x + y ≤ 1 1 − [(1 − x)/(x + y)], if x + y > 1 Mamdani implication: I (x, y) = min(x, y), T = min(x,y). Klir and Yuan 1 implication: I (x, y) = 1 − x + x2 y), T = xy. Definition 3. Selection of appropriate implication algorithm consists of the following steps: 1. Creation relation matrix using fuzzy implication on the rules(for instance, Ali-3 implication [11]). 2. Creation the composed fuzzy relation matrix R = ∪RS , s = 1, ..., n using logical connectives. Every implication has own logical connectives (Definition 2) [11]. 3. Determination new outputs usin maxmin aggregation [12] according to antecedents of the given rules. 4. Calculation of the adequacy of fuzzy model. The index of efficiency is computed as: ρ=

n 

[μY˜ i (x) − (μYˆ i (x)]2 ,

i=1

where i - number of the point of membership functions on input and calculated fuzzy fuzzy data, μY˜ (x) is used in the construction of the fuzzy relation R, μYˆ (x) is obtained membership function using implication based reasoning. 5. Selection the best fuzzy implication. J = min(ρj ), j = 1, m m-number of implication. j

Experimental Selecting Appropriate Fuzzy Implication

43

3 Statement of the Problem Selection of appropriate implication is main objective of this study using traffic problem described IF-THEN rules. Let’s describe linguistic model using the following data. Traffic problem represented by 7 rules which values of antecedent and concequent as follows (Table 1) [14]: Fuzzy rules are represented by its 3 inputs (X1 , X2 , X3 ) and an output (Y ). The membership functions of the three inputs (X1 , X2 , X3 ) are: for (X1 ) Less = (0; 6; 10), Medium = (7; 11; 25), High = (20; 27; 50). for (X2 )Less = (0; 7; 10), Medium = (7; 19; 25), High = (20; 26; 50). for (X3 )Less = (1000; 1200, 1500), Medium = (400; 900; 1200), High = (50; 400; 500). Values of concequent of the rule are: (Y ) Short = (0; 7; 10), Medium = (8; 24; 30), Long = (25; 30; 60) Membership functions [15, 16] for given 7 rules and their three properties (Arrival car, Queuing car, Humidity or Fog) were evaluated (Table 1). Table 1. Fuzzy IF-THEN rule base [14] Rules no

Antecedents

Consequent

X1

X2

X3

Y

1

High

Less

Less

Short

2

High

Less

Medium

Medium

3

High

Less

High

Long

4

High

Medium

Less

Medium

5

High

Medium

Medium

Medium

6

Medium

Less

Less

Short

7

Medium

Medium

Less

Medium

Selection of appropriate implication and performing fuzzy inference is main objective of the considered problem. Used initial data as follows: (X1 ) - Number of cars passing during green light (AC Arrival Car), (X2 ) - Number of cars waiting during the red light (QC-Queuing Car), (X3 ) - Weather variation (FHumidity or Fog). (Y ) - The green light duration (GD). It describe the extension time required for green light on the arrival side. Using above given rule are formulated fuzzy relations (Tables 2, 3, 4, 5, 6, 7 and 8). Intersection of relations are performed using ALI-3 conjunction connective [15]:  0, μRs,k (x, y) + μRs+i,k (x, y) ≤ 1 μs (x, y) = max(μRs,k (x, y), μRs+i,k (x, y)), μRs,k (x, y) + μRs+i,k (x, y) > 1 where s-number of relation and k-number of points on relation, i = 1,…6.

44

S. A. Ahmadov Table 2. Fuzzy relation matrix for the first rule

Input

Output 0

0.328571429

0.657142857

1

0.666666667

0.333333333

0

0

1

1

1

1

1

1

1

0.285714286

0

1

1

1

1

1

0

0.571428571

0

0.264367816

1

1

1

0.269230769

0

1

0

0.196581197

0.489361702

1

0.5

0.2

0

0.666666667

0

0.245551601

0.650943396

1

1

0.25

0

0.333333333

0

0.327014218

1

1

1

1

0

0

1

1

1

1

1

1

1

Table 3. Fuzzy relation matrix for the second rule Input

Output 0

0.3125

0.625

1

0.666666667

0.333333333

0

0

1

1

1

1

1

1

1

0.285714286

0

1

1

1

1

1

0

0.571428571

0

0.24822695

1

1

1

0.269230769

0

1

0

0.185185185

0.454545455

1

0.5

0.2

0

0.666666667

0

0.230769231

0.6

1

1

0.25

0

0.333333333

0

0.306122449

1

1

1

1

0

0

1

1

1

1

1

1

1

0.333333333

0

Table 4. Fuzzy relation matrix for the third rule Input

Output 0

0.32

0.64

1

0.666666667

0

1

1

1

1

1

1

1

0.285714286

0

1

1

1

1

1

0

0.571428571

0

0.255707763

1

1

1

0.269230769

0

1

0

0.19047619

0.470588235

1

0.5

0.2

0

0.666666667

0

0.237623762

0.623376623

1

1

0.25

0

0.333333333

0

0.315789474

1

1

1

1

0

0

1

1

1

1

1

1

1

Experimental Selecting Appropriate Fuzzy Implication

45

Table 5. Fuzzy relation matrix for the fourth rule Input

Output 0

0.3125

0.625

1

0.66667

0.3333333

0

0

0.3125

1

1

1

1

1

1

0.285714286

0.625

1

1

1

1

1

0

0.571428571

1

0.24822695

1

1

1

0.269231769

0

1

0.666666667

0.185185185

0.454545

1

0.5

0.2

0

0.666666667

0.333333333

0.230769231

0.6

1

1

0.25

0

0.333333333

0

0.306122449

1

1

1

1

0

0

1

1

1

1

1

1

1

Table 6. Fuzzy relation matrix for the fifth rule Input

Output 0

0.3125

0.625

1

0.666667

0.3333333

0

0

0.3125

1

1

1

1

1

1

0.2857143

0.625

1

1

1

1

1

0

0.5714286

1

0.24822695

1

1

1

0.2692308

0

1

0.666666667

0.185185185

0.45454545

1

0.5

0.2

0

0.6666667

0.333333333

0.230769231

0.6

1

1

0.25

0

0.3333333

0

0.306122449

1

1

1

1

0

0

1

1

1

1

1

1

1

Table 7. Fuzzy relation matrix for the sixth rule Input

Output 0

0.328571429

0.657142857

1

0.666666667

0.333333333

0

0

1

1

1

1

1

1

1

0.328571429

0

1

1

1

1

1

0

0.657142857

0

0.247311828

1

1

1

0.251798561

0

1

0

0.196581197

0.489361702

1

0.5

0.2

0

0.666666667

0

0.245551601

0.650943396

1

1

0.25

0

0.333333333

0

0.327014218

1

1

1

1

0

0

1

1

1

1

1

1

1

46

S. A. Ahmadov Table 8. Fuzzy relation matrix for the seventh rule

Input

Output 0

0.3125

0.625

1

0.666666667

0.333333333

0

0

1

1

1

1

1

1

1

0.325

0

0.308641975

1

1

1

1

0

0.65

0

0.23364486

0.609756098

1

1

0.253164557

0

1

0

0.185185185

0.454545455

1

0.5

0.2

0

0.666666667

0

0.230769231

0.6

1

1

0.25

0

0.333333333

0

0.306122449

1

1

1

1

0

0

1

1

1

1

1

1

1

Result of conjuction connective is as follow between first and second relation (Table 9): Table 9. Result of conjuction connective (R1 and R2) R1 and R2 1

1

1

1

1

1

1

0

1

1

1

1

1

0

0

0

1

1

1

0

0

0

0

0

1

0

0

0

0

0

0.720965

1

1

0

0

0

0

1

1

1

1

0

1

1

1

1

1

1

1

Now we define a composed fuzzy relation matrix R, R =

7

Ri (Table 10) with the

i=1

membership function as result of conjuction connective of ALI-3 implication: Table 10. Composed fuzzy relation matrix Rcomposed 1

1

1

1

1

1

1

0

1

1

1

1

1

0 (continued)

Experimental Selecting Appropriate Fuzzy Implication

47

Table 10. (continued) Rcomposed 0

0

1

1

1

0

0

0

0

0

1

0

0

0

0

0

0.956732

1

1

0

0

0

0

1

1

1

1

0

1

1

1

1

1

1

1

Table 11. New obtained individual output (Y1) Input 0

0

0

0

0

0

0

0

0.285714

0

0.285714

0.285714

0.285714

0.285714

0.285714

0

0.571429

0

0

0.571429

0.571429

0.571429

0

0

1

0

0

0

1

0

0

0

0.666667

0

0

0.666667

0.666667

0.666667

0

0

0.333333

0

0

0.333333

0.333333

0.333333

0.333333

0

0

0

0

0

0

0

0

0

Y1

0

0.285714

0.666667

1

0.666667

0.333333

0

The next step we calculate individual outputs (Table 11) of the rule using maxmin composition. The index of efficiency is determined on first rule using primary value of the output and obtained value on the the first rule output as follow: ρ1 =

7 

[μY˜ i (x) − (μYˆ i (x)]2 = 0.001927438

i=1

Obtained values of the index efficiency for 2–7 rules are determined as follow: ρ2 = 0.002453586; ρ3 = 0.001886621; ρ4 = 0.002453586; ρ5 = 0.002453586; ρ6 = 9.07029E − 05; ρ7 = 0.001892361. Then we get estimated value on ALI-3 implication ρAli−3 = 0.001879697. For Ali-1 implication obtained values of the index efficiency for 1–7 rules are determined as follow: ρ1 = 0.001033; ρ2 = 0.140883; ρ3 = 0.000298; ρ4 = 0.000258; ρ5 = 0.000258; ρ6 = 0.001033; ρ7 = 0.000258 Then we get estimated value on ALI-1 implication ρAli−1 = 0.020575.

48

S. A. Ahmadov

For Ali-2 implication obtained values of the index efficiency for 1–7 rules are determined as follow: ρ1 = 0.009183673; ρ2 = 0.003587372; ρ3 = 0.005877551; ρ4 = 0.003587372; ρ5 = 0.003587372; ρ6 = 0; ρ7 = 0.00078125 Then we get estimated value on ALI-1 implication ρAli−2 = 0.003800656.For Mamdani implication obtained values of the index efficience for 1–7 rules are determined as follow: ρ1 = 0.444444; ρ2 = 1.445736; ρ3 = 0.444812; ρ4 = 0.445736; ρ5 = 0.445736; ρ6 = 0.444444; ρ7 = 0.444812 Then we get estimated value on Mamdani implication ρMamd = 0.58796. For Klir and Yuan 1 implication obtained values of the index efficience for 1–7 rules are determined as follow: ρ1 = 2.548841; ρ2 = 3.513017; ρ3 = 2.529413; ρ4 = 2.513017; ρ5 = 2.513017; ρ6 = 2.548841; ρ7 = 2.513017 Then we get estimated value on Klir and Yuan 1 implication ρKlirandYuan = 2.668451818. For Lukasiewicz’s implication obtained values of the index efficience for 1–7 rules are determined as follow: ρ1 = 0.006513; ρ2 = 1.00217; ρ3 = 0.930644; ρ4 = 0.00857; ρ5 = 0.00857; ρ6 = 0.006513; ρ7 = 0.00857 Then we get estimated value on Lukasiewicz’s implication ρLukasiewicz = 0.281650251. Ranking of efficient indices of implications is defined appropriate fuzzy implication is Ali-3: ρAli−3 = 0.001879697 < ρAli−2 = 0.003800656  ρAli−1 = 0.020575 ρLukasiewicz = 0.28165025 < ρMamd = 0.58796 < ρKlirandYuan = 2.66845181. So, obtained value J=0.00187969.

4 Conclusion Proposed approach for selecting the appropriate implication is detailed by example. Efficiency index is calculated and the best alternative has been defined where index value is small. Terms are represented by discrete fuzzy numbers in a model. By using these terms it is created fuzzy relation on the rules and is fulfilled fuzzy inference algorithm. In addition, using wide range of dataset and comparing several methods such as Lukasiewicz, Ali-3, Ali-2, Ali-1, Zadeh, Klin and Yuan1, Mamdani appropriate implication which is close to the expert’s opinion is found theoretically. In this work Ali-3 and Ali-2 implications are defined as best options for interpretation of information.Selection of appropriate

Experimental Selecting Appropriate Fuzzy Implication

49

implication is the kernel of suitable demonstration of information. The given approach is possible to use in fuzzy control, artificial intelligence and uncertainty based reasoning. Moreover, ideal implication can be applied for analyzing several problems and selecting appropriate implication facilities.

References 1. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall, Upper Saddle River (1995). ISBN 0-13-101171-5 2. Michał, B., Balasubramaniam, J.: Fuzzy Implications. Studies in Fuzziness and Soft Computing. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69082-5 3. Papadopoulos, B.K., Trasanides, G., Hatzimichailidis, A.G.: Optimization method for the selection of the appropriate fuzzy implication. J. Optim. Theory Appl. 134, 135–141 (2007). https://doi.org/10.1007/s10957-007-9246-5 4. Pagouropoulos, P., Tzimopoulos, C.D., Papadopoulos, B.K.: Selecting the most appropriate fuzzy implication based on statistical data. Int. J. Fuzzy Syst. Adv. Appl. 3, 32–42 (2016). ISSN 2313-0512 5. Wei, J.: Fuzzy implications in lattice effect algebras. Fuzzy Sets Syst. 405, 40–46 (2021). https://doi.org/10.1016/j.fss.2020.04.021 6. Aliev, R., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inf. Sci. 181, 1045–1059 (2011) 7. Reiser, R.H.S., Bedregal, B., Baczy´nski, M.: Aggregating fuzzy implications. Inf. Sci. 253, 126–146 (2013). https://doi.org/10.1016/j.ins.2013.08.026 8. Mathieu, S., Didier, D., Henri, P., Thomas, S.: Learning fuzzy rules with their implication operators. Data Knowl. Eng. 60, 71–89 (2007). https://doi.org/10.1016/j.datak.2006.01.007 9. Suraj, Z., Lasek, A., Lasek, P.: Inverted fuzzy implications in approximate reasoning. Fund. Inform. 143(2), 151–171 (2016). https://doi.org/10.3233/FI-2016-1309 10. Sinuk, V.G., Panchenko, M.V.: Method of fuzzy inference for one class of MISO-structure systems with non-singleton inputs. IOP Conf. Ser. Mater. Sci. Eng. 327 (2018). https://doi. org/10.1088/1757-899X/327/4/042074 11. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, London, Singapore, Hong Kong (2001) 12. Aliev, R., Aliev, F., Babaev, M.: Fuzzy process control and knowledge engineering in Petrochemical and robotic manufacturing, Verlag TUV Rheinland (1991) 13. http://www.scholarpedia.org/article/Triangular_norms_and_conorms 14. Mohanaselvi, S., Shanpriya, B.: Application of fuzzy logic to control traffic signals. In: AIP Conference Proceedings, vol. 2112, no. 1 (2019). https://doi.org/10.1063/1.5112230 15. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS-2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_7 16. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS-2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2

Prediction of Cold Filter Plugging Point of Different Types of Biodiesels Using Various Empirical Models Youssef Kassem1,2,3,4(B) , Hüseyin Çamur1 , Ahmed Hamid Mohamed Abdalla Zakwan1 , and Nkanga Amanam Nkanga1 1 Faculty of Engineering, Mechanical Engineering Department, Near East University,

99138 Nicosia, North Cyprus, Turkey {yousseuf.kassem,huseyin.camur}@neu.edu.tr, {20213770, 20206631}@std.neu.edu.tr 2 Faculty of Civil and Environmental Engineering, Near East University, 99138 Nicosia, North Cyprus, Turkey 3 Energy, Environment, and Water Research Center, Near East University, 99138 Nicosia, North Cyprus, Turkey 4 Engineering Faculty, Kyrenia University, 99138 Kyrenia, North Cyprus, Turkey

Abstract. In this paper, multi-layer perceptron neural network (MLPNN) and Radial basis function neural network (RBFNN) have been used to predict the cold filter plugging point (CFPP) of different types of biodiesel. Moreover, the accuracy of the proposed models is compared with the Quadratic model (QM), and Multiple Linear Regression (MLR). For this aim, estimating monounsaturated (MUFAMEs), polyunsaturated (PUFAMEs), and saturated (SFAMEs), the degree of unsaturation (DU), and long-chain saturated factor (LCSF) were collected and used as input parameters for the proposed models. Among the developed models, the MLPNN and QM models presented significantly better prediction performance based on the value R2 and RMSE. Keywords: CFPP · Biodiesel · MLPNN · RBFNN · QM · MLR

1 Introduction Biodiesel is domestically obtained from refined and waste vegetable oils, animal fats, or other lipids [1]. It has many advantages such as renewable fuel, higher viscosity, density, cold flow properties, and emissions reduction [2]. Because of these advantages, it is gained the scientific community’s attention considerably over the past decade. The characteristics of biodiesel depend on feedstock’s chemical and physical properties; thus, biodiesel’s physicochemical properties depend on the fatty acid profile and its characteristics [3]. Accordingly, the combustion and emissions characteristics are dependent on the type of biodiesel used. Generally, cold flow properties are considered crucial properties that influence the characteristics of the engine [4]. They depend on the fatty acid profile of the source © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 50–57, 2023. https://doi.org/10.1007/978-3-031-25252-5_12

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51

utilized for biodiesel production [3, 4]. The characteristics of biodiesel’s cold flow are the reason that limits its widespread use. One of the important low-temperature properties of biodiesel is the cold filter plugging point (CFPP). Fuel shouldn’t gel early in the cold, and clog the fuel filter [5]. The cold flow properties, mainly, CFPP, of biodiesel must meet the specifications of fuel to utilize the biodiesel directly in the diesel engine or as a blend component in petro-diesel. Therefore, it is necessary to provide a predictive model that can estimate the CFPP of biodiesel with different fatty acid compositions. In this regard, four empirical models, namely, MLPNN, RBFNN, QM, and MLR are developed to estimate the CFPP of biodiesel. In this study, MUFAMEs, PUFAMEs, SFAMEs, DU, and LCSF are used as input variables for the proposed models. The overall flowchart of the current study is illustrated in Fig. 1.

2 Material and Methods 2.1 Data In this work, CFPP value and the fatty acid compositions (Lauric acid, Myristic acid, Palmitic acid, Palmitoleic acid, Stearic acid, Oleic acid, Linoleic acid, Linolenic acid, Arachidic acid, and Paullinic acid) of various types of biodiesel are collected from the previous studies [6–14]. For determining the estimated monounsaturated (MUFAMEs), polyunsaturated (PUFAMEs), saturated (SFAMEs), the degree of unsaturation (DU), and long-chain saturated factor (LCSF) based on the fatty acid compositions, Eqs. (1)–(5) are used. Table 1 lists the statistical parameters of the used variables.   MUFAMs = wt%Cxx : 1 (1) 

PUFAMs = 



wt%Cxx : 2 +

SFAMs =





wt%Cxx : 3

wt%Cxx : 00

  DU = [monounsatuarted Cn : 1] + 2 polyunsaturated Cn : 2, 3

(2) (3) (4)

LCSF = 0.1 × [C16 : 0] + 0.5 × [C18 : 0] + [C20 : 0] + 1.5 × [C22 : 0] + 2 × [C24 : 00]

(5)

2.2 Machine Learning Models (MLMs) MLMs are utilized as a tool to describe a complex system [15, 16]. Wide ranges of ML models are utilized to solve complex problems in a variety of fields [15, 16]. In this study, MLPNN and RBFNN are developed to determine the CFPP of Biodiesel. MLPNN and RBFNN are the most popular artificial neural network approaches for modeling nonlinear and complex processes in the real world [17]. The description of the MLPNN and RBFNN models was given in Ref. [17]. The training (70%) and testing data (30%) were used to develop and validate the models, respectively. The results of the proposed models are compared with observed data.

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Fig. 1. Flowchart of the current study

Table 1. Statistical parameters of mean hourly data during 2020. Variable

Unit

Mean

Standard deviation

Coefficient of variation

Minimum

Maximum

MUFAMEs

wt%

39.68

23.06

58.11

1.92

91.90

PUFAMEs

wt%

35.88

26.02

72.52

0.70

85.30

SFAMEs

wt%

21.56

18.54

85.96

2.00

79.50

DU

wt%

111.43

40.51

36.36

9.90

177.20

LCSF

wt%

4.21

3.19

75.63

0.64

15.95

CFPP

°C

−0.83

8.05

−965.23

−13.00

17.00

Prediction of Cold Filter Plugging Point

53

2.3 QM and MLR models The QM is a mathematical and statistical method polynomial model as expressed below [15]. Y = β0 +

n  i=1

βi xi +

n  i=1

βii xi2 +

n n−1   i

βij xi xj

(6)

i=i+1

where Y is the predicted response, β0 , βi , are related to the main effects and βii and βij to interaction, xi and xj are the independent variables. Moreover, MLR is used to predict the DV of biodiesel. MLR is expressed as Y = β0 + β1 x1 + . . . + βi xi i = 1, 2 . . . n

(7)

where Y , β0 , βi , and xi are defined above. In general, these models aim to show the relationship between the variables as shown in eq. (8).     CFPP = f MUFAMs, PUFAMs, SFAMs, DU .LCSF (8)

3 Results and Discussion 3.1 Estimating the CFPP Using MLPNN and RBFNN Aforementioned,two machine learning models  were utilized to estimate the CFPP of biodiesel. Thus, MUFAMs, PUFAMs, SFAMs, DU, and LCSF are used as input parameters. The best network configuration was found by the trial and error method and selected based on the lowest value of mean squared error (MSE). The best function is selected through several trials in the training phase. The developed MLPNN and RBFNN model architectures for predicting the CFPP of biodiesel are shown in Figs. 2 and 3, respectively. Based on the analysis, it is found that the sum squared error of MLPNN and RPFNN was estimated to be 13.527 and 10.331, respectively based on the training data. For testing data, it is observed that sum squared error was found to be equal to 2.034 and 6.168 for MLPNN and RPFNN, respectively. Fig. 4 shows the scatter plot between the estimated data and actual data of CFPP.

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Fig. 2. The structure of MLPNN for predicting the CFPP of biodiesel.

Fig. 3. The structure of RBFNN for predicting the CFPP of biodiesel.

Prediction of Cold Filter Plugging Point

55

EsƟmated value [ ]

15 10 5 0 -5

R-squared (MLPNN) = 0.753 R-squared (RBFNN) = 0.668

-10 -15 -15

-10

-5

0

5

10

15

Actual data [ ] MLPNN

RBFNN

Fig. 4. Comparison of the estimated data with the observed data using MLPNN and RBFNN

3.2 Estimating the CFPP Using QM and MLR The mathematical equation that was developed using RSM (3) for predicting the CFPP is expressed as shown below. Fig. 5 shows the scatter plot between the estimated data and actual data of CFPP.    CFPP = 24.5 − 4.0 · MUFAMs + 41.1 · PUFAMs + 76.3 · SFAMs−  2  2  2 PUFAMs + 81.1 · SFAMs − 24 · LCSF − 17.6 · MUFAMs + 29.3 ·    24.8 · DU 2 − 10.19 · LCSF 2 + 44.8 · MUFAMs · SFAMs − 51.5 · MUFAMs·     LCSF + 80.3 · PUFAMs · SFAMs − 44.7 · PUFAMs · LCSF − 50.4 · SFAMs· LCSF

(9) CFPP = −10.38 − 0.366 ·



MUFAMs + 5.015 · LCSF + 0.00407 ·



MUFAMs

2

−0.2026LCSF 2

(10)

3.3 Performance Evaluation of Proposed Models The performance of MLPNN and RBFNN is compared with the QM and MLR to evaluate the performance of the proposed models. The values of R-squared and root mean squared error (RMSE) are listed in Table 2. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the MLPNN model.

56

Y. Kassem et al. Table 2. Performance evaluation of the models. MLPNN

RBFNN

QM

R-squared

0.753

0.668

0.728

0.010

RMSE

3.002

3.316

3.080

14.251

EsƟmated value [ ]

Statistical indicator

20 10 0 -10 -20 -30 -40 -50

MLR

R-squared (QM) = 0.728 R-squared (MLR) = 0.01 -15

-10

-5

0

5

10

15

Actual data [ ] QM

MLR

Fig. 5. Comparison of the estimated data with the observed data using MLR and QM.

4 Conclusions CFPP is one of the most important properties of biodiesel. Therefore, four empirical models (MLPNN, RBFNN, QM, and MLR) were developed to determine the CFPP of various types of biodiesel. The results demonstrated that MLPNN and QM models were suitable for predicting the CFPP of biodiesel based on the value R2 and RMSE. In future work, various models with various combinations of parameters including oxidation stability, flash point, viscosity, and density should propose to categorize the most influencing input parameters for predicting the CFPP of the biodiesel.

References 1. Rashid, U., Hazmi, B.: Advances in production of biodiesel from vegetable oils and animal fats. In: Rokhum, S.L., Halder, G., Assabumrungrat, S., Ngaosuwan, K. (eds.) Biodiesel Production: Feedstocks, Catalysts, and Technologies, pp. 1–31. Wiley (2022). https://doi.org/ 10.1002/9781119771364.ch1 2. Dey, S., Reang, N.M., Das, P.K., Deb, M.: A comprehensive study on prospects of economy, environment, and efficiency of palm oil biodiesel as a renewable fuel. J. Clean. Prod. 286, 124981 (2021). https://doi.org/10.1016/j.jclepro.2020.124981 3. Kassem, Y., Çamur, H., Alassi, E.: Biodiesel production from four residential waste frying oils: proposing blends for improving the physicochemical properties of methyl biodiesel. Energies 13(16), 4111 (2020). https://doi.org/10.3390/en13164111

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4. Saeed, R.H.S., Kassem, Y., Çamur, H.: Effect of biodiesel mixture derived from waste frying-corn, Frying-Canola-Corn and Canola-corn cooking oils with various Ages on physicochemical properties. Energies 12(19), 3729 (2019). https://doi.org/10.3390/en1219 3729 5. Sajjadi, B., Raman, A.A.A., Arandiyan, H.: A comprehensive review on properties of edible and non-edible vegetable oil-based biodiesel: composition, specifications and prediction models. Renew. Sustain. Energy Rev. 63, 62–92 (2016). https://doi.org/10.1016/j.rser.2016. 05.035 6. Ramos, M.J., Fernández, C.M., Casas, A., Rodríguez, L., Pérez, Á.: Influence of fatty acid composition of raw materials on biodiesel properties. Bioresour. Technol. 100(1), 261–268 (2009). https://doi.org/10.1016/j.biortech.2008.06.039 7. De Lima Da Silva, N., Benedito Batistella, C., Maciel Filho, R., Maciel, M.R.W.: Biodiesel production from castor oil: optimization of alkaline ethanolysis. Energy Fuels 23(11), 5636– 5642 (2009). https://doi.org/10.1021/ef900403j 8. Sanford, S.D., White, J.M., Shah, P.S., Wee, C., Valverde, M.A., Meier, G.R.: Feedstock and biodiesel characteristics report. Renew. Energy Group 416, 1–136 (2009). https://doi.org/10. 2172/1360190 9. Giakoumis, E.G.: A statistical investigation of biodiesel physical and chemical properties, and their correlation with the degree of unsaturation. Renew. Energy 50, 858–878 (2013). https://doi.org/10.1016/j.renene.2012.07.040 10. Hoekman, S.K., Broch, A., Robbins, C., Ceniceros, E., Natarajan, M.: Review of biodiesel composition, properties, and specifications. Renew. Sustain Energy Rev. 16(1), 143–169 (2012). https://doi.org/10.1016/j.rser.2011.07.143 11. Dunn, R.O.: Cold flow properties of biodiesel by automatic and manual analysis methods. J. ASTM Int. 7(4), 1–16 (2010). https://doi.org/10.1520/jai102618 12. Tang, H., Salley, S.O., Ng, K.S.: Fuel properties and precipitate formation at low temperature in soy-, cottonseed-, and poultry fat-based biodiesel blends. Fuel 87(13–14), 3006–3017 (2008). https://doi.org/10.1016/j.fuel.2008.04.030 13. Moser, B.R.: Influence of blending canola, palm, soybean, and sunflower oil methyl esters on fuel properties of biodiesel. Energy Fuels 22(6), 4301–4306 (2008). https://doi.org/10.1021/ ef800588x 14. Usta, N., Aydo˘gan, B., Çon, A.H., U˘guzdo˘gan, E., Özkal, S.G.: Properties and quality verification of biodiesel produced from tobacco seed oil. Energy Convers. Manag. 52(5), 2031–2039 (2011). https://doi.org/10.1016/j.enconman.2010.12.021 15. Kassem, Y., Othman, A.A.: Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models. Model. Earth Syst. Environ. 8(4), 4661–4686 (2022). https://doi.org/10.1007/s40808-022-01413-7 16. Kassem, Y., Gökçeku¸s, Hüseyin., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 7(3), 1475–1502 (2020). https://doi.org/10.1007/s40808-020-00866-y 17. Kassem, Y., Gokcekus, H.: Do quadratic and poisson regression models help to predict monthly rainfall? Desalin. Water Treat. 215, 288–318 (2021). https://doi.org/10.5004/dwt. 2021.26397

Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem Bü¸sra Altınkaynak1

, Tolunay Göçken1 , Murat Ye¸silkaya2 and Gülesin Sena Da¸s3(B)

, Burak Birgören3

,

1 Department of Industrial Engineering, Alparslan Türke¸s Science and Technology University,

Adana, Turkey [email protected] 2 Niksar Vocational School, Tokat Gaziosmanpa¸sa University, Tokat, Turkey [email protected] 3 Department of Industrial Engineering, Kırıkkale University, Kırıkkale, Turkey [email protected], [email protected], [email protected]

Abstract. In this study, we consider solution approaches used to solve the proposed bilevel linear programming model for an Industrial Symbiosis network. We first solve this model with the well-known Karush-Kuch-Tucker (KKT) approach. However, transforming a bilevel programming model with the KKT approach increases the number of variables and constraints. For this reason, we use the fuzzy programming approach and the fuzzy goal programming approaches as alternatives to the KKT approach. Next, we compare the results of the KKT approach with these methods and examine the suitability of these approaches to solve our bilevel problem. Unlike previous studies, which claimed that fuzzy approaches mostly outperform the KKT approach, in our case, the best solution is obtained with the KKT approach. This is most probably because these approaches ignore the hierarchical nature of the problem. We believe that more research on fuzzy approaches is needed to evaluate the suitability of these approaches for solving bilevel programming problems. Keywords: Industrial symbiosis · Bilevel programming · Fuzzy programming approach · Fuzzy goal programming

1 Introduction Bilevel programming (BLP) problems are hierarchical optimization problems of two or more players [1]. In these problems, optimal decision of the upper decision maker (leader) is constrained by the decision of the lower-level decision maker (the follower) [2]. That is the upper-level decision-makers choose their optimal positions whereas the lower-level decision-makers optimize their objectives given the dominant players’ positions determined at the first stage [3]. BLP is difficult to solve owing, fundamentally, to bad mathematical properties and huge size [4]. Therefore, several methods have been presented to solve BLP. Interested © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 58–66, 2023. https://doi.org/10.1007/978-3-031-25252-5_13

Comparison of Fuzzy Solution Approaches

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readers can refer to [5]. Among these approaches, Karush-Kuch-Tucker (KKT) approach [6, 7], is probably the most popular one. In this approach, the lower-level problem is replaced with the KKT conditions of the problem which results in a single-level problem with nonlinear constraints. Although linearizing these constraints are possible, as the number of constraints and the number of decision variable increase the size of the resultant problem also in-crease. To avoid this, we use the fuzzy programming approach (FPA) and fuzzy goal programming (FGP) approaches to solve our bilevel problem. We prefer these fuzzy approaches since they are known to be successful in dealing bilevel problems without increasing the size of the problem greatly. The first approach we test to solve our problem, which is introduced in the next section, is the FPA proposed by Lai [8] and Shih et al. [9]. This approach offers a solution if there is a collaborative relationship between decision-makers. The second approach that we will use is the FGP method which is extended by [10–14] to solve BLP problems. We summarize the details of the FPA and FGP approaches in Sect. 3. In Sect. 4, we present a comparison of the considered fuzzy approaches with the KKT approach. Finally, we conclude in Sect. 5.

2 A BLP Problem for an Industrial Symbiosis Network In this study, we consider a theoretical Industrial Symbiosis (IS) network located in an eco-industrial park. This network consists of plants from the forest products industry, including a sawmill, a fiberboard plant, a particleboard plant, a pulp and paper producer and a pellet producer. Plants in the network produce final products by using raw materials (rm) and/or by-products (bp) to make a profit. As a result of this production, by-products that could be used by other plants emerge. The park authority wants companies to use these by-products to minimize the total use of raw materials in the park. We assume that each plant uses a single type of by-product and/or raw material to produce a single type of final product. More information about the case study can be found in [15, 16]. Notations used in the proposed model are; Sets I is the set of plants in EIP (i, j ∈ I ) K is the set of bp types (k ∈ K) M is the set of rm types (m ∈ M ) Decision variables rm Qim bp,in Qijk bp,out

Qik

bp,buy Qijk bp,use Qik

amount of rm type m purchased by plant i (tonne) amount of bp type k sold to plant j from plant i (tonne) amount of bp type sold out the park (tonne) amount of bp type k purchased by plant i of plant j (tonne) amount of bp type k used (tonne)

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Parameters Di Capi rm,bp wimk bp

wik rm wim rm,CO2 wm bp,CO2 wk wtrn,CO2 rm pm bp pk fp pi C CO2 Cmtrn,rm Ce Ciksto upp θilow , θi trn,bp Ck e,bp ak e,rm am dij di

fp demand of plant i (m 3 ) production capacity of plant i (m 3 ) conversion rate (cr) for obtaining bp type k by processing rm type m from plant i cr of obtaining fp by using bp type k in plant i cr of obtaining fp by using rm type m in plant i The amount of CO2 released while processing rm type m (tonne) The amount of CO2 released while processing bp type k (tonne) The amount of CO2 emitted during transporting per km (tonne) unit purchasing price of rm type m (/tonne) unit sales price of bp type k (/tonne) unit sales price of fp produced by plant i (/m3 ) tax paid for produced carbon dioxide (/tonne) unit transportation cost per km for rm type m (/tonne) unit cost of energy (/kWh) inventory holding cost of bp type k of plant i (/tonne) lower bound for ratio of bp to rm, upper bound for ratio of bp to rm unit transportation cost per km for bp type k (/tonne) the amount of energy required to process bp type k (kWh/tonne) the amount of energy required to process rm type m (kWh/tonne) distance between plant i and plant j (km) distance between the rm supplier and plant i (km)

The profit of each plant is calculated by considering the difference between the revenue and cost. Revenue of each plant is composed of revenues obtained from selling final products and by-products (1). The cost of each plant consists of (i) by-product and raw material purchasing costs (2a), (ii) transportation costs (2b), (iii) energy costs (2c), (iv) emission-related costs depending on the use of by-products, raw materials and transportation (2d,2e) (v) inventory holding costs (2e). We assume that a holding cost Invi occurs when a plant produces more than demand.   bpsell bp,in  bpsell bp,out fp fp fREV ,i = pi Qi + pik Qijk + pik Qik (1) fCOST ,i =



j∈I k∈K rm rm pm Qim +

m∈M





m∈M

k∈K



trn,bp

Ck

bp,buy

dij Qijk

+

(2b)

j∈I k∈K

e,rm rm C e am Qim +

m∈M



(2a)

j∈I k∈K rm Cmtrn,rm di Qim +



k∈K bpbuy bp,buy pjk Qijk +



e,bp

C e ak

k∈K bp,CO2

C CO2 wk

bp,use

Qik

+

bp,use

Qik

 j∈I k∈K

+

(2c) bp,buy

C CO2 wktrn,CO2 dij Qijk

+

(2d)

Comparison of Fuzzy Solution Approaches



rm rm,CO2 trn,CO2 Qim (C CO2 wm + cCO2 wm di ) + Cisto Invi

61

(2e)

m∈M

In the proposed bilevel model the park authority is the upper-level decision maker who wants to minimize the total use of raw materials in the park to pro-mote the exchange of materials between companies in the network. On the other hand, plants in the network are the lower-level decision-makers who want to maximize their profits. The proposed linear bi-level model (LBP) is as follows;  rm Qim (3) LBP:min i∈I m∈M

s.t. max



fREV ,i − fCOST ,i

(4)

i∈I

s.t. 

bp,use

Qik

rm Qim ,i ∈ I

(5)

rm Qim , i∈I

(6)

m∈M

k∈K





≥ θilow

bp,use

Qik



upp

≤ θi

m∈M

k∈K

fREV ,i − fCOST ,i ≥ 0, i ∈ I 



rm rm wim Qim

+

m∈M





rm wimk Qim =

m∈M k∈K bp,in

Qijk

 m∈M

bp,buy

≤



− Di = Invi , i ∈ I bp,in

Qijk

j∈I k∈K

= Qjik

bp,use

Qik

 bp bp,use wik Qik

k∈K rm,bp

(7)



rm rm wim Qim +



bp,out

Qik

, i∈I

(9)

k∈K

, i, j ∈ I , k ∈ K

(10)

bp,buy

, i ∈ I, k ∈ K

(11)

bp

(12)

Qijk

j∈I

+

(8)



bp,use

wik Qik

≤ Capi , i ∈ I

k∈K

bp,buy bp,in bp,out bp,use rm Qijk , Qijk , Qik , Qik , Qim , Invi

≥ 0, i, j ∈ I , k ∈ K, m ∈ M

(13)

Constraints (5–6) express a lower limit and an upper limit representing the ratio of the by-product used to the raw material used. Constraint (7) ensures that every plant is profitable as long as they are in the network. Constraint (8) ensures that the amount of the final product produced satisfies the demand. The excess amount of final products is stocked. Constraint (9) expresses that a certain amount of by-products can be produced

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B. Altınkaynak et al.

with the use of raw materials. By-products produced can be sold to other plants in the network or to plants outside the park. Constraint (10) is a balance constraint and ensures that the amount of by-product sold to plant j is equal to the amount of byproduct purchased by plant j. Constraint (11), ensures that a plant cannot use more than the amount of by-product purchased. Finally, constraint (12) represents the production capacity of each plant.

3 Fuzzy Solution Approaches for the BLP Problem In this section, we shortly summarize utilized fuzzy solution approaches. 3.1 Fuzzy Programming Approach – FPA In FPA, the leader specifies goals for the control variable and the objective function. This information is modeled through membership functions and transmitted to the follower at the leader’s request. The follower tries to satisfy the leader’s objective, as well as his/her objective. Then, the follower presents the solution to the leader. If the leader accepts the proposed solution, this solution is called a satisfactory solution. If this solution is not suitable, then the leader updates the tolerance values of his/her membership function until a satisfactory solution is reached. This approach aims to maximize the minimum satisfaction level [17, 18]. Trapezoidal membership functions are used for the upper and lower-level objective functions. On the other hand, the triangular membership function is used for the leader’s control variable. When our bilevel model is rearranged according to the FPA, the following model is obtained. max λ s.t. 

(14) 

i∈I

m∈M

   rm,U rm Qim + p1 − i∈I m∈M Qim

p1  

L i∈I fREV ,i − fCOST ,i − TP ≥λ U L TP − TP  rm Qrm,f − m∈M Qim ≥λ Qrm,f − Qrm,l

≥λ

(15) (16) (17)

Eq. (5) − (13)

(18)

λ ∈ [0, 1]

(19)

where Qrm,l and TQrm,f represent the lower and upper bounds for the leader’s objective function, TP L and TP U represent the lower and upper bounds for the follower’s objective function, p1 is the tolerance value, Qrm is the control variable of the leader, and Qrm,U − p1 , Qrm,U + p1 are the lower and upper bounds for the leader’s control variable. This model contains fewer constraints and decision variables compared to the model obtained with the KKT approach. However, this method does not always provide the desired solution, due to the inconsistency between the membership function of the leader’s decision variable and the membership function of the objective functions [10].

Comparison of Fuzzy Solution Approaches

63

3.2 Fuzzy Goal Programming – FGP In the goal programming problem, targets to be reached for each goal are determined precisely by the decision makers. The aim is to minimize the sum of deviations from target values since it is not possible to satisfy all goals simultaneously. However, determining these target values precisely is often difficult for decision makers. In FGP, target values for each goal are represented as a membership function. The decision-maker provides an acceptable range for the target level instead of a single value. In the case of bilevel programming, we define membership functions for each goal and deviation variables by considering the objectives of the leader and the follower. To obtain an FGP model of our bilevel model we defined deviation variables. We assume that d1+ , d1− , d2+ , d2− represent the deviation from the membership functions defined for the leader’s control variable. d3+ , d3− denote deviations from the goal of the membership function defined for the follower’s objective function whereas d4+ , d4− represent deviations from the goal values of the membership function defined for the leader’s objective function. Finally, w1r , w2l , w3 , w4 represent weights for each fuzzy goal. The proposed FGP model is as follows;



 (20) min w1r d1+ + d1− + w2l d2− + d2+ + w3 d3+ + w4 d4− s.t. 

 i∈I



m∈M

 i∈I

m∈M

   rm,U rm Qim + p1 − i∈I m∈M Qim

rm − Qim

p1   i∈I

m∈M

p1

rm,U Qim − p1

 fREV ,i − fCOST ,i − TP L − d3+ + d3− = 1 TP U − TP L  rm Qrm,f − m∈M Qim − d4+ + d4− = 1 Qrm,f − Qrm,l 

i∈I

Eq. (5) − (13)

− d1+ + d1− = 1

(21)

− d2+ + d2− = 1

(22)



(23) (24) (25)

4 Computational Results The results of the considered approaches are summarized in Table 1. In the first and second columns, we present the solution obtained only by considering only the leader’s objective function and the follower’s objective function. Next, we supply the results obtained with the KKT approach, FPA and FGP approaches in columns 3, 4 and 5, respectively. The results obtained by using the FPA enabled us to reach a meaningful result both in terms of profit and raw material use. As expected, plants consumed less raw material

64

B. Altınkaynak et al. Table 1. Solution of the bilevel problem with various solution approaches. Leader’s model

Total raw material used (tonne)

Follower’s model

1665454.5

1759021.1

KKT

FPA

1665454.5

FGP

1709292.0

1759021.5

Sawmill P.

640000.0

640000.0

640000.0

640000.0

640000.0

Particleboard P.

276620.0

276620.0

276620.0

276620.0

337126.0

Fiberboard P.

674446.0

747016.0

674446.0

718283.0

707507.0

Pellet P. Pulp & Paper P. Total by-product used (tonne) Sawmill P.

226.5

7317.8

226.5

226.5

226.5

74162.0

88067.3

74162.0

74162.0

74162.0

492883.4

287882.0

492883.4

367392.0

312466.3

0

0

0

0

0

Particleboard P.

182569.0

182569.0

182569.0

182569.0

96795.0

Fiberboard P.

215213.0

7470.2

215213.0

89721.1

120570.0

Pellet P.

22422.7

11536.8

22422.7

22422.7

22422.7

Pulp & Paper P.

72678.7

86306.0

72678.7

72678.7

72678.7

Total 274833346.0 278550350.0 274832160.0 271393546.0 275947946.0 production cost ($) Sawmill P. Particleboard P. Fiberboard P. Pellet P. Pulp & Paper P. Total profit ($)

103315000.0 103315000.0 103315000.0 103315000.0 103315000.0 42009600.0

41659400.0

41659400.0

41659400.0

45760200.0

107593000.0 102196000.0 107593000.0 104333000.0 105134000.0 797446.0

1053550.0

1012760.0

797446.0

797446.0

21118300.0

30326400.0

21252000.0

21288700.0

20941300.0

122909032.0 131529904.0 122910123.0 127490932.0 122909132.0

Sawmill P.

18866800.0

18866800.0

18866800.0

18866800.0

18866800.0

Particleboard P.

22016300.0

22366500.0

22366500.0

22366500.0

18519500.0

Fiberboard P.

46877700.0

54165100.0

46877700.0

51279800.0

50197600.0

605532.0

360404.0

390223.0

605532.0

605532.0

34542700.0

35771100.0

34408900.0

34372300.0

34719700.0

Pellet P. Pulp & Paper P.

compared to the follower’s model, and more raw materials compared to the leader’s model. In this sense, we could say that reasonable results are obtained. However, the KKT approach provides a better result compared to FPA in terms of raw material use. Because the FPA approach generates a more profitable solution with more raw material use and less by-product use.

Comparison of Fuzzy Solution Approaches

65

The FGP approach provides a solution almost having an equal profit compared to the solution obtained by the KKT approach. However, FGP offers more raw material use compared to other approaches. In this sense, we can say that KKT performs better than the FGP approach. FGP approach almost underestimates the hierarchy of the objectives. It offers a solution having a total profit nearly equal to the one obtained in the leader’s model. On the other hand, FGP requires raw material use as much as the follower’s model.

5 Conclusion In this study, we investigate the suitability and efficiency of some fuzzy solution approaches such as FPA and FGP for a BLP problem. The approaches are selected as an alternative to the KKT approach. As we mentioned previously, the transformation of bilevel models to single objective models with the KKT approach increases the size of the problem. In spite, computational results show that KKT performs better. Although using FGP and FPA is better in terms of the size of the model, these approaches do not outperform KKT in our case. This is most probably due to the fact that these approaches underestimate the bilevel structure of the problem. In this sense, we believe that further studies are needed to develop fuzzy solution approaches that handle bilevel models better. Acknowledgments. This study is supported by the Scientific and Technological Research Council of Turkey (TUB˙ITAK) under 1001 Grants with Project Number: 122M223.

References 1. Dempe, S.: Bilevel Optimization: Theory, Algorithms and Applications. Springer (2018) 2. Caramia, M., Dell’Olmo, P.: Multi-objective optimization. In: Multi-Objective Management in Freight Logistics. Increasing Capacity, Service Level, Sustainability, and Safety with Optimization Algorithms, pp. 21–51. Springer, Cham (2020). https://doi.org/10.1007/978-3-03050812-8_2 3. Zhang, D., Lin, GH.: Bilevel direct search method for leader–follower problems and application in health insurance. Comput. Oper. Res. 41, 359–373 (2014). https://doi.org/10.1016/ j.cor.2012.12.005 4. Angulo, E., Castillo, E., García-Ródenas, R., Sánchez-Vizcaíno, J.: A continuous bi-level model for the expansion of highway networks. Comput. Oper. Res. 41, 262–276 (2014). https://doi.org/10.1016/j.cor.2013.02.022 5. Lachhwani, K., Dwivedi, A.: Bi-level and multi-level programming problems: taxonomy of literature review and research issues. Arch. Comput. Method E. 25(4), 847–877 (2018). https://doi.org/10.1007/s118311-017-9216-5 6. Bard, J.F.: Practical Bilevel Optimization: Algorithms and Applications, vol. 30. SSBM (2013) 7. Bialas, W.F., Karwan, M.H.: Multilevel linear programming. Technical report no. 78-1, May 1978 8. Lai, Y.J.: Hierarchical optimization: a satisfactory solution. Fuzzy Set Syst. 77(3), 321–335 (1996)

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9. Shih, H.S., Lai, Y.J., Lee, E.S.: Fuzzy approach for multi-level programming problems. Comput. Oper. Res. 23(1), 73–91 (1996). https://doi.org/10.1016/0165-0114(95)000860 10. Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Set Syst. 89(2), 215–222 (1997). https://doi.org/10.1016/S0165-0114(96)00100-5 11. Baky, I.A.: Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Appl. Math. Model 34(9), 2377–2387 (2010). https://doi.org/ 10.1016/j.apm.2009.11.004 12. Pramanik, S., Roy, T.K.: Fuzzy goal programming approach to multilevel programming problems. Eur. J. Oper. Res. 176(2), 1151–1166 (2007). https://doi.org/10.1016/j.ejor.2005. 08.024 13. Moitra, B.N., Pal, B.B.: A fuzzy goal programming approach for solving bilevel programming problems. In: Pal, N.R., Sugeno, M. (eds.) Advances in Soft Computing — AFSS 2002. LNCS (LNAI), vol. 2275, pp. 91–98. Springer, Heidelberg (2002). https://doi.org/10.1007/3-54045631-7_13 14. Haeri, A., Hosseini-Motlagh, S.M., Samani, M.R.G., Rezaei, M.: A bi-level programming approach for improving relief logistics operations: a real case in Kermanshah earthquake. Comput. Ind. Eng. 145, 106532 ( 2020). https://doi.org/10.1016/j.cie.2020.106532 15. Ye¸silkaya, M., Da¸s, G.S., Türker, A.K.: A multi-objective multi-period mathematical model for an industrial symbiosis network based on the forest products industry. Comput. Ind. Eng. 150, 106883 (2020). https://doi.org/10.1016/j.cie.2020.106883 16. Da¸s, G.S., Ye¸silkaya, M., Altinkaynak, B., Birgoren, B.: Modeling an industrial symbiosis network using bilevel programming. In: 62nd International Scientific Conference on Information Technology and Management Science of Riga Technical University, pp. 1–6. IEEE Press, New York (2021). https://doi.org/10.1109/ITMS52826.2021.9615312 17. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Set Syst. 1(1), 45–55 (1978). https://doi.org/10.1016/0165-0114(78)900 31-3 18. Zimmermann, H.J.: Fuzzy mathematical programming. Comput. Oper. Res. 10(4), 291–298 (1983). https://doi.org/10.1016/0305-0548(83)90004-7

Decision Making on Students’ Performance Estimation J. M. Babanli(B) Azerbaijan State Oil and Industry University, Azadlig Avenue, 20, Baku AZ1010, Azerbaijan [email protected]

Abstract. A frequent problem in the awarding of scholarships is the identification and proper selection of students who are eligible for scholarships due to the limited quota. In the process of determining scholarship, we use the criteria which evaluated subjectively and some students who have the ability or value that is not so different. In this case, the application of fuzzy logic theory is an effective tool. Thus, fuzzy logic allows to describe the knowledge of experts. This paper devoted to the usage of fuzzy logic on scholarship evaluation. For this purpose, student evaluations of 4 experts on 5 criteria are used and the fuzzy approach is applied proposed by author. The basic of represented method is Zadeh’s fuzzy set theory for aggregation of properties. The objective of this study is to detect the chances of students to get a scholarship and to rank the students according to the evaluation of 5 criteria. Keywords: Fuzzy number · Scholarship · Fuzzy logic · Aggregation · Zadeh’s concept

1 Introduction Scholarships are a supporting factor for students. A scholarship is a form of financial aid given to students. Each educational institution, especially universities, offers many scholarships to students. These scholarships are provided by the government or the private sector in partnership with the university. Evaluation of students eligible for scholarships is based on predetermined criteria. These criteria may be different for each university. In recent years, there are several works related to this problem in the latest literature. Consider such scientific research. [1] is offered by DSS to determine the scholarship. Applying fuzzy logic [2] to this decision support system can determine who gets the scholarship. This system uses the Tsukamoto Fuzzy Logic method with pre-defined criteria, namely: overall grade point average (GPA), distance from the student’s home to campus, and the economic status of the student’s family. Paper [3] is devoted to An Evaluative Study of an Education Scholarship Program BM (BidikMisi) for Students in Indonesia. The method applied in this work is based on the Discrepancy Evaluation Model (DEM). Evaluation of data subjectivity in this study is based on university internal rules. The outcome of the BM is an impetus to increase the efficiency and competitiveness of Indonesian human resources. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 67–76, 2023. https://doi.org/10.1007/978-3-031-25252-5_14

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The Relationship between Scholarships and Student Success is discussed in [4]. Race, Parental marital status, In-state status, father education level, Mother education level, Log of total institutional aid, Log of total need-based aid, HS GPA, Entrance score, CC GPA criteria and crisp data are used for determining scholarship. The research work [5] is devoted to design an expert system based on fuzzy logic for anticipating students’ academic results for ASUM. Reasoning method based on Fuzzy Inference System and Gaussian membership function is discussed here. All calculations performed by using MATLAB package. Disadvantage of this system is dependence of results performed by membership function, type of aggregation and defuzzification methods. Combination of FCM method and SAW in Scholarship of Decision Support Systems is discussed in [6]. Advantage of offered approach is using Fuzzy logic properties. Brilliant but Needy Students Selection Using Fuzzy Logic is represented in [7]. Given work describes Fuzzy Logic Approach (FLA) for developing an evaluation model for finding intelligent students for scholarships. Grade, Interview Marks, School Type, Financial Status is used by author of paper as the input variable. Implementation of fuzzy logic using Sugeno Method of scholarship determination is discussed in [8]. The method used by the author in this study is a quantitative method because in this study the author relies on numerical calculations that use numbers. The author used observation, interview, and literature in data collection. The aim of the work [9] is to describe a neuro-fuzzy approach to classify students into different groups. SVM, neural network, Naive Bayes, and decision tree approaches methods were used in this study. Above mentioned proves that neuro-fuzzy approach is effective compared to the implemented methods, but there are also shortcomings here. These include the choice of membership function, inference algorithm, and training algorithm, which directly affect the results. Designing Decision Support System for Scholarship Prediction Using Adaptive Neuro Fuzzy Inference System Algorithm is detailed in [10]. The researchers created a DSS for predicting scholarship recipients and implemented an artificial neural network method using the Backpropagation method. Based on the results of the research, the design of the decision support system was successfully implemented. However, there are problems waiting to be solved here as mentioned above. In [11–18] is proved that under such conditions, approximate reasoning methodbased approach is effective tool. In this study we analyze the problem a decision making on students’ performance estimation. The rest of the work contains 5 parts. Section 2 gives information about preliminaries. The statement of problem is described in Sect. 3. The basic steps of used approach is represented on the next Section. Last part of the paper demonstrates examples of usage of methods for scholarship issue.

2 Preliminaries Group Decision Making Method suggested by J.Babanli [12]. This method contains given steps:

Decision Making on Students’ Performance Estimation

1. 2. 3. 4. 5. 6.

69

Creating team of the experts which evaluate criteria on alternatives. Evaluation of the alternatives by experts on criteria vector F = (f1 , . . . , fn ), Aggregation of alternative vectors. Calculation the arithmetic mean ϕl (ai ), l ∈ {1, . . . , L} for every importance group Calculation weighted average of values ϕl (ai ).   2 +agg3 − Ranking of the alternatives using distance d (Agg, Q) =  agg1 +4∗agg 6  q1 +4∗q2 +q3  , d- distance between two fuzzy numbers- Q and Agg(ai ). Here Q the 6 highest linguistic term of the scale of estimation.

Definition 1. Aggregation of fuzzy numbers [12]. Let C1 , . . . , Cm be fuzzy numbers. An arithmetic mean-based aggregation of fuzzy numbers, C is defined as follows: m Ci C = i=1 , m Definition 2. Distance between triangular fuzzy numbers [12] Let C1 = (c11 , c12 , c13 ), C2 = (c21 , c22 , c23 ) be two triangular fuzzy numbers. A distance between C1 and C2 is defined as d (C1 , C2 ) = |P(C1 ) − P(C2 )|, where P(C1 ) =

c11 + 4c12 + c13 c21 + 4c22 + c23 , P(C2 ) = . 6 6

3 Statement of the Problem Aim of this study is to solve scholarship problem by using Fuzzy logic-based approach. This multi attribute decision making problem consist of n alternatives A = {a1 , . . . , am } and n criteria F = (f1 , . . . , fn ). Decision making matrix is given in Table 1. Outcomes on the table according to criteria is determining by expert team. Table 1. Preference values of alternatives f1

…

fj

…

fn

…

k f1n

…

f1jk fijk

…

ai

k f11 f1ik

…

fink

…

…

…

…

…

…

am

k fm1

…

k fmj

…

k fmn

a1

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Here, fijk - is the evaluation of k-th expert for i-th alternative and j-th criterion. Criteria are sorted by importance degree and for defining best alternative ranking evaluation is used. So, a* is the best or optimal alternative is found as follow   Agg a∗ = max Agg(a), a∈A

Here Agg(a∗ ) is an aggregated index of the alternatives.

4 Application Numerical example for the discussed problem has 5 alternative-a1, a2, a3, a4, a5 and 5 criteria-f1 - Knowledge Level, f2 -Scientific-experience Knowledge, f3 -Mental World view, f4 -Lesson attendance, f5 -Attitude and Behaviour. Described issue was solved by using the method which is already discussed above. There are 4 experts in a group which evaluates all alternatives one by one. Experts’ evaluations are shown in Tables 2, 3, 4, 5, and 6. Table 2. Values on A1 alternative N

Criteria

Expret 1

Expert 2

Experts 3

Expert 4

1

Knowledge level

G

VG

G

G

2

Scientific- experience knowledge

G

G

M

G

3

Metal world view

VG

M

M

G

4

Lesson Attendance

G

G

G

G

5

Attitude and behavior

VG

G

M

VG

Table 3. Values on A2 alternative N

Criteria

Expret 1

Expert 2

Experts 3

Expert 4

1

Knowledge level

VG

G

G

M

2

Scientific- experience knowledge

G

G

M

G

3

Metal world view

VG

M

M

G

4

Lesson Attendance

VG

G

G

G

5

Attitude and behavior

VG

G

M

VG

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71

Table 4. Values on A3 alternative N

Criteria

Expret 1

Expert 2

Experts 3

Expert 4

1

Knowledge level

VG

VG

G

VG

2

Scientific- experience knowledge

G

VG

G

M

3

Metal world view

VG

M

M

G

4

Lesson Attendance

VG

G

G

G

5

Attitude and behavior

VG

VG

M

VG

Table 5. Values on A4 alternative N

Criteria

Expret 1

Expert 2

Experts 3

Expert 4

1

Knowledge level

G

G

G

G

2

Scientific- experience knowledge

G

G

M

G

3

Metal world view

VG

M

G

G

4

Lesson Attendance

M

G

G

G

5

Attitude and behavior

VG

G

M

VG

Table 6. Values on A5 alternative N

Criteria

Expret 1

Expert 2

Experts 3

Expert 4

1

Knowledge level

VG

G

M

M

2

Scientific- experience knowledge

G

G

M

M

3

Metal world view

VG

M

M

M

4

Lesson Attendance

VG

G

G

G

5

Attitude and behavior

VG

G

M

VG

Criteria vector f i of expert group for each ai alternative are calculated using. K 

fi k

f i = K Here f i -ai is found on the basis of overall opinion of the expert group. The estimation of the criteria are represented by fuzzy numbers according to the codebook shown in Fig. 1. k=1

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μf

i

Very low (VL)

1

0

Medium (M)

Low (L)

0.2

0.5

Good (G)

0.75

Very Good (VG)

1

fi

Fig. 1. Representation of the linguistic terms K 

fi k

k

Using math expression f i = K , f i k = 1, . . . , K the vector f i is determined. For instance, the determined values for a1 are: k=1

G + VG + G + G VG + G + M + G = (0.65; 0.85; 1), f2 = = (0.6; 0.8; 0.95) 4 4 VG + VG + G + M G+G+G+G f3 = = (0.65; 0.85; 0.95), f4 = = (0.6; 0.8; 1) 4 4 VG + G + M + M f5 = = (0.55; 0.75; 0.9) 4

f1 =

Obtained values from Table 3: G+G+M +G G+G+M +M = (0.55; 0.75; 0.95), f2 = = (0.5; 0.7; 0.9) 4 4 G + VG + G + M G+G+M +G = (0.6; 0.8; 0.95), f4 = = (0.55; 0.75; 0.95) f3 = 4 4 M +M +G+G = (0.5; 0.7; 0.9) f5 = 4 f1 =

Obtained values from Table 4: VG + M + M + G VG + M + M + G = (0.55; 0.75; 0.9), f2 = = (0.55; 0.75; 0.9) 4 4 VG + M + M + G VG + M + M + G = (0.55; 0.75; 0.9), f4 = = (0.55; 0.75; 0.9) f3 = 4 4 M + M + M + VG = (0.5; 0.7; 0.85) f5 = 4 f1 =

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73

Obtained values from Table 5: G+G+G+G VG + G + G + G = (0.6; 0.8; 1), f2 = = (0.65; 0.85; 1) 4 4 VG + G + G + G M +G+G+G f3 = = (0.65; 0.85; 1), f4 = = (0.55; 0.75; 0.95) 4 4 VG + G + G + G f5 = = (0.65; 0.85; 1) 4 f1 =

Obtained values from Table 6: VG + G + M + VG VG + G + M + VG = (0.65; 0.85; 0.95), f2 = = (0.65; 0.85; 0.95) 4 4 VG + G + M + VG VG + G + M + VG = (0.65; 0.85; 0.95), f4 = = (0.65; 0.85; 0.95) f3 = 4 4 VG + G + M + VG = (0.65; 0.85; 0.95) f5 = 4 f1 =

For alternatives the arithmetic mean for every importance group ϕ1 (ai ), ϕ2 (ai ), ϕ3 (ai ) values are calculated. Importance criteria subgroups are represented in Table 7. Table 7. Importance Criteria Subgroups Importance rates

Criteria

IR1 (High) (0.5 0.55 0.75)

f1 f2

IR2 (Medium) (0.2 0.35 0.45)

F3

IR3 (Low) (0 0.1 0 .25)

F4 f5

So, φ1 (ai ) =

f 1 + f2 f 4 + f5 , φ2 (ai ) = f3 , φ3 (ai ) = . 2 2

Values for a1 as follows: ϕ1 (a1 ) = (0.6; 0.8; 0.975), ϕ2 (a1 ) = (0.55; 0.75; 0.9), ϕ3 (a1 ) = (0.625; 0.825; 0.975) Obtained values for a2: ϕ1 (a2 ) = (0.55; 0.75; 0.925), ϕ2 (a2 ) = (0.55; 0.75; 0.9), ϕ3 (a2 ) = (0.65; 0.85; 0.975)

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Obtained values for a3: ϕ1 (a3 ) = (0.625; 0.825; 0.95), ϕ2 (a3 ) = (0.55; 0.75; 0.9), ϕ3 (a3 ) = (0.65; 0.85; 0.975) Obtained values for a4: ϕ1 (a4 ) = (0.575; 0.775; 0.975), ϕ2 (a4 ) = (0.55; 0.75; 0.9), ϕ3 (a4 ) = (0.6; 0.8; 0.95) Obtained values for a5: ϕ1 (a5 ) = (0.525; 0.725; 0.9), ϕ2 (a5 ) = (0.5; 0.7; 0.85), ϕ3 (a5 ) = (0.65; 0.85; 0.975) The final aggregate grades for first alternative is calculated using Agg(ai ) = IG1 ϕ1 (ai ) + . . . . + IGl ϕl (ai ) + . . . + IGL ϕL (ai ). IGl , i = 1, . . . L for a1: Agg(a1 ) = (0.5; 0.6; 0.7)(0.6; 0.8; 0.975) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.625; 0.825; 0.975) = (0.41; 0.7875; 1.2325) Obtained result for a2 as follows: The values for a2 are shown: Agg(a2 ) = (0.5; 0.6; 0.7)(0.55; 0.75; 0.9) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.65; 0.85; 0.975) = (0.385; 0.76; 1.2025) The values for a3 are shown: Agg(a3 ) = (0.5; 0.6; 0.7)(0.625; 0.75; 0.9) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.65; 0.85; 0.975) = (0.4225; 0.805; 1.22) The values for a4 are shown: Agg(a4 ) = (0.5; 0.6; 0.7)(0.575; 0.775; 0.975) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.6; 0.8; 0.95) = (0.3975; 0.77; 1.2325) The values for a5 are shown: Agg(a5 ) = (0.5; 0.6; 0.7)(0.525; 0.725; 0.9) + (0.2; 0.3; 0.4)(0.5; 0.7; 0.85)+ (0; 0.1; 0.2)(0.65; 0.85; 0.975) = (0.3625; 0.73; 1.165) Distance between aggregation value of the alternatives and very good (VG) are determined as follows according to Definition 2: d (Agg(a1 ), VG) = |0.7600 − 0.9583| = 0.1983, d (Agg(a2 ), VG) = |0.7375 − 0.9583| = 0.2208 d (Agg(a3 ), VG) = |0.8104 − 0.9583| = 0.1479, d (Agg(a4 ), VG) = |0.785 − 0.9583| = 0.1733 d (Agg(a5 ), VG) = |0.7413 − 0.9583| = 0.2170

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The results obtained are given in Table 8: Table 8. The rank of alternatives Alternative

Distance

(a1 )

0.1983

(a2 )

0.2208

(a3 )

0.1479

(a4 )

0.1733

(a5 )

0.2170

Using distance alternatives are ranked as: a3  a4  a1  a5  a2 . In our case 3rd alternative is the best, because the smallest distance is in this alternative.

5 Conclusion To sum up, it is defined that which student can get scholarship by using fuzzy informationbased method. Used method based on Zadeh’s idea. Determining the chances of students to get a scholarship issue contains 5 criteria, that given criteria and obtained results assists to show the relevance of this method. Obtained result describes effectiveness of the used methodology.

References 1. Sukenda, S., Puspitarani, Y., Wibowo, A.P.W., Yustim, B., Sunjana, S.: Fuzzy logic implementation using the Tsukamoto method as a decision support system in scholarship acceptance. Turkish J. Comput. Math. Edu. 12(11), 1411–1417 (2021). https://doi.org/10.48047/rigeo.11. 1.34(3) 2. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, New Jersey, London, Singapore, Hong Kong (2001). https://doi.org/10.1142/4766 3. Aliyyah, R. R., Rosyidi U., Yazid, R.: An Evaluative Study of an Education Scholarship Program (BidikMisi) for Students in Indonesia. 1st International Conference on Advance and Scientific Innovation (ICASI) IOP Conf. Series: J. Physics: Conf. Series 1175 (2019). https:// doi.org/10.1088/1742-6596/1175/1/012171 4. Ganem, N. M., Michelle M.: The Relationship between Scholarships and Student Success: An Art and Design Case Study. Edu. Research Int., 2011, 8 p. (2011). https://doi.org/10.1155/ 2011/743120 5. Goni, I., Gumpy, J.M., Zira, P.B.: Designing a fuzzy rule based system to predict students academic performance in adamawa State University Mubi. Arch. Appl. Sci. Res. 10(2), 28–35 (2018) 6. Trisudarmo, R., Sediyono, E., Suseno, J.E.: Combination of Fuzzy C-Means clustering methods and simple additive weighting in scholarship of decision support systems. Adv. Social Sci., Edu. Humanities Res. 547, 161–169 (2021). https://doi.org/10.2991/assehr.k.210430.025

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7. Aazagreyir, P., Damnyag, J.B.K., Kuuboore, M.: Brilliant but needy students selection using fuzzy logic. Int. J. Comput. Eng. Inform. Tech. 11(8), 178–185 (2019) 8. Sitanggang, B. A., Gunawan, I., Irawan, Parlina, I., Siregar, Z. A., Implementation of fuzzy logic using sugeno method of scholarship determination. J. Artificial Intell. Eng. Appl., 1(2), 135–141 (2022) 9. Do, Q. H., Chen, J.-F..: A Neuro-Fuzzy Approach in the Classification of Students’ Academic Performance. Computational Intell. Neuroscience. 2013, 7 pages. https://doi.org/10.1155/ 2013/179097 10. Pujianto, A., Kusrini, Sunyoto, A.: Designing decision support system for scholarship prediction using adaptive neuro fuzzy inference system algorithm. Conf. Series: J. Physics: Conf. Series 1140 (2018). https://doi.org/10.1088/1742-6596/1140/1/012049 11. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev R., Kacprzyk J., Pedrycz W., Jamshidi M., Sadikoglu F. (eds) ICAFS-2018. Adv. Intel. Syst. Comput., vol. 896, pp. 42–50. Springer, Cham (2018). https://doi.org/10.1007/978-3030-04164-9_10 12. Babanli, J.M.: Fuzzy approach for evaluation of student’s performance. In: 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing, ICAFS-2020. Adv. Intel. Syst. Comput., vol. 1306, pp. 140–147 (2020). https://doi.org/10.1007/978-3= 030-64058-3_18 13. Zadeh, L.A.: A Very Simple Formula for Aggregation and Multicriteria Optimization. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst., 24(6), 961–962 (2016). https://doi.org/10.1142/ S0218488516500446 14. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: ICAFS2020, Adv. Intel. Syst. Comput., 1306, 10-21 (2021). 15. Aliev, R.A., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inform. Sci. 181, 1045–1059 (2011) 16. Mirzakhanov, V.E., Gardashova L.A.: Modification of the Wu-Mendel approach for linguistic summarization using IF-THEN rules. J. Exp. Theoretical Artif. Intell., 77–97 (2019). https:// doi.org/10.1080/0952813X.2018.1518998 17. Adilova, N.E.: Construction of fuzzy control system rule-base with predefined specificity. Adv. Intell. Syst. Comput, vol. 896, pp. 901–904 (2019). Doi:https://doi.org/10.1007/978-3030-04164-9_119 18. Gardashova, L.A., Salmanov, S.: Using Z-number based information in personnel selection problem. Lecture Notes in Networks and Systems, 362, 302–307(2021). https://doi.org/10. 1007/978-3-030-92127-9_42

A Comparative Analysis of the Different CNN Models Using Fuzzy PROMETHEE for Classification of Kidney Stone Fahreddin Sadıko˘glu1,2

, Özlem Sabuncu1(B)

, and Bülent Bilgehan1

1 Department of Electrical and Electronic Engineering, Near East University, Nicosia,

Mersin 10, Turkey {fahreddin.sadikoglu,ozlem.sabuncu,bulent.bilgehan}@neu.edu.tr 2 Odlar Yurdu University, Koroglu Rahimov Street, 13 AZ1072 Baku, Azerbaijan [email protected]

Abstract. A kidney stone is the crystallization of acid salts and minerals in the kidneys. It is a urinary system disease with a rapidly increasing prevalence. Computed tomography (CT) imaging is preferred for imaging kidney stone disease. This study aims to compare the accuracy capabilities of deep learning models in classifying abdominal CT images. In this paper, we examine the use of pre-trained deep learning models to distinguish between patients with and without kidney stones. A dataset of 681 previously not used before images was obtained from the public hospital in Cyprus and used to train and test five pre-trained models. This study also aims to evaluate and compare deep learning models in kidney stone classification using the multi-criteria decision-making technique. The performance of the various deep learning methods is evaluated using the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) test. The test uses a set of very important conditions for assessment with related weights associated with the kidney stone. The overall result reflects the value of each assessment as well as the overall performance of the model. The PROMETHEE test identified the most suitable deep learning method to be the Inception-V3 algorithm. Keywords: Kidney stone · Deep learning · CNN models · Fuzzy PROMETHEE · Medical image

1 Introduction Kidney stone disease is a common health problem worldwide. It is an increased urinary system disease of human health and affects approximately 12% of the world population [1]. It refers to the formation of stones in the collecting ducts of the kidneys or renal tubules. This disease affects kidney function and can obstruct the urinary system [2]. The first step in the detection and management of kidney stone disease is the imaging of the kidneys. Imaging the kidneys, diagnostic and therapeutic data can be obtained [3]. In patients with kidney stones, non-contrast CT is often used to scan the kidneys. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 77–84, 2023. https://doi.org/10.1007/978-3-031-25252-5_15

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Kidney stones have different compositions, absorb a lot of radiation, and can be easily visualized without the need for contrast [4]. Radiologists need to manually scan multiple CT sections to diagnose kidney stone disease. This process is time-consuming. Instead, automatic classifiers have been developed to relieve the work of radiologists. Deep learning (DL) methods have high accuracy potential in medical analysis compared to human experts for disease detection and assessment. DL algorithms are capable of achieving a reproducible result in less time than it takes a person to make an assessment. It also has the potential to evaluate numerous features, including those missed by radiologists [5]. Deep neural networks use tags to extract features from complex data. Convolutional neural networks (CNNs), one of the deep learning algorithms, have a deep architecture and therefore are successful in extracting distinctive features [6]. CNN’s are used in image recognition tasks. They are used for many tasks such as image classification, segmentation, and detection [7]. The paper [8] introduced a hybrid method of computer vision and deep learning algorithm to be effective to detect kidney stones. The task is to enable the automatic prediction of kidney stones. Several other research papers are using different types of deep learning algorithms such as ResNet-101 quoting the prediction success percentage [9]. The researchers moved further ahead to classify the type of kidney stone and also identify the type that can lead to predicting the cause of the kidney stone. It is for this reason that deep learning with higher accuracy should be applied to obtain the initial classification. Therefore, a precise evaluation of the available methods should be undertaken to identify the best-performing algorithm. In this study, five CNN models were used for kidney stone classification using CT images. In this study, CNN models used for the classification of kidney stones are discussed and analyzed. A multi-criteria decision-making method known as Fuzzy PROMETHEE is used for analysis and ranking. The article is organized as follows: Sect. 1 is an introduction to the article. Sect. 2 discusses the dataset, deep learning models, and training for this article, and Fuzzy PROMETHEE used for analysis and comparison of models. Sect. 3 shows the results of multi-criteria decision-making methods. Finally, Sect. 4 describes the conclusion.

2 Materials and Methods 2.1 Dataset Deep networks need a lot of data to provide high performance. In this study, after securing the ethics committee’s approval, a dataset was constructed consisting of 681 abdominal CT images. The abdominal CT images were collected from the Department of Radiology associated with Dr. Burhan Nalbanto˘glu State Hospital. The dataset includes images of two different classes: with a kidney stone and without a kidney stone. These images are labelled separately by the radiologist as images with and without kidney stones to train the network. In the CT scan images of 120 patients, 45 of the images belong to the normal group and 75 belong to the kidney stone patients. The data collected is comprised of 216 kidney stones and 465 non-kidney stone images. Figure 1 shows a sample of kidney stone and non-kidney stone images from the dataset.

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Fig. 1. Dataset description

2.2 Deep Learning Models Deep convolutional neural networks (CNN) are trained on datasets containing many images, such as ImageNet. They have high success in image classification. It is used for medical image classification purposes properly to its high success [10]. The transfer learning technique is used for a pre-trained network using ImageNet [11]. In this study, five different pre-trained CNN models use for kidney stone detection. These are; Inception-V3, NasNet-Mobile, InceptionResNet-V2, Xception, and DenseNet-201. Some parameters of these pre-trained networks are fine-tuned. These networks are trained with our raw CT images for the classification task. During the training, techniques such as rotation and enlargement apply to the images used to prevent the problem of overfitting. Figure 2 illustrates a training process for Xception. The performance of the CNN models was evaluated using the test images. The results are evaluated as true positive (TP), true negative (TN), false positive (FP) and false negative (FN). 2.3 Evaluation Methods The classification evaluation is based on many parameters. These parameters are derived from the training and test results. The true-positive (TP), true-negative (TN), falsepositive (FP), and false-negative (FN) values are subtracted from the test results. These are the parameters used to evaluate test accuracy, sensitivity, and specificity. (1) is used to calculate test accuracy. (2) is used to calculate the sensitivity. (3) shows the specificity calculation. Test Accuracy =

(TP + TN ) (TP + FN + FP + TN )

(1)

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Fig. 2. Training progress Xception

Sensitivity =

TP (TP + FN )

(2)

Specificity =

TN (TN + FP)

(3)

3 Fuzzy-Based MCDM Models The PROMETHEE technique, a multi-criteria decision-making technique, is based on comparing alternatives according to the selected criteria. It is an easier and more efficient method than other techniques. It can be used for real-life decision problems [12]. The paper [13] used the multi-criteria decision-making theory. This study aimed to evaluate and compare the best model for diagnosing a retinal disease. For this purpose, the decision theory they are interested in is Fuzzy PROMETHEE. Many factors affect the cancer treatment process. Therefore, various treatment procedures need to be evaluated. Fuzzy PROMETHEE decision-making theory was used to evaluate the best non-pharmacological treatment option in the paper [14]. These techniques were evaluated and compared according to certain criteria. The paper [15] aims to unravel the complexity of different diagnostic models for COVID19. For this, multi-criteria decision-making (MCDM) methods are used to compare Covid-19 diagnostic models and determine the most effective model. In this work, the fuzzy PROMETHEE method was applied to deep convolutional neural network models. After all the parameters needed for the classification by CNN models were collected, each criterion used a visual PROMETHEE decision lab program. Table 1 shows the parameters and weights of the criteria including the values of the parameters as used for the analysis. The Visual PROMETHEE Decision program was used in this study to rank alternative methods. The data in Table 1 was applied to the Visual PROMETHEE Decision program. The criteria required for the program are entered, and the weights of all criteria were determined. The criteria required for the program were entered based on the data obtained from the training and testing phase of five different CNN models. The weights of all criteria were determined. Preference functions and threshold values were entered for each criterion for analysis.

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Table 1. Fuzzy based visual PROMETHEE application for the classification of CNN models CNN models

SN

SP

Time

TP

FN

FP

TN

NL

Inception-V3

95,34

100,00

96 min 51 s

41

2

0

93

316

InceptionResNet-V2

79,06

88,17

286 min 21 s

34

9

11

82

825

NasNet-Mobile

86,04

95,69

379 min 33 s

37

6

4

89

914

Xception

65,11

68,81

59 min 13 s

28

15

29

64

171

DenseNet-201

67,44

73,11

151 min 52 s

29

14

25

68

709

TA: Test accuracy, SN: Sensitivity, SP: Specificity, TP: True-positive, FN: False-negative, FP: False-positive, TN: True-negative, NL: Number of layers.

4 Results The performance analysis of the different models is examined using the fuzzy PROMETHEE. Positive (Phi+) and negative (Phi−) flow values for PROMETHEE-I partial sequencing results and net (Phi) flow values for PROMETHEE-II were calculated with Visual PROMETHEE software. The Fuzzy-PROMETHEE comparison results of CNN models based on the specified criteria are shown in Table 2. Table 2. Complete Ranking of CNN models used to classify kidney stones. Rank

Phi

Phi+

Phi−

Inception-V3

0,6402

0,7847

0,1445

NasNet-Mobile

0,1711

0,5277

0,3567

InceptionResNet-V2

−0,0445

0,4405

0,4850

Xception

−0,3678

0,2454

0,6132

DenseNet-201

−0,3989

0,2257

0,6246

Table 2 lists the Phi, Phi+ and Phi− values and provides a ranking of the CNN models. The application of PROMETHEE indicates the most suitable model for this application. The positive outranking flow (Phi+) with the highest value shows the model that best fits the selected criteria. According to this, the Inception-V3 model is successful compared with other models. The comparison between the different models has been further evaluated using the action profile matrice generated using the Fuzzy PROMETHEE. The decision-makers relative importance (weights) and information priorities are applied for evaluation. Figures 3–7 shows each CNN model’s positive and negative side for selected nine criteria (accuracy, sensitivity, specificity, time, true positive, false negative, false positive and true negative and the number of layers). According to the action profile matrices, the model with the highest positive value shows the best fitting of the selected nine criteria.

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Fig. 3. Action profile for InceptionResNet-V2 model

Fig. 4. Action profile for Inception-V3 model

Fig. 5. Action profile for NasNet-Mobile model

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Fig. 6. Action profile for Xception model

Fig. 7. Action profile for DenseNet-201 model

Figures 3–7 indicates the performance of each model based on the selected weights. Inception-V3 (Fig. 4) is the most applicable model to identify kidney stones under all conditions.

5 Conclusion In this study, the Fuzzy PROMETHEE technique is used to compare the performance of different CNN models. Multi-criteria decision-making techniques offer sensitive and meaningful solutions to experts at the decision-making stage. The effectiveness of the alternatives was evaluated according to the selected criteria, and the experts determined the corresponding weights. The Visual PROMETHEE software ranking test results indicate the Iınception-V3 model to be the most successful compared with the other models regarding the highest positive flow value (Phi+ = 0,784) and action profile matrices showing the best fitting of selected criteria.

References 1. Alelign, T., Petros, B.: Kidney stone disease: an update on current concepts. Adv. Urol. 2018, 1–12 (2018). https://doi.org/10.1155/2018/3068365 2. Evan, A.P.: Physiopathology and etiology of stone formation in the kidney and the urinary tract. Pediatr. Nephrol. 25(5), 831–841 (2010). https://doi.org/10.1007/s00467-009-1116-y 3. Rao, P.N.: Imaging for kidney stones. World J. Urology 22(5), 323–327 (2004). https://doi. org/10.1007/s00345-004-0413-0 4. Brisbane, W., Bailey, M.R., Sorensen, M.D.: An overview of kidney stone imaging techniques. Nat. Rev. Urol. 13(11), 654 (2016). https://doi.org/10.1038/nrurol.2016.154

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5. Mazurowski, M.A., Buda, M., Saha, A., Bashir, M.R.: Deep learning in radiology: an overview of the concepts and a survey of state of the art with a focus on MRI. J. Magn. Reson. Imaging 49(4), 939–954 (2019). https://doi.org/10.1002/jmri.26534 6. Tajbakhsh, N., et al.: Convolutional neural networks for medical image analysis: full training or fine-tuning. IEEE Trans. Med. Imaging 35(5), 1299–1312 (2016). https://doi.org/10.1109/ TMI.2016.2535302 7. Ker, J., Wang, L., Rao, J., Lim, T.: Deep learning applications in medical image analysis. IEEE Access 6, 9375–9389 (2017). https://doi.org/10.1109/ACCESS.2017.2788044 8. Black, K.M., Law, H., Aldoukhi, A., Deng, J., Ghani, K.R.: Deep learning computer vision algorithm for detecting kidney stone composition. BJU Int. 125(6), 920–924 (2020). https:// doi.org/10.1111/bju.15035 9. Lopez, F., et al.: Assessing deep learning methods for the identification of kidney stones in endoscopic images. In: 43rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 2778–2781 (2021). https://doi.org/10.1109/EMBC46164. 2021.9630211 10. Sabuncu, Ö., Bilgehan, B.: Performance evaluation for various deep learning (DL) methods applied to kidney stone diseases. In: 2021 Int. Conf. Forthcoming Networks Sustainability in AIoT Era (FoNeS-AIoT) IEEE, pp. 1–3 (2021). https://doi.org/10.1109/FoNeS-AIoT54873. 2021.00010 11. Dodge, S., Karam, L.: Human and DNN classification performance on images with quality distortions. ACM Trans. Appl. Percept. 16(2), 1–17 (2019). https://doi.org/10.1145/3306241 12. Brans, J.-P., De Smet, Y.: PROMETHEE methods. In: Greco, S., Ehrgott, M., Figueira, J.R. (eds.) Multiple Criteria Decision Analysis. ISORMS, vol. 233, pp. 187–219. Springer, New York (2016). https://doi.org/10.1007/978-1-4939-3094-4_6 13. Saleh, N., Salaheldin, A.M.: A benchmarking platform for selecting optimal retinal diseases diagnosis model based on a multi-criteria decision-making approach. J. Chin. Inst. Eng. 45(1), 27–34 (2022). https://doi.org/10.1080/02533839.2021.1983466 14. Batur Sir, G.D.: Evaluating treatment modalities in chronic pain treatment by the multi-criteria decision-making procedure. BMC Med. Inform. Decis. Mak. 19(1), 1–9 (2019). https://doi. org/10.1186/s12911-019-0925-6 15. Mohammed, M.A., et al.: Benchmarking methodology for selection of optimal COVID-19 diagnostic model based on entropy and TOPSIS methods. IEEE Access 8, 99115–99131 (2020). https://doi.org/10.1109/ACCESS.2020.2995597

Developing Efficient Frontier for Investment Portfolio: A Fuzzy Model Approach Leyla R. Hasanova(B) Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]

Abstract. Investment in financial securities is a compound process involving decision concerning possible expected rates of return and risk. As a rule, decision maker often deals with insufficient data while selecting investment portfolio, due to uncertain business environment. Markowitz’s portfolio theory is a methodology in financial world that aims to maximize investment portfolio expected return for a given level of risk or minimize the risk of investment for a certain level of expected return. The classic mean-variance approach to portfolio selection is performed in this paper under the assumption that the returns and risk of financial securities are fuzzy values, which can successfully integrate the experts’ knowledge and the managers’ subjective opinion. The real financial world is very sensitive and influenced by changes in political-economic environment. Therefore, classical approach based only on historical data may lead to inaccurate results. The methodology performed in this paper considers fuzzy environment which contributes to actuality of this study. The aim of this paper is to develop fuzzy efficient frontier for portfolio consisting of eight assets. Modeling of sample investment portfolio is provided by using statistical data provided by Yahoo Finance web-platform and expert opinion. The software based on C# programming language is developed for determining efficient portfolios and constructing fuzzy efficient frontier. Obtained results of this study completely elucidate the efficiency of the proposed approach. Keywords: Mean-variance model · Fuzzy sets · Portfolio selection · Efficient frontier

1 Introduction The formation of an investment portfolio [1] is a process of making decision associated with the distribution of funds between several assets with the objective to obtain financial returns in condition of risk and uncertainty. The classic mean-variance approach to portfolio selection problem, introduced initially by Markowitz [2], has played a key role in the formation and development of modern portfolio theory. The goal of Markowitz theory is maximizing return of portfolio while simultaneously minimizing risk of investments. This method also explained the process of maximization the expected rate of return and minimization the risk of investment through proper diversification. Therefore, an optimal combination of the assets in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 85–93, 2023. https://doi.org/10.1007/978-3-031-25252-5_16

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portfolio for maximizing the expected rate of return should be selected by investors. A key factor in this process is the correlation between the returns of securities as well as the weights of securities in the portfolio. Thus, at the same correlation coefficients between securities’ returns, alternative portfolios correspond to different values of risk (standard deviation), due to various weights of assets [3, 4]. The fundamental assumption of Markowitz’s mean-variance model says that the environment of financial markets in future can be accurately predicted based on asset’s historical data, namely, the mean and covariance of financial securities in future is resembling to the past one. [5]. It is hardly possible to assure this kind of assumption for contemporary ever-changing asset markets in real life. In addition, to statistical data, there are several factors which may have influence on future expected returns of stocks, such as economical and financial behaviors of the enterprises, their business development strategies, etc. This is ignored in classical approach. Using fuzzy models permits remove demerits and allows the incorporation of the expert knowledge. Several researchers have paid special attention to the formation of fuzzy portfolio. In paper [6] author suggested a fuzzy portfolio model for defining efficient portfolios in the context of behavioral analysis. Researcher developed a fuzzy portfolio model with the focus on various investor risk attitudes. Author demonstrated numerical example of a portfolio selection problem to address the issue presented by a diversity of investor risk attitudes. The study [7] perform the fuzzy portfolio optimization problem with the asset returns are performed in the shape of fuzzy numbers. A mean-absolute deviation risk function model and Zadeh’s extension principle are employed for solving portfolio optimization problem with fuzzy returns. Membership functions for return and risk were represented. In paper [8] authors use developed fuzzy portfolio model by applying Genetic Algorithm (GA) to define optimal values of risky assets. The effectiveness of proposed method is represented with numerical examples. As it was mentioned above, the aim of an investor is to compose a portfolio that provides maximum return with minimum acceptable risk. This process involves two important components: return and risk. Following portfolio theory, we use the term efficient frontier, which is a set of efficient portfolios, having the minimum risk measured with standard deviation for any given expected return. [9] Each point on the frontier represents a portfolio of investment assets. Usually, the portfolios that comprise the efficient frontier are the most diversified ones. Having given the risk attitude of the investor, the optimal portfolio is defined by selecting the mean and standard deviation on the frontier that together represent the most desirable utility and then pursue the weights of the assets in that portfolio. This paper studies the problem of constructing an efficient frontier by determining a set of efficient investment portfolios based on optimization model with the use of fuzzy numbers. For this purpose, software based on C# programming language has been developed. In this paper historical data for 8 stocks obtained on Yahoo Finance platform was used. The study framework involved several steps: a. Considering historical data for stock returns, financial reports of companies the expected quarterly returns are defined by experts in the shape of fuzzy numbers for each security;

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b. On the base of previous information, the average annual return and risk are calculated for each asset, covariance matrix is created. c. Two bounds of efficient frontier are determined: portfolio with the lowest risk and portfolio with the highest expected return based on optimization model d. Employed software allows to minimize the risk and maximize returns for these portfolios simultaneously. e. Additional efficient portfolios with the best risk-returns characteristics are defined and efficient frontier is developed.

2 Preliminaries Definition 1. Arithmetic Operations on Fuzzy Numbers [9–16] Arithmetic operations on fuzzy numbers such as addition (1), subtraction (2), multiplication (3) and division (4) are performed below: Suppose A and B are two fuzzy numbers and Aα and Bα their α-cuts     Aα = a1α , a2α ; Bα = bα1 , bα2 (1) Then we can write Aα + Bα = [aα1 , aα2 ] + [bα1 , bα2 ] = [aα1 + bα1 , aα2 + bα2 ]

(1)

Aα = {x/μA (x) ≥ a}; Ba = {x/μB (x) ≥ a} (A − B)α = Aα − Bα = [aα1 − bα2 , aα2 − bα1 ], ∀α ∈ [0, 1]

(2)

(A · B)α = Aα · Bα = [aα1 , aα2 ] · [bα1 , bα2 ] ∀α ∈ [0, 1]

(3)

Aα : Bα = [aα1 , aα2 ] : [bα1 , bα2 ] ∀α ∈ [0, 1]

(4)

where

Definition 2. Fuzzy Minimum and Maximum of Fuzzy Numbers [10, 11]. The set R of real numbers has linear order. For ∀x, y ∈ R the pair (R, ≤) as mentioned above is a lattice. It worth noting, that fuzzy numbers are not structured in linear order; they may be ordered fractionally. It is essential to extend the lattice operation max and min to fuzzy minimum m˜in and fuzzy maximum m˜ax while ordering of fuzzy numbers. Take into consideration two fuzzy numbers A, B ⊂ R. Fuzzy minimum and fuzzy maximum we may define as: m˜in(A, B)(z) =

sup

min[A(x), B(y)]

(5)

min[A(x), B(y)]

(6)

z=min(x,y)

m˜ax(A, B)(z) =

sup z=max(x,y)

By using α-cuts we define ∀α ∈ [0, 1] m˜in(Aα , Bα ) = [min(aα1 , bα1 ), min(aα2 , bα2 )]

(7)

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m˜ax(Aα , Bα ) = [max(aα1 , bα1 ), max(aα2 , bα2 )]

(8)

Definition 3. Absolute Value of Fuzzy Number [9, 10] Absolute value of fuzzy number is identified as:  max(A, −A), for R+ abs(A) = 0, for R− Definition 4. Mean –Variance Model. The Mean-variance model [3] evaluates the investment portfolio return and risk by defining mean and standard deviation of return distribution. Let n be the set of financial securities considering for investment and Rt = (r1t , r2t , r3t , …, rnt ) are their returns at the t th scenario, t = 1,…, T. An investment portfolio x = (w1 , …, wn ) ∈ X ⊆ Rn , relates to the vector of proportions of the incipient budget to be allocated in each  security, suppose X is a number of reasonable portfolios, given by, X = {(w1 , …, wn ) | ni=1 wi = 1, wi ≥ 0, i = 1,…, n}. Here, ni=1 wi = 1 is a normalized budget constraint. To estimate the return of investment portfolio x, we use the following formula: n E(x) = r˜i wi (9) t=1

The variance of investment portfolio returns R(x) is defined such as: n n σ2 = σik wi wk i=1

k=1

(10)

where σik is the covariance between returns of ith and k th assets Definition 6. Efficient Frontier. The efficient frontier is referred as the set of efficient portfolios that provide the maximum expected return for a certain degree of risk or the minimum risk for a specified degree of expected return. Portfolios that located under the efficient frontier are inefficient as they do not offer sufficient return for the given level of risk. Investment portfolios which congregate to the right of the efficient frontier are inefficient because they have relatively high level of risk for the specified rate of return.

3 Problem Definition and Solution Method Assume that eight securities Si (i = 1, 2, . . . , 8) are viewed by an investor to select the superior portfolio that will give the optimal allocation of resources among these securities. The success of the proposed strategy of investor is measured by higher returns and lower risk. Securities issued by following companies have been randomly chosen: Apple Inc., Pfizer Inc., Netflix Inc., Coca Cola Company, Tesla Inc., Unilever Plc., Micron Technology Inc., Moderna Inc. In order to construct efficient frontier, two bounds have to be determined: 1) investment portfolio with the lowest risk and appropriate return. and 2) investment portfolio with the highest return and relevant risk. Variations within these bounds shape the efficient frontier of portfolios. To determine the abovementioned bounds for risk and return, an investor must settle the optimization problems below: n n σik wi wk (11) min DP = i=1

k=1

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subject to w ∈ W;

n i=1

wi = 1; wi ≥ 0; , i = 1, 2, . . . ., n

where, DP -is the variance of portfolio σik -is the covariance between securities i and k wi -is the weight of ith security wk -is the weight of k th security  σp = DP

(12)

where, σp - is a standard deviation of portfolio max Rp =

n t=1

r˜i wi

(13)

subject to w ∈ W w ∈ W;

n i=1

wi = 1; wi ≥ 0; , i = 1, 2, . . . ., n

where Let (w1 , . . . , wn ) be an optimal value of risk obtained in Problem 11, 12 with opti ) be an optimal result of (13) with optimal value of return mal σp and (w1 . . . , wn1   return and risk of portfolios range in the intervals [ nt=1 r i xi ; nt=1 r i xi ] and R p . The   [ ni=1 nk=1 σik xi xk ; ni=1 nk=1 σik xi xk ] respectively. At the next step we select 4 values of return within this interval and based on optimization model the minimum risk for chosen expected return values is defined. Obtained results allow us to construct efficient frontier on the graph with the Risk on horizontal axis and Expected return on vertical axis. The analysis conducted based on dataset of securities for the period February 1, 2021, to January 30, 2022 was taken from Yahoo finance website. The data consisting of the monthly closing prices of abovementioned eight securities have been used. The v −vit ∗ 100%, t = 1, 2, …, monthly return of the ith security is calculated by rit = i(t+1) vit th 12, where vi(t+1) and vit are the closing prices of i security in months t + 1 and t, respectively. The Table 1 performs the monthly returns of securities: Table 1. Monthly returns of stocks

M1 M2

0.009 0.076

0.082 0.067

-0.032 -0.016

0.076 0.033

-0.011 0.062

0.083 0.052

-0.036 -0.024

M12

-0.0075

-0.007

0.023

0.001

-0.015

0.079

-0.022

…………………………….

0.154 0.366 -0.055

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In order to facilitate further calculations quarterly returns will be considered for each security. Expert opinion based on comprehensive analysis of historical data and financial reports of the enterprises is used to define quarterly returns for each security in the shape of fuzzy numbers. The expected quarterly returns are evaluated as performed in Table 2: Table 2. Expected quarterly returns of securities Quarter 1 Quarter 2 Quarter 3 Quarter 4 (0.010,0.011,0.012) (0.066,0.069,0.072) (0.030,0.0318,0.033) (0.0078,0.008,0.009) (0.048,0.050,0.053) (0.063,0.067,0.070) (0.057,0.060,0.063) (0.0057,0.0059,0.006) …………… (0.078,0.082,0.086) (0.266,0.280,0.294) (-0.019,-0.020,-0.021) (-0.190,-0.199,-0.210)

Based on expected quarterly returns covariance matrix has been created (Table 3), expected average annual returns and variance have been defined (Table 4). Table 3. Covariance Matrix 0.001 0.000 0.001 0.000 ………………………… 0.003 0.004 0.006 -0.002

0.001

0.000

0.000

0.003

0.003

-0.001

-0.005

0.030

Table 4. Average annual returns and variance of securities Stock

Average annual return

Variance

S1

(0.0285, 0.03, 0.0315)

(0.00046, 0.00059, 0.000740)

S2

(0.0433, 0.0456, 0.0479)

(0.00042, 0.00056, 0.00074)

S3

(−0.0018, 0.0004, 0.0026)

(0.00172, 0.00210, 0.00252)

S4

(0.0017, 0.0021, 0.0025)

(0.00069, 0.00086, 0.00105)

S5

(0.0383, 0.0419, 0.0455)

(0.00583, 0.00700, 0.00829)

S6

(0.0005, 0.0018, 0.0031)

(0.00081, 0.00097, 0.00114)

S7

(0.0005, 0.0024, 0.0042)

(0.00122, 0.00149, 0.00179)

S8

(0.0283, 0.0356, 0.0429)

(0.02521, 0.03010, 0.03546)

Considering abovementioned data two bounds of efficient frontier (12,13) and then interim efficient portfolios are defined. Return and risk (Standard Deviation) for each case are represented in Table 5. The portion of investment in each security for relevant portfolio is demonstrated in Table 6. Based on data represented in Table 5 Fuzzy Efficient frontier has been constructed with the expected return on vertical axis and risk on horizontal axis. (see Fig. 1).

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Table 5. A set of efficient portfolios Efficient portfolios

Return

RISK (%)

I

(0.0151, 0.0166, 0.0182)

(0.000, 0.1324, 1.2862)

II

(0.0200, 0.0216, 0.0233)

(0.000, 0.1976, 1.3202)

III

(0.0260, 0.0278, 0.0296)

(0.000, 0.2133, 1.3712)

IV

(0.0325, 0.0345, 0.0365)

(0.000, 0.6760, 1.5357)

V

(0.0400,0.0422,0.0444)

(1.1762, 1.7022, 2.1701)

VI

(0.0433,0.0456,0.0479)

(2.0525, 2.3614, 2.7164)

Table 6. Portion of investment in each stock for a set of efficient portfolios Efficient portfolios

Weights of stocks in portfolio (%) S1

S2

S3

I

44.928

0.000

0.000

II

36.701

11.203

0.000

III

21.961

28.909

0.000

IV

0.400

57.685

V

0.000

84.948

VI

0.000

100

S4

S5

S6

S7

S8

9.947

0.000

26.144

18.981

0.000

21.492

0.000

13.849

16.754

0.000

33.780

0.000

0.470

14.880

0.000

0.000

34.782

0.000

0.000

7.133

0.000

0.000

15.052

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.000

Fig. 1. Fuzzy efficient frontier

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4 Conclusion The primary purpose of this research is to design fuzzy efficient frontier for investment portfolio. Originally, some important concepts and definitions were covered. The real statistical data and experts’ opinion were employed to illustrate methodology. Every point on the developed fuzzy efficient frontier performs an optimal combination of financial securities that provide the highest rate of return for any given level of risk. The proposed methodology allows investors to derive a set of efficient portfolio considering fuzzy environment and make a decision depending on their risk preferences. Further study of this issue can be extended to the developing the efficient frontier by using Z numbers theory.

References 1. Bakar, N.A., Rosbi, S.: Efficient frontier analysis for portfolio investment in Malaysia stock market. Sci. Int., Lahore 30(5), 723–729 (2018) 2. Markowitz, H.: Portfolio Selection: Efficient Diversification of Investments. John Wiley Sons, New York (1959). https://doi.org/10.2307/2975974 3. Hasanova, L.: Portfolio selection model using z-numbers theory. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 308–315. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_43 4. Park, S., Lee, S.: Linear programing models for portfolio optimization using a benchmark. Eur. J. Finance 25(2), 1–23 (2018). https://doi.org/10.1080/1351847x.2018.1536070 5. Zhang, W.-G., Wang, Y.-L., Chen, Z.-P., Nie, Z.-K.: Possibilistic mean–variance models and efficient frontiers for portfolio selection problem. Inf. Sci. 177(13), 2787–2801 (2007). https:// doi.org/10.1016/j.ins.2007.01.030 6. Tsaur, R.-C.: Fuzzy portfolio model with different investor risk attitudes. Eur. J. Oper. Res. 227(2), 385–390 (2013). https://doi.org/10.1016/j.ejor.2012.10.036 7. Liu, S.-T.: A fuzzy modeling for fuzzy portfolio optimization. Expert Syst. Appl. 38, 13803– 13809 (2011) 8. Abiyev, R.H., Menekay, M.: Fuzzy portfolio selection using genetic algorithm. Soft Comput. 11, 1157–1163 (2007). https://doi.org/10.1007/s00500-007-0157-z 9. Aliev, R.A., Aliev, R.R.: Soft Computing and its Applications. World Scientific (2001). https:// doi.org/10.1142/4766 10. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I and Part II. World Scientific (2018). https://doi.org/10.1142/10936 11. Aliev, R.A., Pedrycz, W., Huseynov, O.H., Kreinovich, V.: The general theory of decisions. Inform. Sci. 327, 125–148 (2016). https://doi.org/10.1016/j.ins.2015.07.055 12. Aliev, R.A., Huseynov, O.H.: Decision Theory with Imperfect Information, p. 444. World Scientific, Singapoure (2014) https://www.worldscientific.com/worldscibooks/10.1142/9186 13. Gardashova, L.A.: Application of operational approaches to solving decision making problem using Z-numbers. J. Appl. Math. 5(9), 1323–1334 (2014). https://doi.org/10.4236/am.2014. 59125 14. Aliev, R.A., Pedrycz, W., Alizadeh, A.V., Huseynov, O.H.: Fuzzy optimality based decision making under imperfect information without utility. Fuzzy Optimization and Decision Making, Springer, Germany. 12(4), 357–372, (2013) https://link.springer.com/article/10.1007/s10 700-013-9160-2

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15. Alizadeh, A.V.: Application of the fuzzy optimality concept to decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 542–549. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_69 16. Aliyeva, K.R.: Demand forecasting for manufacturing under Z information. Procedia Comput. Sci. 120, 509–514 (2017). https://doi.org/10.1016/j.procs.2017.11.272

Impact of Online Education Classes on Students’ Satisfaction: The Case of Near East University Saide Sadıko˘glu , Sahin ¸ Akda˘g(B)

, and Murat Tezer

Near East University, Nicosia, Northern Cyprus {saide.sadikoglu,sahin.akdag,murat.tezer}@neu.edu.tr

Abstract. In this study, it is aimed to reveal student satisfaction regarding the use of distance education in classes of asynchronous joint courses at Near East University, and the opinions of the students, who are the end users, about these processes. The research method was determined as a mixed research method. In the research, both quantitative and qualitative methods were used together. The population of the research consists of 120 students of the Faculty of Tourism who take their common courses at the university through distance education. A questionnaire consisting of 20 items was used to collect the data. According to the results of the research, it was seen that the satisfaction of the students with the use of distance education in the courses was good. In general, the students stated that they did not encounter any problems in taking the courses online or face-to-face and that they did not experience any difference. Students have a positive attitude towards distance education. They also stated that they had the advantage of better learning by watching the missed lessons many times later. Apart from this advantage, students also stated that they do not have to pay for travel, accommodation, and other expenses for distance education. Keywords: Distance education · Asynchronous · Joint distance courses · Satisfaction · Attitude

1 Introduction With the rapid developments in technology have also been reflected in the education sector and have revealed the necessity of restructuring education systems. One of the education systems that emerged from this point of view is distance education. Distance education, which started by mail in 1728, has progressed with technology until today [1]. Distance learning is a discipline that teaches, learns, and tries to eliminate the limitations of learning resources and the problems created by these limitations while using existing technologies [2]. Distance Education is the realization of education when students and teachers are separated in terms of time and space When we look at the common features of the definitions, distance education; It is a system that takes advantage of the technology at the highest level and eliminates the elements of space and time between the educator and the trained, by following an effective way in reaching information sources and transporting students [3]. Dixon and Pelliccione [4] stated that it is possible to support © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 94–100, 2023. https://doi.org/10.1007/978-3-031-25252-5_17

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knowledge sharing and thus social communities through remote online communications between students from different countries. Distance education provides many benefits such as sustainability, flexibility in the learning process, time-saving, opportunity to continue working [5], equal opportunity, individualization of learning, global learning environments, receiving training on new subjects, benefiting from new technologies and methods [6]. In the epidemic process, not only primary, high school, and university students but also distance education is affected. As it is known, the Covid-19 epidemic, which affected the whole world, affected all the lives of people, and required certain changes. These changes have affected people’s entire lives, both personal and professional. Education The process of education has undoubtedly been affected by these changes and institutions have begun to give more importance to distance education methods and technologies. In this study, it is aimed to reveal student satisfaction regarding the use of distance education in classes of asynchronous joint courses at Near East University, and the opinions of the students, who are the end users, about these processes.

2 Research Method Mixed method research was preferred in the study. Mixed method research emerges as a research method in which practitioners gather and combine quantitative and qualitative data around the same subject to achieve better in subjects such as verification, logical testing, detail and research breadth, and interpretation [7]. While the survey method was used as a quantitative research method in the research, the interview was used as one of the qualitative research methods. At the same time, the mixed method is a method that increases the efficiency rate because it makes the result more valuable by evaluating multiple dimensions of perception together, making the findings more verifiable by examining from different perspectives, being more suitable for discussion and dialogue, and enabling to use qualitative and quantitative methods [7]. 2.1 Participants The participants of this research consist of 120 undergraduate students studying at the Near East University School of Tourism and Hotel Management in the spring semester of 2021–2022. The participants of the research consist of two parts. For the application of the questionnaire in the quantitative research department, 100 students who took their courses in the form of distance education within the high school were formed. In the qualitative research department, 20 students who were chosen on a voluntary basis among the students who took these courses and used the distance education system (UZEM) were determined to get user opinions. Moodle learning management system is used as the learning management system in the courses. When students click on https:// uzem.neu.edu.tr/, the login screen appears. They can log in by typing their username and password on the screen.

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2.2 Data Collection Tools In the collection of quantitative data, the questionnaire form “Satisfaction Questionnaire for Use of Distance Education in Common Courses” developed was used in [8]. The questionnaire was in a 5-point Likert type (From 1: Absolutely Disagree to 5: Absolutely Agree) and consisted of 20 items in total. Some sub-research topics were included in the survey questions; these are “1-Satisfaction with the course content”, “2. System and interface competence”, “3. Opinions about the instructors”, “4. Satisfaction and suitability of exams”, “5. Technical and institutional functioning”. Three field experts were consulted on the applicability of the questionnaire in universities in Northern Cyprus and face validity was ensured. For the reliability study of the questionnaire, the Cronbach alpha test was applied to the data obtained for 20 items in the SPSS 24 program. The Cronbach alpha coefficient was found to be 0.84 and the questionnaire was found to be reliable. In the qualitative part of the study, an unstructured interview form consisting of 2 open-ended questions for students and developed by taking the opinions of researchers and experts was used. Question 1. Do you think it is an advantage to take courses with distance education? Question 2. Do you plan to take the courses you will take in the future with distance education again? 2.3 Data Analysis Because of the Covid-19 Pandemic, the questionnaire and interview form were written in Google Forms. Students were asked to access this form and fill out the questionnaire form. In the analysis of quantitative data, descriptive statistics of the survey items were made using SPSS 24 software, and mean and standard deviation values were given. The content analysis method was used for the answers to open-ended questions. In addition, coding was done, and the expressions were explained as themes. 2.4 Results The data obtained through the questionnaire and interview forms were transformed into tables and presented in this section. As research finding, firstly, the average and standard deviation values of the questionnaire items are given in Table 1 as quantitative findings. In general, when Table 1 is examined, students have positive thoughts about “Satisfaction with the course contents”, “System and interface competence”, “Opinions about the instructors”, “Satisfaction with the exams and the appropriateness of the exams”, and “Technical and institutional functioning”. In addition, when the mean values were examined, they gave the answers of “I agree” and “I absolutely agree” to the questionnaire items. It can be said that students’ satisfaction with the use of distance education in courses is generally good. Content analysis was used to obtain the qualitative findings of the research, and the data obtained from the two open-ended questions were explained as themes in Table 2 and Table 3. With the emergence of new variants after the Covid-19 pandemic, universities continued to offer some, but not all, courses online in the form of distance education. When

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Table 1. Average and standard deviation values of the questionnaire items. No

Items

Average

Standard deviation

1

In terms of course content, PDF Text files are sufficient 4.10

0.899

2

In terms of course content, PPT text files are sufficient

4.23

0.987

3

In terms of course content, videos are enough

3.97

1.105

4

The language of the lecturers can be understood in the videos

3.85

1.102

5

The examples given in the lessons are enough

3.64

1.012

6

Course contents are up to date

3.88

1.123

Satisfaction with the course contents

System and interface competence 7

Instructional videos about the use of the system are enough

3.94

1.256

8

The functioning of the education system in which you receive distance education is sufficient

3.86

0.954

9

Announcements published in the system are sufficient

3.38

0.987

10

The system interface is user-friendly

3.65

0.895

11

Access to course materials is sufficient

3.42

0.999

Opinions about the instructors 12

Online communication between the instructor and the student is sufficient

3.98

1.111

13

The method used by the teaching staff in the lecture is sufficient

4.22

1.138

14

The teaching staff gives active feedback to the student during the learning process

4.25

1.125

Satisfaction and suitability of exams 15

It is convenient to conduct exams in a face-to-face classroom environment

1.96

1.001

16

The questions asked in the exams are in accordance with the course content

3.94

1.203

17

Exam questions are understandable

3.86

1.119

Technical and institutional functioning 18

Any time you encounter a problem, the necessary assistance is provided

3.85

0.886

19

Technical glitches in the system are fixed on time

4.16

0.982

20

The student is informed about the updated works

4.21

1.085

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Table 2 is examined, the students also stated that it is useful to have their courses in the form of distance education, and it is helpful and saving for them. In addition, the students mostly stated that they did not encounter any problems in taking the courses online or face-to-face and that they did not experience any difference. Students have a positive attitude towards distance education. They also stated that they had the advantage of better learning by watching the missed lessons many times later. Apart from this advantage, students also stated that they do not pay for travel, accommodation, and other expenses for distance education. Some students stated that it was difficult for them to take mathematics courses in the form of distance education. Table 2. Average and standard deviation values of the questionnaire items. Theme

N

When new variants came out, it was useful to take the courses with distance education

15

Helps and saves a lot

18

Has no problems taking courses both online and face to face

17

Have positive attitudes to distance education

16

Learn the courses better by watching videos many times

16

No need to travel, no money for accommodation, no other costs

19

Family support advantage

10

Difficulty in online math class

5

Students can take their courses professionally from online systems

12

Missed classes can be followed from the course page at the distance education system

16

When Table 3 is examined, all of the students gave the answer “Yes” to the situation of taking courses again with distance education in the near future. In general, the majority of students stated that they did not encounter any problems in distance education. However, very few students stated that they had problems due to the internet infrastructure in their homes. In addition, the students stated that they thought of taking the courses that they did not do well and were not successful in before, in the form of distance education. Table 3. Students’ views about taking courses again with distance education in the near future. Theme

N

To take courses with distance education at the near future

20

Do not have problems with distance education

15

To take courses that were not well-done before

6

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2.5 Discussion On the subject, according to the data obtained from the master’s thesis studied by Yadigar (2010) [9], students stated that they would like to choose distance education again in the future and that the technical infrastructure was properly prepared. This result is in parallel with the results of this study. However, in addition to these positive results, according to the other result obtained from the thesis, it was seen that the content of the program was insufficient, there was a need for improvement in participation and feedback, and there were also criticisms. After this thesis, after twelve years, no such result was found in this research. This result found in this study was seen as a reflection of the positive results achieved in distance education. Literature [10] conducted the research using a mixed method with 16 lecturers from three different universities. As a result of this research conducted in [10], it was found that the instructors’ knowledge about distance education is not clear, there is no common opinion because they make lecture-based explanations, they find themselves technically competent, they find distance education less useful than traditional education due to the lack of interaction for students. It has been found to be problematic in terms of infrastructure and usability. Unlike this study, students mostly stated that they did not encounter any problems in terms of both systematic and instructional aspects. In [8], in which the views of lecturers and students about the teaching of courses through distance education were examined, the average satisfaction with distance education in common courses was determined as 56.4%, and it was concluded that the students were partially satisfied. In this study, when the averages of the survey items are taken into account, it has been concluded that the satisfaction level of the students is at the level of “agree” and that the students are satisfied with the distance education courses.

3 Conclusion and Recommendation Considering the findings of the research, it was seen that the satisfaction of the students in the use of distance education in the courses was good. In general, the students stated that they did not encounter any problems in taking the courses online or face-to-face and that they did not experience any difference. Students have a positive attitude towards distance education. They also stated that they had the advantage of better learning by watching the missed lessons many times later. Apart from this advantage, students also stated that they do not have to pay for travel, accommodation, and other expenses for distance education. Universities will have to take the necessary precautions in this regard, considering that students may have difficulties in coming back to the university and starting their classes, as their accommodation, transportation, and other costs are reduced by distance education. Since the mathematics course is a difficult course in general, it is natural for students to have difficulties in distance education. However, in order to overcome these difficulties, it is necessary to take necessary precautions in distance education and conduct new research.

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References 1. Ak, A., Oral, B., Topuz, V.: Evaluation of distance learning process of Marmara University vocational school of technical sciences (in Turkish). SEAT J. 2(1), 71–80 (2018). Retrieved https://dergipark.org.tr/en/download/article-file/624965 2. Bozkurt, A.: The past, present and future of the distance education in Turkey (in Turkish). 3(2), 85–124 (2017). Retrieved https://dergipark.org.tr/en/download/article-file/403827 3. Erturgut, R.: Organizational, social, pedagogic components of the internet basic distance education (in Turkish). Bili¸sim Teknolojileri Dergisi 1(2), 79–85 (2008). Retrieved https:// dergipark.org.tr/en/download/article-file/75244 4. Dixon, K., Pelliccione, L.: Reactions to online learning from novice students in two distinct programs. In: Atkinson, R., McBeath, C., Jonas-Dwyer, D., Phillips, R. (eds.) Beyond the Comfort Zone: Proceedings of the 21st ASCILITE Conference, pp. 255–262 (2004). Retrieved http://www.ascilite.org.au/conferences/perth04/procs/dixon 5. Sadeghi, M.: A shift from classroom to distance learning: advantages and limitations. Int. J. Res. Engl. Educ. 4(1), 80–88 (2019). Retrieved http://ijreeonline.com/article-1-132-en.pdf 6. Gürer, M.D.E., Tekinarslan, M.D., Açık, G.: Fundamentals of open and distance learning (in Turkish). Pegem Akademi 1–28 (2021) 7. Creswell, J.W., Sözbilir, M.: Introduction to mixed methods research. Pegem Akademi (2017) 8. Erfidan, A.: Perspectives of Lecturers and Undergraduate Students on University Distance Education Courses: The Case of Balikesir University (in Turkish) (2019). Retrieved https:// dspace.balikesir.edu.tr/xmlui/handle/20.500.12462/5606 9. Yadigar, G.: Evaluation of the effectiveness of distance education program (in Turkish). Unpublished Master’s Thesis, Ankara (2010). Retrieved https://dspace.gazi.edu.tr/handle/20. 500.12602/188231 10. Yıldız, M.: The Relationships Among Distance Education Instructors’ Knowledge, Belief and Practices Towards Distance Education (in Turkish). Unpublished Master’s Thesis, Hacettepe Üniversitesi E˘gitim Bilimleri Enstitüsü, Ankara (2015). Retrieved http://www.openaccess. hacettepe.edu.tr:8080/xmlui/handle/11655/1741

Decision Making on Selection of Ferritic Stainless Steel Mustafa Babanli1

, Latafat Gardashova2(B)

, and Tural Gojayev1,2

1 Azerbaijan State Oil and Industry University, Azadlig Avenue 34, Nasimi, Baku, Azerbaijan 2 Azerbaijan University, Jeyhun Hajibeyli Street 71, Nasimi, Baku, Azerbaijan

[email protected]

Abstract. The selection of proper material based on fuzzy based MCDM methods for engineering purposes has gained importance in recent years. When selecting a material for a specific application based on properties, appropriate selection method must be applied to make sure that the suitable material has been selected and it will remain convenient for its intended application. Thus, scientists have developed different selection methods in accordance with all these reasons. This article aims to choose an optimal alloy alternative of the ferritic type of stainless steel, while using the Fuzzy logic-based method on the material properties of FY, FT, young’s modulus, density, CTE, and ThrmCond. For this purpose, Fuzzy logic is an effective tool and is well-established and applied in the scientific literature for the representation of reliable information. To describe a basic characteristic of ferritic stainless steel, fuzzy logic is useful because of inaccurate information. In this paper, material selection based on the criteria is used and a fuzzy-based approach is applied, which is proposed by Babanli. The essence of this particular technique is Zadeh’s fuzzy set concept for aggregation of features. Keywords: Fuzzy number · Fuzzy logic · Aggregation · Zadeh’s concept · Material selection · Stainless steel

1 Introduction In order to make a decision when selecting a material, engineers have to take into consideration the balance between cost, quality, resistance, performance and other related indicators. The essential object of material selection in the matter of product design is to reduce cost while reaching outcome performance objectives [1]. To attain such goals, engineers have to apply qualitative and quantitative methods [2]. The necessity of material selection in manufacturing has dramatically increased in latest years. In this article, the primary object is to choose an optimal alloy option of the ferritic type of stainless steel that will be used in production. The particular type of stainless steels called ferritic are cost-effective, price-stable, and resist against corrosion. By contrast with austenitic steel, ferritic steel has weak thermal enlargement, strong thermal conductivity. The ferritic steels are broadly employed

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 101–112, 2023. https://doi.org/10.1007/978-3-031-25252-5_18

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in producing automotive parts, industrial machinery and household device sectors. Constructive implementations of these materials in the construction sector are, however, limited, due to some barriers [3]. Li Y. et al. [4] discussed the modelling of the corrosion characteristics of FerriticMartensitic steels in water above a critical threshold. They forecasted 7 essential independent variables, including, oxygen concentration, flow-rate, heat, exposure duration, key chemical compound and outside state of steels by implementing a controlled artificial neural network (ANN). K.A. Cashell et al. [5] studied ferritic stainless steels in structural implementations. The empirical data was added by numerical analysis for the purpose of study a broad range of parameters. This study experimentally investigated the effect of heating temperature and holding duration on heating on the stress-strain behavior after a fire of three grades of ferritic stainless steel.. Honysz R. et al. [6] made an attempt to apply fuzzy logic to the study of artificial neural networks with radial basis functions (RBF), multilayer perceptron with 1 and 2 hidden layers (MLP) and universalized regression neural networks (GRNN) those were applied for modeling. Li-An Xie et al. [7] experimentally investigated the effect of heating temperature and holding duration on heating on the stress-strain behavior after a fire of three grades of ferritic stainless steel (e.g., EN 1.4003, 1.4016, 1.4509). The test outcomes demonstrated that the 3 grades treated very distinctly after exposure to upraised temperatures due to microstructure changes throughout heating and chilling down to room temperature. Zhige Wang et al. [8] investigated laser treatment of 430 ferritic stainless steel for enhanced mechanical specifications. These outcomes could be useful with the purpose of locally alter the behavior of moderate chrome ferritic stainless steel to reach industrial demands. But the selection problem of the ferritic steel depending on the characteristics should be solved. For solving this problem, we need a new approach. In this paper, we will discuss implementation of a new technique for selection of ferritic stainless steel. Ferrites have better durability, ductility and strength, and also an appealing appearance. They can be quite economical and effective. Although, it has lots of appealing specifications, ferritic stainless steels are underused at present in structural implementation because of the lack of credible information. Today, Fuzzy logic is an effective tool that has proved itself in scientific literature in representation of reliable information [9]. To describe basic characteristic of ferritic stainless steel, fuzzy logic is useful, because inaccurate information exists there [10]. The application of fuzzy based approach to the materials selection problem is a new addition to the broad range of methods convenient for the engineers. Throughout the publications on fuzzy based materials selections, there are a broad variety of techniques used to achieve the material selections. This is because of an innate quality achievable within the structure of fuzzy approach. The “fuzziness” of fuzzy logic enables human explication. Fuzzy logic based decision making has an important role if the information is under state of ambiguity [11, 12]. The aim of the paper is to present a neuro-fuzzy approach to select candidate Ferritic stainless steel based on the material specifications of FY (yield strength), FT (tensile strength), young’s modulus (a measure of elasticity), density, CTE (the coefficient of linear thermal expansion) and ThrmCond (thermal conductivity).

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The comparative analysis shows that the neuro-fuzzy approach is better than the other implemented methods, but there are also shortcomings here. These include the choice of membership function, inference algorithm, and training algorithm, which directly affect the results [10]. In this article, we discuss the decision-making problem on material selection. The paper consists of 5 sections. Basic formulas used in the research are described in Sect. 2. Section 3 ensures the problem statement. When it comes to Sect. 4, which is connected to the offered way of fuzzy based decision-making and the implementation of the procedure to the material selection problem. Section 5 provides the results and concludes the paper.

2 Preliminaries The considered problem is addressed by implementing the “Group Decision Making” Method. This particular method, introduced by J.Babanli [10, 13]. The steps of algorithm are as follow: 2.1. Identification of an expert team for criterion assessment. 2.2. Determination of criterions by the experts. 2.3. The result of the evaluation is summarized based on the following formula: K 

fi =

k=1

fi k (1)

K

Here f i - ai is established on the basis of total review of the group of experts. Every element of f i = (fi1 , ..., fij , ..., fin )T . fij is defined as: K 

f ij =

k=1

fijk

K

(2)

2.4. Calculation of the arithmetic mean [10]. 2.5. Determination of weighted mean of values ϕl (ai ) based on alternatives: Agg(ai ) = IG1 ϕ1 (ai ) + . . . . + IGl ϕl (ai ) + . . . + IGL ϕL (ai ).

(3)

Here, IGl , i = 1, . . . L is the coefficient representing the necessity of groups. 2.6. Alternatives ai are ranked based on their indexes, i = 1, ..., n. For that purpose Agg(ai ) is compared based on the distance distance to the fuzzy number Q, that denotes the utmost linguistic term of the scale of prediction. a1  a2 if d(Agg(a1 ), Q) < d(Agg(a2 ), Q). Here d - is the distance between fuzzy numbers. Therefore, an alternative that has a near distance to the fuzzy number Q is considered as higher-up. The distance d is determined by using the following formula:    agg1 + 4 ∗ agg2 + agg3 q1 + 4 ∗ q2 + q3   (4) − d (Agg, Q) =   6 6

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3 Statement of the Problem Solution of material selection problem by applying fuzzy logic based approach is the primary object of the article. In this paper, A = {a1 , . . . , am }, are alternatives and F = (f1 , . . . , fn ) is a criterion vector. Value of alternatives are calculated by a single expert. It illustrates that expert assesses every alternative concerning the criterion given (Table 1). Table 1. Priority values of alternatives f1

…

fj

…

fn

…

k f1n

…

f1jk fijk

…

ai

k f11 f1ik

…

fink

…

…

…

…

…

…

am

k fm1

…

k fmj

…

k fmn

a1

Here, fijk - is the assessment of k-th expert for i-th alternative and j-th criterion. Criterions are grouped by significance degree. The considering problem of ranking leads to the search for an best alternative. So, a* is the best or optimal alternative is obtained as follow:     Agg a* = max Agg(a), where Agg a* is an aggregated index of the alternatives. a∈A

(5)

Table 2. Material specifications of candidate Ferritic stainless steel UNS

Industry

FY (MPa)

FT (MPa)

Young’s modulus

Density (g/cm3 )

CTE (μm/m*°C)

ThrmCond. (W/m*k)

S43000

430

205

415

200

7.80

10.4

26.1

S44627

E-Brite

275

450

200

7.66

9.9

16.7

S44635

Monit

515

620

200

7.80

10

16

S44660

Sea-Cure

450

585

214

7.70

9.5

16.4

S44735

29–4C

415

550

200

7.67

9.2

15.2

S44800

29–4–2

415

550

200

7.70

9.2

15.1

4 Application In this section of the paper, selection of the ferritic stainless-steel problem is discussed. Assume that we have a MCDM problem, in which there are 6 alternatives (A1,…,6) and 6 criteria (f1 , …, f6 ). Alternatives are given below:

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A1-AS43000-430; A2-S44627-E-Brite; A3-S44635-Monit; A4-S44660-Sea-cure; A5-S44735-29-4C; A6-S44800-29-4-2. Criterions are shown below (properties): f1 -Fy(MPa); f2 - Ft(MPa); f3 -Young’s Modulus; f4 -Density(g/cm3); f5 - (CTE(μm/m•°C); f6 - Thrmcond (W/m•K)). Each option is evaluated in proportion to criteria (Table 2). Discussed problem was solved based on the methodology produced by J.Babanli [10]. A team consists of 1 expert. Each alternative is evaluated by one expert-specialist in materials. Initial evaluation by specialist in materials is illustrated in Table 3 and 4 below (Tables 5 and 6): Table 3. Initial data Fy

Ft

Ym

a

b

c

a

b

c

a

B

c

196.8

205

211.15

406.7

415

427.45

196

200

204

264

275

283.25

441

450

463.5

196

200

204

494.4

515

530.45

607.6

620

638.6

196

200

204

432

450

463.5

573.3

585

602.55

209.72

214

218.28

398.4

415

427.45

539

550

566.5

196

200

204

398.4

415

427.45

539

550

566.5

196

200

204

Table 4. Initial data (continue) D

CTE

ThrmCond

a

b

c

a

b

c

a

b

c

7.566

7.8

7.956

10.192

10.4

10.712

25.578

26.1

26.622

7.4302

7.66

7.8132

9.702

9.9

10.197

16.366

16.7

17.034

7.566

7.8

7.956

−9.8

−10

−10.3

−15.68

−16

−16.32

7.469

7.7

7.854

9.31

9.5

9.785

16.072

16.4

16.728

7.4399

7.67

7.8234

9.016

9.2

9.476

14.896

15.2

15.504

7.469

7.7

7.854

9.016

9.2

9.476

14.798

15.1

15.402

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Fy

Ft

YM

a

b

c

a

b

c

a

0.32541

0.3379 34404

0.3473 0.645 91 0.658 58 0.677 59 0.324 19 0.3303 24864

0.33641

0.428 02 0.44481 0.4574 0.698 28 0.712 03 0.732 64 0.324 19 0.3303 7688 14646

0.33641

0.779 82 0.8112 7466

0.8348 0.952 67 0.971 6 65327

0.33641

0.684 54 0.7120 25896

0.7326 0.900 29 0.918 16 0.944 96 0.345 14 0.35168 0.35821 39101

0.633 24 0.6585 84255

0.6775 0.847 92 0.864 72 0.889 91 0.324 19 0.3303 9421

0.33641

0.633 24 0.6585 84255

0.6775 0.847 92 0.864 72 0.889 91 0.324 19 0.3303 9421

0.33641

1

b

0.324 19 0.3303

c

Table 6. Normalized decision matrix (continue) D a

CTE b

c

a

ThrmCond b

0.03647 0.03683 0.03707 0.04048 0.040798876

c

a

b

c

0.04128 0.06397 0.06477 0.06557

0.03626 0.03662 0.03685 0.03973 0.0400354424 0.04049 0.04991 0.05042 0.05093 0.03647 0.03683 0.03707 0.00996 0.009650034

0.00919 0.00098 0.00049 0

0.03632 0.03668 0.03691 0.03913 0.039424663

0.03986 0.04946 004996

0.03628 0.03663 0.03686 0.03869 0.038966591

0.03939 0.04766 0.04813 0.04859

0.03632 0.03668 0.03691 0.03869 0.038966591

0.03939 0.04751 0.0479

0.05046 0.04844

Criteria vector f i of expert for each ai alternative are determined by using (2). The estimations of the criteria are denoted by fuzzy numbers according to the codebook illustrated in Fig. 1.

Decision Making on Selection of Ferritic Stainless Steel

μf

i

Very low (VL)

1

0

Low (L)

0.25

Medium (M)

0.5

107

Good (G)

Very Good (VG)

0.65

1

fi

Fig. 1. Codebook of the linguistic terms

By using math expression (2), the vector f i is identified. For example, the calculated values for A1,…,A6 are in accordance with the Table 2 rows. Each row describes one alternative, and values of criteria on the first alternative are: f1 = (0.32541; 0.337934404; 0.3437254864) ..... f6 = (0.06397; 0.06477; 0.06557) Results of the a2 are as follows: f1 = (0.42802; 0.4444817688 ; 0.457414646) ..... f6 = (0.04991; 0.05042; 0.05093) Results of the a3 are as follows: f1 = (0.77982; 0.81127466; 0.834865327) ..... f6 = (0; 0.000489; 0.000977) Results of the a4 are as follows: f1 = (0.68454; 0.712025896; 0.732639101) ..... f6 = (0.049459; 0.04996; 0.050461)

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Results of the a5 are as follows: f1 = (0.63324;0.658584255;0.67759421) ..... f6 = (0.047664; 0.048128; 0.048592) Results of the a6 are as follows: f1 = (0.63324;0.658584255; 0.67759421) ..... f6 = (0.047514; 0.047975; 0.048436). For each alternative ϕ1 (ai ), ϕ2 (ai ), ϕ3 (ai ) values are calculated. The subgroups of the importance criteria are described in Table 7. Table 7. Importance rate of criteria Importance rates

Criteria

IR 1 (High) (0.5 0.65 0.7)

f1 f2

IR 2 (Medium) (0.2 0.25 0.3)

f4

IR 3 (Low) (0 0.1 0 .3)

f5 f6

So, φ1 (ai ) =

f 1 + f2 + f3 f 5 + f6 , φ2 (ai ) = f4 , φ3 (ai ) = 3 2

Values for a1 are as follows: φ1 (a1 ) = (0.431839003; 0.442272848; 0.453780.6; 0.8; 0.975); φ2 (a1 ) = (0.03647; 0.03683; 0.03707); φ3 (a1 ) = (0.05223; 0.05279; 0.05342) .

Decision Making on Selection of Ferritic Stainless Steel

Obtained values for a2 are as follows: φ1 (a2 ) = (0.483499257;0.495714489; 0.50882); φ2 (a2 ) = (0.03626;0.03662; 0.03685); φ3 (a2 ) = (0.04482;0.04523; 0.04571). Obtained values for a3 are as follows: φ1 (a3 ) = (0.685559559;0.704391376; 0.72376); φ2 (a3 ) = (0.03647;0.03683; 0.03707); φ3 (a3 ) = (0.00547; 0.00507; 0.0046) . Obtained values for a4 are as follows: φ1 (a4 ) = (0.643325393; 0.660620127; 0.6786) ; φ2 (a4 ) = (0.03632; 0.03668; 0.03691) ; φ3 (a4 ) = (0.0443; 0.04469; 0.04516) . Obtained values for a5 are as follows: φ1 (a5 ) = (0.601783424; 0.617866813; 0.63464); φ2 (a5 ) = (0.03628; 0.03663; 0.03686); φ3 (a5 ) = (0.04317;0.04355; 0.04399). Obtained values for a6 are as follows: φ1 (a6 ) = (0.601783424; 0.617866813; 0.63464); φ2 (a6 ) = (0.03632; 0.03668; 0.03691); φ3 (a6 ) = (0.0431; 0.04347; 0.04391). The final aggregate grades for first alternative is calculated using (4): For a1: Agg(a1 ) = (0.431839003;0.442272848; 0.45378)(0.5; 0.65; 0.7)+ (0.03647163;0.036828926; 0.03707)(0.2; 0.25; 0.3) + (0.052227753; 0.052785073;0.05342)(0; 0.1; 0.3) = (0.223213828; 0.30196309; 0.34479 ).

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For the second alternative by applying the same procedure, the final aggregated values were calculated. The value for a2 is shown below: Agg(a2 ) = (0.4835; 0.49571; 0.50882)(0.5; 0.65; 0.7) + (0.03626; 0.03662; 0.03685)(0.2; 0.25; 0.3) + (0.04482; 0.04523; 0.04571)(0; 0.1; 0.3) = (0.249; 0.33589; 0.38094). The value for a3 is shown below: Agg(a3 ) = (0.685559559;0.704391376; 0.72376)(0.5; 0.65; 0.7) + (0.03647; 0.03683; 0.03707)(0.2; 0.0.25; 0.3) + (0.00547; 0.00507; 0.0046)(0; 0.1; 0.3) = (0.32896; 0.43912; 0.48752). The value for a4 is shown below: Agg(a4 ) = (0.643325393; 0.660620127; 0.6786)(0.5; 0.65;0.7) +(0.03632; 0.03668; 0.03691)(0.2; 0.25; 0.3) + (0.0443;0.04469; 0.04516)(0; 0.1; 0.3) = (0.30816; 0.41525; 0.46887). The value for a5 is shown below: Agg(a5 ) = (0.601783424; 0.617866813; 0.63464)(0.5; 0.65; 0.7)+ (0.03628; 0.03663; 0.03686)(0.2; 0.25; 0.3) + (0.04317; 0.04355; 0.04399)(0; 0.1; 0.3) = (0.308147529; 0.41513; 0.4685). The value for a6 is shown below: Agg(a6 ) = (0.601783424;0.617866813; 0.63464)(0.5; 0.65; 0.7)+ (0.03632;0.03668; 0.03691)(0.2; 0.25; 0.3)+ (0.0431;0.04347; 0.04391)(0; 0.1; 0.3) = (0.30816; 0.41513; 0.46849) The distance between the aggregation value of an alternative and very good is determined in accordance with (5) as follows: d (Agg(a1 ), very good ) = |0.295975955 − 0.95833| = 0.662354045 d (Agg(a2 ), very good ) = |0.32892 − 0.95833| = 0.62941 d (Agg(a3 ), very good ) = |0.42882 − 0.95833| = 0.52951 d (Agg(a4 ), very good ) = |0.40634 − 0.95833| = 0.55199 d (Agg(a5 ), very good ) = |0.40619219 − 0.95833| = 0.55213781 d (Agg(a6 ), very good ) = |0.40619 − 0.95833| = 0.55214

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The results obtained are given in Table 8: Table 8. The rank of alternatives Alternative

Distance

(a1 )

0.662354045

(a2 )

0.62941

(a3 )

0.52951

(a4 )

0.55199

(a5 )

0.55213781

(a6 )

0.5521

The smallest distance has a higher rank. So, a3  a4  a6  a5  a2  a1 .

5 Discussion and Conclusion The particular method applied in this article for solving material selection problem is a fuzzy information-based method, which development is based on Zadeh’s ideas and concepts. Determining the best alternative of ferritic stainless steel involves 6 criteria, which helps us to express the relevance of the method. Fuzziness is used for assessment of criteria and criteria importance. The obtained results represents effectiveness of the proposed method.

References 1. Babanli, M.B., Qardashova, L.A., Gojayev, T.L.: Selection of gear material by using fuzzy AHP method. Sci. J. Proc. Azerbaijan High Tech. Educ. Inst. 24(1), 52–59 (2022) 2. Neufill, R.: Materials selection maximizing overall utility. Met. Mater. 4(6), 378–382 (1988) 3. Manninen, T., Säynäjäkangas, J.: Mechanical properties of ferritic stainless steels at elevated temperature. In: Conference: Stainless Steel in Structures - Fourth International Experts Seminar (2012). https://www.academia.edu/9039435 4. Li, Y., et al.: Modelling and analysis of the corrosion characteristics of ferritic-martensitic steels in supercritical water. Materials. 12(3), 409 (2019). https://doi.org/10.3390/ma1203 0409 5. Cashell, K.A., Baddoo, N.R.: Ferritic stainless steels in structural applications. Thin-Walled Struct. 83, 169–181 (2014). https://doi.org/10.1016/j.tws.2014.03.014 6. Honysz, R.: Modeling the chemical composition of ferritic stainless steels with the use of artificial neural networks. Metals 11(5), 724 (2021). https://doi.org/10.3390/met11050724 7. Li-An, X., et al.: Post-fire stress-strain response of structural ferritic stainless steels. J. Constr. Steel Res. 196 (2022). https://doi.org/10.1016/j.jcsr.2022.107389 8. Zhige, W., Justin D.„ Pierre, L., Sébastien, D.: Laser treatment of 430 ferritic stainless steel for enhanced mechanical properties. Mater. Sci. Eng. 831 (2022). doi.org/https://doi.org/10. 1016/j.msea.2021.142205

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9. Aliev, R.A.: Uncertain Computation-Based Decision Theory. World Scientific Publishing, Singapore (2017) 10. Babanli, M.B.: Fuzzy Logic-based Material Selection And Synthesis. World Scientific Publishing Company, Singapore (2019) 11. Zadeh, L.A.: A very simple formula for aggregation and multicriteria optimization. Int. J. Uncertainty Fuzz. Knowl.-Based Syst. 24(6), 961–962 (2016). https://doi.org/10.1142/S02 18488516500446 12. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 42–50. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-041649_10 13. Babanli, J.M.: Fuzzy approach for evaluation of student’s performance. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 140–147. Springer, Cham (2021). https://doi.org/10.1007/978-3-03064058-3_18

Multicriteria Group Decision Making on Information System Project Selection Using Type-2 Fuzzy Set Aygul Dadasheva(B) Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]

Abstract. Multicriteria group decision making (MCDM) approach using fuzzy set for Information System (IS) Project Selection evaluation and selection is represented in this paper. The selection of the projects is also considered as the evaluating process for each project’s idea and the idea which has the highest priority has been chosen. In the competitive environment evaluating and selecting the right and reliable IS Projects can be considered as the main factor for the corporate competition ability. Evaluation imprecision which is modeled by trapezoidal fuzzy type 2 set characterizes linguistic term. Information technologies project selection problem is represented to indicate the approach sensitivity with information processing efficiency, system reliability, cost of implementation and three alternatives. Keywords: IT project selection · Multicriteria group decision making · Type- 2 fuzzy set · TOPSIS

1 Introduction Today, in organizations information system (IS) which are related to information technologies, business processes have been rapidly developed [1]. Evaluation and selection of IS projects is a complex and challenging process but effective IS Project could help organizations in understanding the strategy and the using of them for firstly reaching business goals instead of to decide developing the new one. Often this process is based on multiple decision makers, multiple criterial selection [2]. ˙In this paper, as the selection method we used TOPSIS method which presented by type 2 trapezoidal fuzzy sets. For the best possible option selection, we need appropriate justification in which using the structured approach of analysis of the universal performance of options which are available. Multicriteria decision making (MCDM) methods are used in the real-world alternatives ranking. Aim of the MCDM is involved with ranking process of different alternatives. As human preferences have the inherent uncertainty, estimating the alternative with the exact numbers is hard. Developing the system to help decision makers in the IS projects selection, in this article we present an effective multicriteria approach with type- 2 fuzzy set. Modelling of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 113–121, 2023. https://doi.org/10.1007/978-3-031-25252-5_19

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the human subjectiveness and uncertainty of decision making process, linguistic term are characterized by the trapezoidal type 2 fuzzy numbers [3, 4]. Avoiding the unreliable and complicated comparing process of type-2 fuzzy numbers which is necessary in MCDM, applying the dominance degree concept applied new algorithm is developed. In the following sections, firstly IS project selection type- 2 fuzzy multicriteria group decision making (MCDM) problem is formulated. It is possible to use MCDM also as decision support too; while making the decisions which include multi criterions to evaluate and to select simultaneously. Sequentially, the new created algorithm model has been shown for the type -2 fuzzy MCDM problem solving. The second part represents given preliminaries. Information system project selection problem has been shown in Sect. 3. At the Sect. 4 problem solution which included the numerical example which illustrates applying the new proposed TOPSIS method with trapezoidal fuzzy type 2 sets in IS Project Selection and the main outcomes have been represented. At the result, the ranking of fuzzy numbers is based on the fuzzy sets’ right and left sides areas.

2 Preliminaries Definition 1.  A- type-2 fuzzy set in X discourse universe which represented by type-2 membership function. α = {((x, u), μ(x, u) )|∀x ∈ X , ∀u ∈ Jx ⊆ [0, 1], 0 ≤ μ(x, u) ≤ 1} A A A

(1)

In the below mentioned Fig. 1 trapezoidal interval type 2 fuzzy set example has been shown.

H1 ( A1U ) H 2 ( A1U ) H1 ( A1L ) H 2 ( A1L )

0

aiU1

aiL1 aiU1 aiL2

aiL3 aiU3 aiL4 aiU4

Fig. 1. Interval type-2 fuzzy sets

Definition 2. Multicriteria group decision matrix which created by the different decision makers (DM) is determined by Wang method for ranking and comparing of each criterion for every DM and preferring alternative with the maximum value to other options. U˜ = (u1 , u2 , u3 , u4 ; wu ) and V˜ = (v1 , v2 , v3 , v4 ; wv ) are type 2 fuzzy numbers and (m0u , n0u ) and (m0v , n0v ) are these numbers centroid points, then: 1. If m0u  m0v (m0u ≺ m0v ) then U˜  V˜ (U˜ ≺ V˜ ),

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2. If m0u = m0v and n0u = n0v , then U˜ ≈ V˜ . 3. If m0u = m0v then, U˜  V˜ (U˜ ≺ V˜ ) is resulted from n0u  n0v (n0u ≺ n0v ). Definition 3. If to consider that the A˜ is the given pairwise comparison matrix, it confirms suitable properties (reciprocity and consistency) [5]. In pairwise matrix constraints are described in the following: ˜ A˜ ij A˜ ji = A(1)

(2)

A˜ ij A˜ jk = A˜ ik

(3)

3 Statement of the Problem If to consider that the MC group decision making problem includes 3 criterion – C1 , C2 , C3 and 3 alternatives – A1 , A2 , A3 . C1 - Information processing efficiency; C2 - System Reliability; C3 - Cost of Implementation: In evaluating and the selection of Information System (IS) Project by fuzzy MCDM approach has been used which has been below mentioned [6, 7]. Evaluation imprecision [8] is represented and modelled by fuzzy trapezoidal type-2 numbers which is characterized by linguistic term. In the following problem (A˜ ij ) is represented consistent comparison pairwise matrix and in this matrix all consistency conditions are verified [9]. Using the TOPSIS method we will choose the best alternative. The matrix shown below is pairwise comparative matrix (A˜ ij ): ⎡

1 A˜ 12 ⎢˜ ⎢ A21 1 ˜Aij = ⎢ ⎢. .. ⎢. . ⎣. ˜An1 A˜ n2

⎤ ... A˜ 1n ⎥ ... A˜ 2n ⎥ ⎥ .. ⎥ .. . . ⎥ ⎦ ...

(4)

1

Consistent matrix components met all consistency conditions which are formulated in (1–3). The fuzzy weight for each criterion is calculated with minimizing objective function and the TOPSIS method is applied.

4 Solution of the Problem Step-1: Criteria identification and from the top to the lower levels building the hierarchy by the determination of criterion. Step-2: Pairwise comparison matrices construction which includes all criterions in hierarchy system dimensions. Linguistic variables which used in the pairwise matrices of comparisons and scales in interval fuzzy type-2 are represented in Table 1.

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Linguistic variables

Trapezoidal 2-type Interval fuzzy numbers

Extremely High (EH)

(7,8,9,9;1) (7.2,8.2,8.8,9;0.8)

Very High (VH)

(5,6,8,8;1) (5.2,6.7,8,8;0.8)

Intermediate (I)

(3,4,6,7;1) (3.4,4.2,6,6.8;0.8)

Good (G)

(1,2,4,5;1) (1.4,2.2,3.8,4.8,0.8)

Equal (E)

(1,1,1,1;1) (1,1,1,1;1)

Table 2. The comparison pairwise matrix for the 1st decision maker for the criteria. C1

C2

C3

C1

E

1/G

1/G

C2

G

E

1/G

C3

G

G

E

Table 3. The pairwise comparison matrix for the second decision maker for the criteria. C1

C2

C3

C1

E

E

1/I

C2

E

E

1/I

C3

I

I

E

Table 4. The pairwise comparison matrix for the third decision maker for the criteria. C1

C2

C3

C1

E

1/G

1/G

C2

G

E

1/G

C3

G

G

E

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The pairwise comparison matrices in 2-type interval fuzzy sets are represented in the following (Tables 2, 3 and 4): ⎤ ⎤ ⎡ ⎡ 1 a˜ 12 ... a˜ 1n 1 a˜ 12 ... a˜ 1n ⎢ a˜ 2n 1 ... a˜ 2n ⎥ ⎢ 1/˜a21 ... a˜ 2n ⎥ ⎥ ⎥ ⎢ ⎢ ⎢ ⎥  (5) = A=⎢ . . . ⎥ ⎢ .. . . . .. .. ⎥ ⎣ .. .. . . .. ⎦ ⎣ . ⎦

1/˜an1 1 a˜ n2 ... 1 a˜ n1 a˜ n2 . . . 1 Step-3: Determination of group decision making pairwise matrix. This matrix has been presented in Table 5. Table 5. The pairwise comparison matrix for the group decision making for the criteria. C1

C2

C3

C1

(1,1,1,1:1) (1,1,1,1:1)

(1,0.5,0.25, 0.2;1) (1,0.7,0.45,0.26, 0.2,0.8;0.8)

(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)

C2

(1,2,4,5;1) (1.4.2.2.3.8,4.8;0.8)

(1,1,1,1;1) (1,1,1,1;1)

(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)

C3

(3,4,6,7;1) (3.4,4.2,3, 3.8,0.8)

(3,4,6,7;1) (3.4,4.2,3, 3.8,0.8)

(1,1,1,1;1) (1,1,1,1;1)

Step-4: Construction of consistent pairwise matrix. Table 6. Consistent pairwise matrix C1

C2

C3

C1

(1,1,1,1:1) (1,1,1,1;1)

(1,1,1,1:1) (1,1,1,1;1)

(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)

C2

(1,1,1,1;1) (1,1,1,1;1)

(1,1,1,1;1) (1,1,1,1;1)

(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)

C3

(1,2,4,5;1) (1.4.2.2.3.8,4.8;0.8)

(1,2,4,5;1) (1.4.2.2.3.8,4.8;0.8)

(1,1,1,1;1) (1,1,1,1;1)

Step-5: Calculation the fuzzy weights for each criterion. Fuzzy type 2 matrix expressed in Table 6 by four crisp matrices are defined as below indicated in Table 7, 8, 9 and 10:

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A. Dadasheva Table 7. Crisp matrix 1 C1

C2

C3

C1

1.0

1.0

1.0

C2

1.0

1.0

1.0

C3

1.0

1.0

1.0

Table 8. Crisp matrix 2 C1

C2

C3

C1

1.0

1.0

0.5

C2

1.0

1.0

0.5

C3

2.0

2.0

1.0

Table 9. Crisp matrix 3 C1

C2

C3

C1

1.0

1.0

0.25

C2

1.0

1.0

0.25

C3

4.0

4.0

1

Table 10. Crisp matrix 4 C1

C2

C3

C1

1.0

1.0

0.2

C2

1.0

1.0

0.2

C3

5.0

5.0

1.0

Achievement function is to minimize objective function [10]: ⎤ ⎡ 4 4   (nij + pij )⎦ min ⎣ i=1 j=1

 1

wi − wi mij + + (wi − wi mij ) 2 where

 1

wi − wi mij + + (wi − wi mij ) pij = 2 nij =

(6)

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Goals and constraints: 1w1 − w1 + n11 − p11 = 0, 1w2 − w1 + n12 − p12 = 0, 0.5w3 − w1 + n13-p13 = 0. 1w1 − w2 + n21 − p21, 1w2-w2 + n22 − p22, 0.5w3 − w2 + n23 − p23. 2w1 − w3 + n31 − p31, 2w2-w3 + − -n32 − p32, 1w3 − w3 + n33 − p33. W1 + W2 + W3 = 1, W1 > 0, W2 > 0, W3 > 0. Bellowed results are obtained by using Linear programming and weights are obtained as: Objective function: Z = min(n11 + p11 ) + (n12 − p12 ) + nij + pij ) = 0. w1 (0.33; 0.25; 0.16; 0.143; 1, 1) (0.29; 0.24; 0.17; 0.15 : 0.8, 0.8) w2 (0.33; 0.25; 0.16; 0.143; 1, 1) (0.29; 0.24; 0.17; 0.15 : 0.8, 0.8) w3 (0.33; 0.5; 0.66; 0.71; 1, 1) (0.41; 0.52; 0.66; 0.71 : 0.8, 0.8) Step-6: Determination of the best alternative using TOPSIS method. The alternative with the best utility is selected [11, 13]. After the construction of normalized matrix, the weighted normalized matrix has been created and the ideal and the negative ideal solutions has been determined. At the next step, the closeness to the ideal solution has been calculated and then the alternatives have been ranked. Table 11 shows the alternatives’ interval type- 2 fuzzy scores of with respect to criteria. Table 11. Alternatives’ interval type- 2 fuzzy scores of with respect to criteria A1

A2

C1

(0.009;0.001;0.007;0.025;1,1) (0.001;0.002;0.006;0.0018;0.8,0.8)

(0.001;0.002;0.011;0.03;1,1) (0.001;0.003;0.006;0.027;0.8,0.8)

C2

(0.011;0.021;0.074;0.17:1,1) (0.013;0.024;0.064;0.14:0.8,0.8)

(0.002;0.005;0.02;0.049:1;1) (0.003,0.006,0.017,0.040;0.8,0.8)

C3

(0.017,0.043,0.16,0.36;1,1) (0.022,0.050,0.14,0.30;0.8,0.8)

(0.012,0.030,0.12,0.29;1,1) (0.015,0.035,0.10,0.23;0.8,0.8)

C1

(0;0.008;0.035;0.01:1,1) (0.004;0.009;0.03;0.078:0.8,0.8)

C2

(0.002,0.004,0.015,0.037;1,1) (0.002,0.004,0.012,0.030;0.8,0.8

C3

(0.005,0.012,0.056,0.15;1,1) (0.006,0.014,0.048,0.12;0.8,0.8)

A3

After the ideal (Si * ) and negative ideal (Si ’ ) solutions’ determination, the separation measures for each alternative have been calculated. The separation of the ideal and negative ideal alternative is below mentioned:

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Si ’

A1

(0.320.340.290.17:1.1) (0.380.330.300.30: 0.8,0.8)

(0.310.130.210.65:1,1) (0.110.150.200.20:0.8,0.8)

A2

(0.310.240.160.18;1,1) (0.250.220.160.14:0.8,0.8)

(0.190.290.410.52:1,1) (0.260.320.410.44:0.8,0.8)

A3

(0.310.270.400.65:1,1) (0.220.310.410.43:0.8,0.8)

(0.320.320.210.17:1,1) (0.360.300.220.18:0.8,0.8)

The results after the relative closeness to the ideal solution (Ci * ) calculation have been shown: Ci * A1

(0.49 0.28 0.42 0.79:1.1)(0.23 0.31 0.41 0.41:0.8, 0.8)

A2

(0.38 0.55 0.72 0.74:1, 1)(0.51 0.59 0.72 0.76:0.8, 0.8)

A3

(0.51 0.54 0.34 0.21:1, 1) (0.62 0.49 0.35 0.30:0.8, 0.8)

The best alternative is second alternative. The ranking method is based on type 2 fuzzy set right and left sides areas.

5 Conclusion The right Information System project selection is the main component of effective management technology. The main purpose of this paper is finding the best alternative with TOPSIS method with fuzzy weights. The effectiveness of the represented TOPS˙IS method is illustrated by the numerical example. Reliable preferences over the choice criteria are shown by fuzzy type-2 set in the represented work. Using the suggested approach, the best alternative has the highest result, and the second alternative has been chosen.

References 1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965) 2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning – I. Inform. Sci. 8(3), 199–249 (1975) 3. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning1. Inform. Sci. 8, 199–249 (1975) 4. Gardashova, L.A.: Application of operational approaches to solving decision making problem using Z-numbers. J. Appl. Math.. 5(9), 1323–1334 (2014). https://doi.org/10.4236/am.2014. 59125 5. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iran J. Fuzzy Syst. 18(4), 37–49 (2021)

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6. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 7. Huseynova, N.F.: Decision making on tourism by using natural language processing. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 741–747. Springer, Cham (2022). https://doi.org/10.1007/978-3030-92127-9_98 8. Oztaysi, B.: A Group decision making approach using interval type-2 fuzzy AHP for enterprise information system project selection. J. Multiple-Val. Logic Soft Comput. 24(5–6), 475–500 (2015) 9. Dadasheva, A.N.: Analysis of consistency of pairwise comparison matrix with fuzzy type-2 elements. Lect. Notes Netw. Syst. 362, 324–330 (2022) 10. Sadikoglu, G., Dovlatova, Kh. J.: Investigation of preference knowledge of decision maker on consumer buying behaviour. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions-ICSCCW-2019, AISC, vol. 1095, pp. 613–621. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35249-3_78 11. Aliyeva, K.: Multifactor personnel selection by the fuzzy TOPSIS method. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 478–483. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_64 12. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 42–50. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-041649_10 13. Aliyeva, K.R.: Facility location problem by using Fuzzy TOPSIS Method. B-quadrat verlags, pp. 55–59. Uzbekistan (2018). https://doi.org/10.34920/2018.4-5.55-59

Forecasting Demand in the Commodity Market of Food Products Using Neural Networks Mikayilova Rena Nuru1,2(B) 1 Digital Economy and ICT, Azerbaijan State Economic University, Baku 1147, Azerbaijan

[email protected] 2 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku 1010, Azerbaijan

Abstract. When opening a new commercial enterprise, a correct predictive estimate of the demand for the goods of this firm should be given. This work is devoted to the use of neural networks for demand forecasting, by determining the demand elasticity coefficient, which will allow commercial enterprises to give a correct predictive estimate of the demand for their goods in the commodity market. It is known that forecasting is a probabilistic scientifically substantiated judgment about the trends of the phenomenon under study in the future. On the other hand, it should be noted that: - demand is an important factor in the study of the commodity market; - when opening a new commercial enterprise, a correct predictive assessment of the demand for the goods of a given company in the commodity market should be given; - demand and supply appear on the commodity market not spontaneously, but are formed and act according to the relevant laws; relevant laws; - human experience and intuition are among the main sources of information for forecasting demand and future market characteristics; - it is impossible to obtain statistical data in advance for a certain period of time. The paper considers the features of forecasting demand in the commodity market and substantiates the relevance of using neural networks (which is more adequate to the market model in the presence of uncertainty factors) for their forecasting than the methods of extrapolation of trends that are actively used in solving economic problems. The issue of choosing the type of neural network for approximating and predicting the elasticity coefficient of demand for food and non-food products is considered. Keywords: Commodity market · Neural networks · Elasticity coefficient of demand · Radial basic neural network · Regression neural networks · Forecasting demand

1 Introduction A very difficult stage in the study and forecasting of the commodity market is the modeling process [1–4]. The main “participants” in the process of modeling the commodity market are supply and demand, and most importantly, the establishment of a balance system. However, the establishment of a balance system between supply and demand in the commodity market is not enough, it is necessary to identify contradictions © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 122–129, 2023. https://doi.org/10.1007/978-3-031-25252-5_20

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between producers and consumers, between sellers and buyers, and thus determine the purposefulness of each element operating in the market. In the economic literature, there are various approaches to the definition of the categories of supply and demand [4–8]. In this work, demand is understood as the quantity of a good or service that will be purchased at a certain price for a certain period. It is useless to try to determine demand without price, since it changes precisely depending on it. The law of demand operates other things being equal, the demand for goods in quantitative terms varies inversely with price. This happens for two reasons: first, when the price drops, the consumer wants to buy more of the good (the income effect); secondly, when the price of a product decreases, it becomes cheaper relative to other goods, and it becomes relatively more profitable to purchase it (substitution effect). Demand and supply appear on the commodity market not spontaneously but are formed and act according to the relevant laws, and thus, demand functions (the volume of goods that customers are able to buy) and supply functions (the volume of goods that are able to sell to customers) are born. The law of demand does not work in three cases: – in case of excessive demand caused by the expected increase in prices; – for some rare and expensive goods (gold, jewelry, antiques, etc.), which are a means of investing money; – when switching demand for better and more expensive goods. The basic point in the study of the process of supply and demand is to determine the point of market equilibrium. Market equilibrium is the balance between the opposite directions of producers and consumers in the system of commercial activity. A balanced price is an important commodity market indicator. Excess or shortage of goods in the commodity market is difficult to determine, and information about prices is available to both producers and consumers. It is important for enterprises to determine the quantitative impact on the magnitude of demand that a change in the price of products, consumer incomes or prices of substitute goods produced by competitors can have. When opening a new commercial enterprise, a correct predictive estimate of the demand for the goods of this firm should be given. It is known that forecasting is a probabilistic scientifically substantiated judgment about the trends of the phenomenon under study in the future. It should be noted that the main sources of information for forecasting demand and future market characteristics are: • extrapolation of tendencies, processes, patterns of development of which in the past and present are quite well known; • model of the process under study, reflecting the expected or desired trends in its development; • human experience and intuition; • The above confirms the fact that: • demand is an important factor in product market research;

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• when opening a new commercial enterprise, a correct predictive estimate of the demand for the goods of this company in the commodity market should be given; • supply and demand appear on the commodity market not spontaneously, but are formed and act according to the relevant laws; • Not in all cases the law of demand is formed and act according to the relevant laws; • Human experience and intuition are among the main sources of information for forecasting demand and future market performance; • It is not possible to obtain statistical data in advance for a certain period of time. Since demand is influenced by more uncertainty factors, we propose the following application of neural networks to predict the demand elasticity coefficient. Recently, neural networks [9] have been used to solve forecasting problems, the application of which is based on the well-known ability of a neural network to approximate arbitrary functions of many variables [10]. Neural networks, due to their approximation abilities, allow solving a wide range of forecasting problems, regardless of their specific content, while being based only on experimental data. When using neural networks, a lot of time and computational resources are spent only at the stage of its training, and the trained neural network finds a solution very quickly, and therefore the method seems to be very promising for practical applications. This work is devoted to the use of neural networks for demand forecasting, in order to determine the demand elasticity coefficient, which will allow commercial enterprises to give a correct predictive estimate of the demand for their goods in the commodity market. The work is structured as follows. The introduction discusses the features of demand forecasting in the commodity market and substantiates the relevance of using neural networks (which is more adequate to the market model in the presence of uncertainty factors) for their forecasting than the trend extrapolation methods that are actively used in solving economic problems. Section 2 describes basic concepts such as demand elasticity, radial basis neuron, and neural networks and regression neural networks. Section 3 discusses the issue of choosing a neural network for approximating and predicting the elasticity coefficient of demand for food and non-food products using data for 2009–2020 [11, 12]. The results obtained are described in the conclusion section.

2 Basic Definitions Let us present the following basic definitions for solving the stated problem. Definition 1. Coefficient of Price Elasticity of Demand. The measure of the response of one value to a change in another is called elasticity. Elasticity measures the percentage change in one economic variable when another changes by one percent. In this regard, it is easy to see that price elasticity of demand, shows how much the quantity demanded for a product will change in percentage terms when its price changes by one percent.

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If we denote the price P, and the quantity demanded Q, then the coefficient of price elasticity of demand Er is equal to: EP =

Q ; P

(1)

where  is the change in demand, %;  price change, %; The elasticity coefficient is defined as the ratio of the increase in demand to the increase in price: Ep =

P1 − P0 Q1 − Q0 P1 + P0 Q1 − Q0 .100 : .100 = . Q1 + Q0 P1 − P0 (Q1 − Q0 ) : 2 (P1 − P0 ) : 2

(2)

where Q0 , Q1 —the amount of demand before and after the price change, pcs, P0 , P1 — the initial and new price, rub. If the absolute value of the price elasticity of demand is greater than 1, then we are dealing with a relatively elastic demand. In other words, a change in price in this case will lead to a greater quantitative change in the quantity demanded. If the absolute value of the price elasticity of demand is less than 1, then demand is relatively inelastic. In this case, a change in price will entail a smaller change in the quantity demanded. With an elasticity coefficient equal to 1, one speaks of unit elasticity. In this case, a change in price leads to the same quantitative change in the quantity demanded. Definition 2. Radial Basic Neuron. The structure of a radial basic neuron is shown in Fig. 1. A radial basic neuron (RBN) calculates the distance between the input vectors X and the weight vector W, then multiplies it by a fixed threshold B.

Fig. 1. Radial basic neuron

Definition 3. Radial Basic Neural Network (RBNS). Consists of two layers: a hidden radial base layer of S 1 neurons and an output linear layer of S 2 neurons. The elements of the first layer of the RBNS calculate the distances between the input vector and the weight vectors of the first layer. The threshold vector B and the distances are multiplied element by element. The output of the first layer can be expressed by the formula. A1 = radbas(W − X  · B),

(3)

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where A1 – is the output of the first layer; the radbas function is the radial basis function; W – is the weight matrix of the first layer of the network; X – is the input vector; B – is the threshold vector of the first layer. According to the formula, radial basic neurons with a weight vector close to X will generate values close to 1. If the neuron has an output of 1, then this value will be transferred to its linear neurons by the weights of the second layer. Radial basic neural networks are trained in three stages. Definition 4. Regression Neural Networks (NRS) have the same first layer as RBNS, but the second layer is constructed in a special way. To approximate functions, generalized regression neuron networks are often used. It has as many neurons as there are target < input vector/target vector > pairs. The weight matrix W is the set of target rows. The target value is the value of the function being approximated in the training set. The main task of developing a neural network solution is to choose the optimal architecture of the neural network. In this regard, for the task we will use the following types of neural networks [9]: radial basic (RBF), and generalized regression (GRNN), which are most often used to solve the problem of approximating experimental data. On the other hand, the choice of neural network architecture, which one will be better and more practical, depends in most cases on the conditions of the problem. According to the above, in the next section, we consider the issues of choosing a neural network solution model for predicting the demand elasticity coefficient.

3 Choosing a Neural Network Architecture for Predicting the Coefficient of Demand Elasticity To solve the forecasting problem, consider the statistical data, which are given in [11–15] and presented in Table 1. When calculating the demand elasticity coefficients, formula 2 of definition 1 was used. From the table and from Fig. 2 the elasticity coefficient of 2016 differs sharply from the rest, the reason is that it was in this year that the forced devaluation of the manat was carried out in the republic. Based on this, we will not consider the statistical data of this year due to its spontaneity. Approximation of the demand elasticity coefficient was carried out using the following methods: 1. Exponential smoothing method. As a result, the following approximation formula is obtained: y = 0.0005x6 − 0.0169x5 + 0.2378x4 − 1.6342x3 + 5.7216x2 − 9.6351x + 6.9855, with Correlation Coefficient (R): = 0.88295 Coefficient of Determination (R2 ) = 0.7796. To approximate the trend line, the Toolkit MS Excel was used. 2. A method using a generalized regression (GRNN) neural network with Correlation Coefficient (R): = 0. 98040 Coefficient of Determination (R2 ) = 0. 96119.

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3. A method using a radial basic neural network, in which Correlation Coefficient (R): = 1.0 Coefficient of Determination (R2 ) = 1.0. Based on the newrb function, a radial basis neural network (RBNN) was created to approximate the points, which are given in Table 1. A fragment of the source code of the constructed network is described below: e = 0.002; % target RMSE (Root mean squared error) Sp = 1; % scatter value of the radial basis neural network. % definition of the sequence of arguments of the approximated function P. P = [99.9000 106.1000 108.7000 100.9000 101.9000 101.8000 105.4000 114.5000 102.0000 102.9000 103.6000; 108.4906 115.6522 119.5489 110.6918 111.9318 111.6751 116.8182 116.8874 105.0992 106.1995 102.0305]; % determination of the values of the approximated function corresponding to P. T = [1.6368 0.9420 0.7306 0.9674 0.8853 0.4276 0.7719 1.8006 1.0872 0.8435 −0.1693]; [net tr] = newerb(P,T,e,sp); % creation of a radial base network. %Next, network operation is emulated. The obtained results show that the best model for approximating and predicting the demand elasticity coefficient is a model built based on a radial basic neural network. Table 1. Statistical data for determining the demand elasticity coefficient Years

In % to the previous year Consumer price index: food and non-food products (percentage)

Trade turnover

Coefficient of elasticity (absolute values)

2009

99.9000

108.4906

1.6368

2010

106.1000

115.6522

0.9420

2011

108.7000

119.5489

0.7306

2012

100.9000

110.6918

0.9674

2013

101.9000

111.9318

0.8853

2014

101.8000

111.6751

0.4276

2015

105.4000

116.8182

0.7719

2016

115.6000

117.5097

15.6391

2017

114.5000

116.8874

1.8006

2018

102.0000

105.0992

1.0872

2019

102.9000

106.1995

0.8435

2020

103.6000

102.0305

−0.1693

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Exponential Smoothing 40

Value

20 0 -20

1

2

3

4

5

6

7

8

9

10

11

Data Point Actual

Forecast

Poly. (Forecast)

Fig. 2. Dynamics of changes in the coefficient of elasticity of demand

4 Conclusion According to the constructed models, a forecast was made for the demand elasticity coefficient for 2022, which once again confirms that the demand elasticity coefficient will be lower than 1. This forecast confirms that a price change will entail a smaller change in demand. This statement says that there is currently an unstable situation in the commodity market, which in turn relates to the economic situation in the world. Further research on this topic should be carried out in the field of diagnosing and forecasting commodity markets based on an integrated approach, where, along with economic indicators and extrapolation methods, it is necessary to consider methods using neural networks.

References 1. Gorbunov, V.K.: Mathematical Modeling Of Market Demand, 212 p. (2018). http://conf. svmo.ru/files/2020/ThesesSaransk2020.pdf. (in Russian) 2. Korolev, A.V.: Economic-Mathematical Methods and Modeling, 255 p. (2016). https://public ations.hse.ru/pubs/share/folder/inbly3btur/202051943.pdf. (in Russian) 3. Blagodatskikh, V.G., Yaroshevich, N.Yu.: Research of the sectoral structure of the industrial products market: a dynamic approach. (in Russian) Izvestia USUE, 6(74), p. 102–115 (2017) 4. Zemskova, A.V.: Modeling the behavior of consumers of services. (in Russian) NRU ITMO J. 3, 183–192 (2014) 5. Anurin, V.F.: Marketing research of the consumer market (in Russian) SPb.: Peter. 270 p. (2006) 6. Evstafieva, S.V.: Forecasting market conditions (in Russian) Saratov: FGBOU,70 p. (2013) 7. Zharikov, A.V., Goryachev, R.A.: Forecasting demand and sales volume (in Russian) N/Novgorod: NGU, 39 p. (2017) 8. Luginin, O.E.: Economic and mathematical methods and models: theory and practice with problem solving (in Russian) Rostov n/D: Phoenix (2009) 9. Beale, M.H., Hagan, M.T., Demuth, H.B.: Neural Network Toolbox. User’s Guide. – Natick: Math Works, Inc., 435 p. (2014)

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10. Hornik, K, Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359 (1989) 11. Consumer Price Index (pre-trade, percentage) (in Azerb.). https://www.azstat.org/portal/tbl Info/TblInfoList.do;JSESSIONID=1AD665579B19CAFCD98E7481AF1EB5DF 12. General indicators of trade (in Azerb.). https://www.azstat.org/portal/tblInfo/TblInfoList.do? vw_cd=MT_ATITLE 13. Gardashova, L.A.: Application of DEO method to solving fuzzy multiobjective optimal control problem. Appl. Comput. Intell. Soft Comput. 2014(268), 1–7(2014). https://doi.org/10. 1155/2014/971894 14. Iskandarov, E.K., Ismayilov, G.G., Ismayilova, F.B.: Diagnostic operation of gas pipelines based on artificial neuron technologies. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 787– 791. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_103 15. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, New Jersey (2001)

Introducing Uncertainty-Based Dynamics in MADM Environments Debora Di Caprio1(B)

and Francisco J. Santos Arteaga2

1 University of Trento, 38122 Trento, Italy

[email protected]

2 Universidad Complutense de Madrid, 28223 Madrid, Spain

[email protected]

Abstract. One of the main problems faced by the literature on Multi-Attribute Decision-Making (MADM) methods, which constitutes an inherent assumption that remains undiscussed through the different publications, is the fact that rankings are definitive. As a result, these models do not account for any of the consequences derived from the uncertainty inherent to the evaluations or the potentially strategic reports delivered by the experts. That is, once the ranking is computed, the decision makers (DMs) should select the first alternative, concluding the applicability and contribution of the corresponding model. There are no potential regret or uncertainty interactions triggered by the quality of the reports or their credibility. However, the results of the ranking are not always those preferred by the DMs, who may have to proceed through several alternatives, particularly if the evaluations provided by the experts fail to convey the actual value of the corresponding characteristics. This problem has not been considered in the MADM literature, which has incorporated fuzziness and imprecision to its models, but not accounted for the consequences of credibility in terms of regrettable choices and the combinatorial framework that arises as soon as this possibility is incorporated into the analysis. We define a MADM setting designed to demonstrate the ranking differences arising as DMs incorporate the potential realizations from an uncertain evaluation environment in their choices. We illustrate the substantial ranking modifications triggered by the subsequent dynamic and regret considerations while introducing important potential extensions within standard MADM techniques. Keywords: Uncertainty · MADM · Regret · Credibility · TOPSIS

1 Introduction We study a scenario where a decision maker (DM) receives a set of evaluations regarding the criteria defining different alternatives. However, as is generally the case, the evaluations received exhibit uncertainty regarding their actual realizations [2, 4]. Given the fact that the alternative selected may not perform according to expectations, the ranking obtained should help determining both the initial choice made by the DM as well as any further one in case of suboptimal performance by the initial alternative selected © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 130–138, 2023. https://doi.org/10.1007/978-3-031-25252-5_21

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[3, 5]. Accounting for the effects of uncertainty regarding the potential realizations of the different characteristics defining the alternatives implies formalizing the capacity of the DM to design an evaluation plan based on the current information available about each alternative, the type of uncertainty considered and the set of potential realizations. The DM must account for the different combinatorial possibilities determined by the number of alternatives that he is willing to evaluate whenever the ranking involves regrettable decisions [1]. These sequential considerations must be implemented when defining the decision process within the corresponding MADM technique. We define an ordering environment where the evaluations assigned to the alternatives acknowledge the uncertainty inherent to the reports of the expert(s). We illustrate the substantial ranking modifications triggered by the dynamic and regret considerations formalized while also introducing important potential extensions within the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and, mainly, any similar MADM technique.

2 TOPSIS We start by describing the basics of TOPSIS before extending its main structure to incorporate credibility and regret. As a Multi-Attribute Decision-Making (MADM) technique, TOPSIS is generally applied to rank a series of alternatives based on criteria evaluations received from one or more experts. TOPSIS computes two ideal reference points per criterion, a positive and a negative one, and calculates the relative distance between the characteristics defining each alternative and both reference values. The main steps defining the implementation of TOPSIS are described below. The m alternatives evaluated are denoted by A1 , A2 , ..., Am , while the n criteria applied to perform the evaluations are given by C1 , C2 , ..., Cn . The performance evaluation of alternative Ai , i = 1, ..., m, with respect to criterion Cj , j = 1, ..., n, is denoted by xij and summarized through a decision matrix defined as follows: C1

C2

…

Cn

A1

x11

x12

x1n

A2

x21

x22

… …

x2n

Am

xm1

xm 2

…

xmn

W = [ w1 , w2 ,..., wn ]

The terms wj , j = 1, ..., n, represent the importance assigned by the expert(s) to each criterion j. Given the values composing the decision matrix and the fact that criteria can be either positive or negative, the set of alternatives is ranked through the following steps.

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Step 1. The decision matrix is normalized to allow for a direct comparison across criteria. The evaluations received from the expert(s) are normalized via xij rij =  i

xij2

, i = 1, ..., m, j = 1, ..., n;

(1)

Step 2. Each column of the decision matrix is multiplied by the weight describing the relative importance of each criterion vij = wj rij , j = 1, ..., n;

(2)

giving place to the weighted normalized decision matrix. Step 3. The criteria used to evaluate the alternatives consist of either positive or negative qualities. Ideal positive, vi+ , and negative, vi− , values are computed for each criterion. The vectors summarizing the ideal criteria values are defined as follows   A+ = ν1+ , ..., νn+ (3) with   vi+ = maxj (vij )|j ∈ positive criterion

(4)

  vi− = minj (vij )|j ∈ negative criterion

(5)

when considering the best positive values, and   A− = ν1− , ..., νn−

(6)

where   vi− = mini (vij )|j ∈ positive criterion

(7)

  vi− = maxi (v ij )|j ∈ negative criterion

(8)

when dealing with the worst negative values. Step 4. The distances between the evaluations reported for each alternative and the ideal values, both positive and negative, are given by di+

⎡ ⎤1/2 n  2

νj+ − νij ⎦ , i = 1, ..., m =⎣

(9)

j=1

di−

⎡ ⎤1/2 n  2

νj− − νij ⎦ , i = 1, ..., m =⎣ j=1

(10)

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Step 5. Given the di+ and di− values obtained for each Ai , the position of an alternative within the ranking is determined by its relative distance from the negative ideal solution Ri =

di−

di+ + di−

i = 1, ..., m

(11)

The highest score that may be obtained by an alternative corresponds to a value of Ri = 1, while the lowest one is given by Ri = 0. If the reports were strategic, the rankings obtained would represent the preferences of the expert(s) providing the evaluations received by the DM.

3 An Illustrative Numerical Exercise The effects derived from the incorporation of sequential regrettable decisions are described numerically, using a simple example to illustrate the behavior of TOPSIS. Consider an evaluation framework consisting of three alternatives and two criteria. The following decision matrix summarizes the main characteristics of the strategic problem analyzed. C1

C2

8

0

A1 A2 A3

4 4 0 8 W = [w1 , w2 ] = [0.5,0.5]

Assume that both criteria are desirable, that is, higher values represent more valuable alternatives. The results derived from this numerical setting can be intuitively inferred before solving the model. Clearly, under the standard assumptions applied when implementing TOPSIS, the three alternatives should be equally ranked by the DM. C1

C2

A1

0.4472

0

A2 A3

0.2236 0

0.2236 0.4472

The weighted normalized decision matrix is given by leading to a value of Ri = 21 , i = 1, 2, 3. That is, the DM should be indifferent between the three alternatives. The above intuition and results prevail when defining an uncertain scenario where the evaluations represent the best potential performance of each alternative per criterion, allowing for the actual realizations to be as high as the values reported to the DM. In this

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case, highly valued alternatives are expected to perform better to the extent reported in the evaluations. Consider the following decision matrix. Whose entries correspond to the expected value of the uncertain realizations conditioned by the evaluations of the expert(s), r xik  1 r xr xik dxik , where xik describes the upper domain limit of the uniform distribution 0

ik

defined by the reports received by the DM, such that, for instance, 8 0

r x11

0 1 8 x11 dx11 .

1 r x11 dx11 x11

=

In this case, the same Ri = 21 , i = 1, 2, 3, would also be obtained for all

alternatives. C1

C2

A1

4

0

A2 A3

2 0

2 4

The uncertainty inherent to the evaluations leads to a natural question: what would happen if the DM could consider the potential results from solving this uncertainty when selecting the current alternative. In this regard, what would happen if the initial choice was not optimal, and the DM had to select a different alternative. The answer given by the above model is simple, it does not matter, since all alternatives are equally ranked, and any choice constitutes a perfectly viable strategy. We illustrate how this is not the case if the DM is allowed to consider the potential consequences from his current choice when selecting a given alternative.

4 Perception-Based Evaluation Intervals We differentiate between the evaluations received from the experts and the potential r ∈ X be the evaluation received realizations that may be observed by the DM. Let xik k r ) contained from the expert regarding alternative i and criterion k. Consider the set W − (xik r in Xk , which includes the whole set of potential realizations xik ∈ [0, xik ] that may be r ∈ X . Any potential observation observed by the DM leading to a lower utility than xik k r of xik must be defined with respect to xik , accounting for the uncertainty inherent to the r ]. potential realizations that may be observed by the DM, i.e. [0, xik r − The set W (xik ), defining the potential worsenings that may be observed relative to r ∈ X , equals xik k (12) where S(μ) defines the support of the corresponding density function μ assigned to the k th criterion.

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A similar intuition should be applied when considering negative criteria, with the set of potential realizations defining the worsening being located above the evaluations provided by the experts. 4.1 Value Functions The following functions define the expected utility values received by the DM when observing realizations from alternative i and criterion k and accounting for the possibility of regretting the initial choice and observing alternative j. The combinatorial regret r process defined involves two alternatives and is conditioned by the relative values of xik r . and xjk r

xik r r V (xik , xjk , xik , xjk ) = 0

⎡ 1 ⎢ r ⎣ xik

xik 0

xr

1 r (xik )dxjk + xjk

 jk xik

⎤  1  ⎥ r r ≤ xjk xjk − c dxjk ⎦dxik , xik r xjk (13)

r

xik r r V (xik , xjk , xik , xjk ) =



⎡ r xik

0

1 ⎢ r ⎣ xik

r xjk

xik 0

1 r [xik ]dxik + xik xr

1 r (xik )dxjk + xjk

 jk xik

⎤

(14)

 1  ⎥ r r xjk − c dxjk ⎦dxik , xik > xjk r xjk

To simplify the presentation, we have assumed linear utility functions, u(xik ) = xik , ∀i, k. We have also introduced a cost, c, to penalize the DM for not selecting the most suitable alternative as his first choice and having to proceed with the next one. The number of combinations that must be defined by the DM when accounting for three alternatives equals six, a dimension that continues increasing as additional alternatives are incorporated into the analysis. The costs would also have to be incremented accordingly as additional potentially regrettable alternatives are considered by the DM.

5 Analysis Table 1 presents the set of potential combinations that may be defined based on the three alternatives composing the decision problem. The expected utilities obtained per criterion are determined by the pairs of potential realizations that may be observed when penalty costs are either omitted or incorporated to the value function. The resulting weighted decision matrix absent penalty costs, together with the corresponding Ri values, is given by

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D. Di Caprio and F. J. Santos Arteaga Table 1. Combinatorial evaluations and expected utilities.

Alternatives

C1 values

C2 values

V (C1 )

V (C2 )

V (C1 , c)

V (C2 , c)

A1 A2

([0,8], [0,4])

([0], [0,4])

4.333

2

4.308

1.9

A1 A3

([0,8], [0])

([0], [0,8])

4

4

4

3.9

A2 A1

([0,4], [0,8])

([0,4], [0])

4.333

2

4.258

2

A2 A3

([0,4], [0])

([0,4], [0,8])

2

4.333

2

4.258

A3 A1

([0], [0,8])

([0,8], [0])

4

4

3.9

4

A3 A2

([0], [0,4])

([0,8], [0,4])

2

4.333

1.9

4.308

Ri

C1

C2

A1 A2

0.348

0.161

0.5

A1 A3

0.321

0.321

0.856

A2 A1

0.348

0.161

0.5

A2 A3

0.161

0.348

0.5

A3 A1

0.321

0.321

0.856

A3 A2

0.161

0.348

0.5

The following order is defined among the different pairs of alternatives A1 A3 ∼ A3 A1  A1 A2 ∼ A2 A1 ∼ A2 A3 ∼ A3 A2 . The strict order obtained illustrates how the DM prefers to choose the first and third alternatives over any combination including the second one. This is the case despite the positive potential realizations available when the first or third alternative underperform in one of the evaluation criteria. The symmetry in the evaluations follows from the specific design of the model, while that obtained for the A1 A3 and A3 A1 pairs results from the absence of penalty costs. We introduce these costs below and analyze the resulting evaluation differences. Assume that the value functions incorporate a penalty cost equal to c = 0.1. The following weighted decision matrix – with the corresponding Ri values assigned to each pair of alternatives – is obtained.

C1

C2

Ri

A1 A2

0.248

0.109

0.5

A1 A3

0.230

0.224

0.848

A2 A1

0.245

0.115

0.506

A2 A3

0.115

0.245

0.506

A3 A1

0.224

0.230

0.848

A3 A2

0.109

0.248

0.5

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The order of preferences defined among the alternatives is given by A1 A3 ∼ A3 A1  A2 A1 ∼ A2 A3  A1 A2 ∼ A3 A2 . As in the costless scenario, the DM prefers the first and third alternative over any other combination that includes the second one. However, in this case, the DM considers also the second alternative as a potentially more stable choice before proceeding with either the first or the third one. This change in preferences reflects the introduction of costs, which implies that the choice order determines the expected utility received. The rankings obtained in the three scenarios analyzed are summarized in Fig. 1.

Fig. 1. Ri values across alternatives and regret scenarios.

6 Conclusions We have defined an evaluation framework designed to illustrate the ranking differences arising as DMs incorporate the potential realizations from an uncertain environment in their choices. The combinatorial complexity of the model increases in the number of potential alternatives composing the regret path, which limits the applicability of the model when considering long paths. However, when accounting for two or three regrettable decisions per path, the model remains manageable and can be easily applied to a variety of MADM techniques.

References 1. Di Caprio, D., Santos Arteaga, F.J.: Combinatorial abilities and heuristic behavior in online search environments. Oper. Res. Perspect. 8, 100179 (2021). https://doi.org/10.1016/j.orp. 2021.100179 2. Di Caprio, D., Santos Arteaga, F.J.: A novel perception-based DEA method to evaluate alternatives in uncertain online environments. Comput. Ind. Eng. 131, 327–344 (2019). https://doi. org/10.1016/j.cie.2019.04.007 3. Santos-Arteaga, F.J., Di Caprio, D., Tavana, M.: A self-regulating information acquisition algorithm for preventing choice regret in multi-perspective decision making. Bus. Inf. Syst. Eng. 6(3), 165–175 (2014). https://doi.org/10.1007/s12599-014-0322-8

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4. Santos Arteaga, F.J., Tavana, M., Di Caprio, D.: A new model for evaluating subjective online ratings with uncertain intervals. Expert Syst. Appl. 139, 112850 (2020). https://doi.org/10. 1016/j.eswa.2019.112850 5. Tavana, M., Santos Arteaga, F.J., Di Caprio, D.: The value of information as a verification and regret-preventing mechanism in algorithmic search environments. Inf. Sci. 448–449, 187–214 (2018). https://doi.org/10.1016/j.ins.2018.03.032

Analyzing the Digital Marketing Strategies Role in Post Pandemic Recovery Period Khatira J. Dovlatova(B) Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]

Abstract. Modern information technologies (IT) in business area has brought about important evolution in today’s market place well as formulation of digital markets. Digital markets created new opportunities and chances for various economic businesses and consumers. Utilizing such opportunities require accurate marketing strategies in fuzzy environment according to multi criteria decision making problems. This paper focused on digital marketing strategies within the post pandemic period of organizations in uncertain environment. The article investigated digital marketing strategies within the given criteria for managing the crisis by organizations. The aim of the study is to evolve attribute, methodology how to selecting the most suitable digital marketing tools for a business and market in post pandemic recovery period. To make a decision on given fuzzy problems, multi criteria decision making methods should be used. In this article, fuzzy multi criteria decision making problems with Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods are applied to choose the best digital marketing strategy. The obtained results of solving the given problem which TOPSIS and AHP fuzzy multi criteria decision making methods can be used to choose the most appropriate strategy for companies in post pandemic recovery period. Applied AHP method gives eigenvectors and using them as weights decision maker can solve problem by using TOPSIS method. Keywords: Fuzzy AHP · Fuzzy TOPSIS · Decision making · Eigenvalue · Eigenvector · Digital marketing

1 Introduction Modern digital communication plays a main role in the development of the market economy, which has prearranged the development of new ways of marketing communications and marketing tools. There are different approaches to digital marketing between researchers and this process influences choosing the best marketing strategy in taking into account the given criteria. But in research scientists did not use fuzzy information for analyzing the given situation. A lot of multi criteria decision techniques as (AHP, Analytic Network Processing - ANP, and TOPSIS), mathematical programming

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 139–146, 2023. https://doi.org/10.1007/978-3-031-25252-5_22

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(Linear Programming, Goal Programming or Mixed-Integer Programming) and others are existed for solution of decision-making problems [1–4]. The Fuzzy TOPSIS method represents comparatively suitable practice samples, particularly in actual problems where individual opinions are obtained by linguistic data. For the mentioned goals a fuzzy multi criteria decision making method, which is an extension of the F-TOPSIS approach is used. This paper is focused as the literature is reviewed as stated by the different criteria and methods used for the digital marketing strategy selection problem in fuzzy environment. The scientific approach of this paper is to take into consideration the given criteria for selection the best digital marketing strategy. To solve problems in digital sphere, alternatives are based on various criteria’s necessary to be selected.

2 Preliminaries Definition 1. The Equation with Fuzzy Numbers [5]: bij = (bij,l , bij,m , bij,u ),

 bij = (1, 1, 1)  bij,l > 0 i, j = 1, 2......., n

i = j. (1)

The formula summarizes a fuzzy comparison matrix  B which constitutes the following elements,   1 1 1 1 , i, j = 1, 2, ...n, i = j. (2) = , , bij = bij,u bij,m bij,l bij Definition 2. Determination of Fuzzy Weights [6]:  B ⊗ w˜ = λ˜ l ⊗ w, ˜

(3)

where  B, fuzzy mutual comparison matrix of type [n × m]. Components of the fuzzy matrix  B, fuzzy vector w˜ and fuzzy eigenvalue λ˜ are assumed as triangular fuzzy numbers which may be demonstrated as positioned by w˜ = (wl , wm , wu ), λ˜ = (λl , λm , λu ). Definition 3. Consistency Index (CI) and Consistency Ratio (CR) [7, 8]: ˜ as described in the previous Given the fuzzy eigenvalue problem  B ⊗ w˜ = λ˜ l ⊗ w, part and define the principal fuzzy eigenvalue λ˜ = (λl , λm , λu ) and corresponding fuzzy eigenvectors w˜ = (wl , wm , wu ). For the Bl ,Bm ,Bu matrix calculate the CI and CR according to [9, 10]. Definition 4. Construction of Weighted Normalized Decision Matrix [11]. bij = wj × rij

(4)

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Definition 5. Positive and Negative Ideal Solution. Positive ideal solution F ∗ and negative ideal solution F − for the weighted normalized fuzzy decision matrix can be obtained on base of the weighted normalized grading. Positive ideal solution matrix is defined with formula (5), the negative ideal solution matrix based on formula (6) [12, 13]:   F ∗ = (max bij /j ∈ J ), (min bij /j ∈ J [i = 1, 2, 3, ..., m] = {b1∗ , b2∗ , ..., b1n } (5) and the negative-ideal F − solutions are calculated as follows:   F − = (min bij /j ∈ J ), (max bij /j ∈ J [i = 1, 2, 3, ..., m] = {b1− , b2− , ..., b1N − } (6) Definition 6. Obtaining the Separation Measures for Each Alternative from Ideal and Negative Ideal Alternative Is: Si∗ = [

2  b∗j − bij ]1/2

Si = [

2  b∗j − bij ]1/2

i = 1, ..., n

(7)

Definition 7. Relative Closeness to the Ideal Solution [7]. Ci∗ = Si /(Si∗ + Si )

(8)

3 Statement of the Problem Digital marketing strategies are influenced by different economical processes. The factors influencing digital marketing strategies are analyzed as attribute that has a main role in the global market environment. In a fuzzy environment the pairwise comparison matrix of attribute is exhibited by linguistic factors which are shown by triangular fuzzy numbers. MCDM problem involves 5 criteria and 5 alternatives for digital marketing A1 , A2 , A3 , A4 , A5 . C1 - Budget; C2 - Marketing strategy goals; C3 - The age of the audience; C4 - The company’s staff preference; C5 - frequency. Table 1. Shows the comparison of attributes (criteria) under competency into triangular fuzzy numbers and final step to obtain consistency ratio of this shown fuzzy matrix (1,2). Aim of this paper use the obtaining eigenvectors from consistent matrix as weights of attributes for ranking alternatives in the given decision matrix [8].

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K. J. Dovlatova Table 1. Fuzzy matrix of the criteria

Attribute C1

C2

C3

C4

C5

C1

(1,1,1)

(2.3,3.33,5)

(3.3,5,10)

(1,1,1)

(0.3,0.5,1)

C2

(0.2,0.3,0.4) (1,1,1)

(0.01,0.02,0.03) (0.55,0.56,0.57) (1,2,3)

C3

(0.1,0.2,0.3) (0.2,0.3,0.4)

(1,1,1)

C4

(1,1,1)

(1.75,1.79,1.81) (1.43,1.67,2)

(1,1,1)

(10,11.11,12.5)

C5

(1,2,3)

(0.33,0.5,1)

(0.08,0.09,0.1)

(1,1,1)

(2.5,3.3,5)

(0.5,0.6,0.7)

(0.2,0.3,0.4)

4 Solution of the Problem In research paper we analyzed the best alternative to take into account the given attribute. Fuzzy pairwise comparison matrix of the attribute for multi-criteria problem is given in Table 1 [10, 14]. Stage 1. First stage express the pair-wise comparison reciprocal fuzzy matrix  B bij = for the attribute C1 ,C2 ,…,Cn by evaluating the priority values as fuzzy numbers  B divided by three crisp (bij,l , bij,m , bij,u ), (i, j = 1, 2, ..., n). Given the fuzzy matrix  matrices Cl , Cm , Cu are defined based on [7] as follows: ⎤ ⎤ ⎡ ⎡ 1 b12,l ... b1k,l 1 b12,m ... b1k,m ⎥ ⎥ ⎢ ⎢ ... ... ⎥ Bm = ⎢ ⎥ Bl = ⎢ ⎦ ⎣ 1/b12,u ⎣ 1 ... b2k,l 1 ... b2k,m ⎦ 1/b12,m 1/b1k,u 1/b2k,u ... 1 1/b1k,m 1/b2k,m ... 1 ⎤ ⎡ 1 b12,u ... b1k,u ⎥ ⎢ ... ⎥ Bm = ⎢ ⎣ 1/b12,l 1 ... b2k,u ⎦ 1/b1k,l 1/b2k,l ... 1 Stage 2. Defined matrices are used for obtaining of a system of fuzzy linear homogeneous equations [15]. Bl wl + Bm wm + Bu wu − λl wl − λm wm − λu wu = 0

(10)

where are:Bl = 2Bl + Bm = 3 Bm = Bl + 4Bm + Bu = 6 Bu = Bm + 2Bu = 3 (11) After using (9) we defined three crisp matrices (Tables 2, 3 and 4): .

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Table 2. Bl and Bl

Bl

Bl

1 0.2 0.1 1 1

2.5 1 0.2 1.75 0.33

3.33 0.01 1 1.43 2.5

1 0.55 0.5 1 0.08

0.33 1 0.2 10 1

3 0.7 0.4 3 4

8.33 3 0.7 5.29 1.17

11.67 0.04 3 4.52 8.33

3 1.66 1.6 3 0.25

1.17 4 0.7 31.11 3

Table 3. Bm and Bm Bm

1 0.3 0.2 1 2

Bm 3.33 1 0.3 1.6 0.5

5 0.2 1 1.67 3.33

1 0.56 0.6 1 0.09

0.5 2 0.3 11.11 1

6 1.8 1.2 6 12

20.83 6 1.8 10.72 3.33

33.33 0.12 6 10.1 20.83

6 3.36 3.6 6 0.54

3.33 12 1.8 66.94 6

25 0.08 3 5.67 13.33

3 1.7 2 3 0.29

2.5 8 1.1 36.11 3

Table 4. Bu and Bu Bu 1 0.4 0.3 1 3

5 1 0.4 1.82 1

10 0.03 1 2 5

1 0.57 0.7 1 0.1

1 3 0.4 12.5 1

Bu 3 1.1 0.8 3 8

13.33 3 1.1 5.42 2.5

Stage 3. Eigenvalues of Bl , Bm and Bu are obtained with MATLAB software program: λl = 15.37; λm = 34.85; λu = 21.63. λl , λm , λu are calculated by given formula: ⎧ ⎧ λ = 2λl + λm ⎪  ⎪ ⎪ ⎨ 15.37 = 2λl + λm ⎨ l −69.7 = −2λl − 8λm − 2λu 34.85 = λl + 4λm + λu ⇔ ×(−2) ⇔ λm = λl + 4λm + λu ⇔ ⎪ ⎪ 21.63 = λm + 2λu ⎩ ⎪ ⎩ 21.63 = λm + 2λu λu = λm + 2λu  −48.07 = −2λl − 7λm ⇔ ⇔ λl = 4.96, λm = 5.45, λu = 8.09. (12) 15.37 = 2λl + λm

Stage 4. By homogenous fuzzy linear equations eigenvectors also are obtained (3): Eigenvectors of Bl , Bm and Bu are obtained with MATLAB package: wl =

n n n    w l λl wm w u λu , wm = , wu = ; where sl = wi,l , sm = wi,m , su = wi,u . s l λm sm s u λm i=1 i=1 i=1

(13)

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wl = [−0.45, −0.2, −0.13, −0.81, −0.25] Sl = −1.86 wm = [0.45, 0.21, 0.13, 0.8, 0.29] Sm = 1.9 wu = [0.47, 0.23, 0.13, 0.77, 0.32] Su = 1.93

(14)

Applying the mentioned software program, the following eigenvectors are obtained: wl = [0.23, 0.1, 0.07, 0.41, 0.14], wm = [0.24, 0.12, 0.07, 0.42, 0.15], wu = [0.37, 0.17, 0.1, 0.59, 0.25]

(15)

Stage 5. In accordance to [5] consistency index and consistency ratio for B˜ matrix are obtained by using following formulas [5]: CI =

0.11 5.45 − 5 = 0.11, CR = = 0.1, CR = 0.1 ≤ 0.10 5−1 1.12

(16)

Implementing the offered formula, the eigenvalues, CI and CR ratio are obtained. CR is 0.1, the proposed matrix  B is consistent. Stage 6. Constructed weighted normalized decision matrix (4) (Table 5 and 6). Table 5. Fuzzy matrix of the attribute Attribute C1 C2 C3 C4 C5 weights (0.23,0.24,0.37) (0.1,0.12,0.17) (0.07,0.07,0.1) (0.41,0.42,0.59) (0.14,0.15,0.25) A1

(1,2,3)

(2,3,4)

(1,1,1)

(4,5,6)

(5,6,7)

A2

(5,6,7)

(3,4,5)

(1,2,3)

(2,3,4)

(6,7,8)

A3

(2,3,4)

(2,3,4)

(2,3,4)

(1,1,1)

(2,3,4)

A4

(1,1,1)

(5,6,7)

(7,8,9)

(5,6,7)

(1,1,1)

A5

(1,2,3)

(1,1,1)

(2,3,4)

(3,4,5)

(3,4,5)

Table 6. Weighted normalized Fuzzy matrix of the attribute A1 A2 A3 A4 A5

C1 w (0.018,0.037,0.085) (0.088,0.110,0.199) (0.035,0.055,0.114) (0.018,0.018,0.028) (0.018,0.037,0.085)

A1 A2 A3 A4 A5

C2 w (0.013,0.024,0.046) (0.02,0.032,0.057) (0.013,0.024,)0.046 (0.034,0.048,0.08) (0007,0.008,0.011)

C4 w (0.1,0.128,0.216) (0.05,0.077,0.144) (0.025,0.026,0.036) (0.125,0.154,0.252) (0.078,0.102,0.18)

C3 w (0.004,0.004,0.006) (0.004,0.009,0.018) (0.009,0.013,0.024) (0.03,0.034,0.055) (0.009,0.013,0.024)

C5 w (0.038,0.049,0.095) (0.045,0.057,0.108,) (0.015,0.024,0.054) (0.015,0.024,0.054) (0.023,0.032,0.068)

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Stage 7. Calculated the relative closeness to the ideal solution (8).

Si*

S i'

A1

0.08 0.09

0.13

A1 0.08 0.14

0.21

A2

0.08 0.08

0.12

A2 0.08 0.15

0.23

A3

0.12 0.15

0.24

A3 0.02 0.06

0.10

A4

0.08 0.10

0.20

A4 0.11 0.14

0.23

A5

0.10 0.10

0.16

A5 0.05 0.10

0.16

Ci∗ = Si /(Si∗ + Si ) = [(0.08/(0.08 + 0.08) + 0.14/(0.14 + 0.09) + 0.21/(0.21 + 0.13)]/3 = 0.57 Ci∗ = (0.57, 0.61, 0.25, 0.56, 0.45) Rank the preference order: A2 > A4 > A1 > A5 > A3 . According to calculation of relative closeness to the ideal solution the best alternative (close to the ideal solution) is A2 for using in the post pandemic recovery period.

5 Conclusion The result of contrasting the features of the market and the selection attribute for digital marketing strategies (budget, marketing strategy goals, audience age, competence of the company’s staff, the frequency of use of tools), the main tools are chosen for the post pandemic recovery period. In this paper we use the development of AHP and TOPSIS multi-criteria methods for fuzzy problem. Applying F-AHP and F-TOPSIS multi-criteria decision-making problem is solved. F-AHP method is characterizes with using the pairwise comparison matrices of the attribute and define eigenvectors for using in F-TOPSIS method which can help to choose the best alternative. The suggested method can be implemented for different issues that associated to solve large decision-making problems in business especially in post pandemic recovery period.

References 1. Ayhan, M.B.: A fuzzy Ahp approach for supplier selection problem: a case study in a gearmotor company. IJMVSC 4(3), 11–23 (2013). https://doi.org/10.5121/ijmvsc.2013.4302 2. Dovlatova, K.J.: Decision making in investment by application of the analytic hierarchy process (AHP). B-quadrat verlags, pp. 226–228 (2018) 3. Vargas,V. R.: Using the analytic hierarchy process (AHP) to select and prioritize projects in a portfolio PMI Global Congress – North America Washington (2010) 4. Huseynova, N.F.: Decision making on tourism by using natural language processing. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 741–747. Springer, Cham (2022). https://doi.org/10.1007/978-3030-92127-9_98

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5. Cabala, P.: Using the analytic hierarchy process in evaluating decision alternatives Oper. Res. Dec. 1(1), 1–23 (2010) 6. Kardi Teknomo’s Homepage. https://people.revoledu.com/kardi/tutorial/AHP/purchase.html 7. Nadaban, S., Dzitac, S.: Neutrosophic TOPSIS: A General View. 6th ICCCC (2016). https:// doi.org/10.1109/icccc.2016.7496769 8. Laarhoven, V., P. J. M., Pedrycz, W.: A fuzzy extension of Saaty‘s priority theory. Fuzzy Sets Syst. 11(1–3), 229–241 (1983). https://doi.org/10.1016/S01650114(83)80082-7 9. Saaty, T.L.: Theory and applications of the analytic network process: decision making with benefits, opportunities, costs, and risks RWS Publications, 3rd edn. (2005) 10. Dadasheva, A.: Analysis of consistency of pairwise comparison matrix with fuzzy type-2 elements. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 324–330. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_45 11. Kumar, Dr. A. A.: Factors influencing customers buying behavior. J. Market. Consumer Res. Int. Peer-reviewed J. 27, 30–34 (2016) 12. Aliyeva, K.: Facility location problem by using fuzzy topsis method. Chem. Technol. Control Manag. 3, 55–59 (2018). https://doi.org/10.34920/2018.4-5.55-59 13. Aliyeva, K.: Multifactor personnel selection by the fuzzy TOPSIS method. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 478–483. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_64 14. Aliev, R.A.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iran J. Fuzzy Syst. 18(4), 37–49 (2021). https://doi.org/10.22111/IJFS. 2021.6175 15. Prascevic, Z., Prascevic, N.: Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. Tehniˇcki vjesnik 23(1), 57–64 (2016). https://doi. org/10.17559/TV-20140212113942

Artificial Intelligence and Digital Economy: Development Prospects Ali Abbasov

and Ramin Rzayev(B)

Institute of Control Systems of ANAS, B.Vahabzadeh Street 9, 1141 Baku, Azerbaijan [email protected], [email protected]

Abstract. The digitalization of the state economy implies the formation of a stable and secure information and telecommunications infrastructure for high-speed transmission; the ability to store and process large amounts of data, accessible to all organizations and households; the use of advanced software by government agencies, local governments, and organizations. Obviously, the main benefits from the digitalization of the economy lie in the plane of solving problems related to productivity growth, cost minimization, automation, and production efficiency. It is possible to analyze levels of data that are beyond human understanding, which in turn allows companies to personalize experiences, customize products (services) and identify growth opportunities with speed and accuracy that were not possible before. However, the implementation of the Digital Economy project is only the first step towards creating the image of the economy of the near future. According to the unanimous opinion of experts, the main “actor” that allows consumers and businesses to get the maximum benefit out of the Digital Economy will be Artificial Intelligence, which will significantly change the world and will be used everywhere in the economy. Companies that do not consider the phenomenon of Artificial Intelligence and do not respond to its penetration into day-to-day life are not capable of innovating and reengineering their business models. At best, these companies will lose their competitive advantage, and at worst, they will simply disappear. Keywords: Artificial intelligence · Digital economy · Productivity · Digital skill

1 Introduction Currently, the place and role of Artificial Intelligence (AI) tools and methods in business and the world economy are topics of stormy discussion among specialists in various fields, as it’s perfectly natural that AI could lead to radical, perhaps unprecedented, changes in the setup and work of people. The current level of development of AI methods and tools is not in its infancy, but a significant part of the synergistic effect from its application is still ahead. Today, AI is actively penetrating our daily lives – literally into all spheres of human life, ensuring safety and increasing productivity, considering the new challenges of the present time it offers new transformation opportunities for consumers, business, and society. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 147–153, 2023. https://doi.org/10.1007/978-3-031-25252-5_23

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AI has enormous potential to influence the development of the entire global economy. Combined with key technologies such as the Internet of Things (IoT) [1, 2], Big Data Analytics (BDA) [2] or Blockchain [3], AI can become the basis for economic growth and thus ensure competitiveness and the creation of new high-tech jobs. According to forecasts, due to the application of AI technologies, the volume of the global economy by 2030 may increase by the additional e13.33 trillion, which is significantly higher than the current combined output in China and India. e5.6 trillion of this amount is expected to come from exponential productivity growth, and e7.73 trillion – from consumption spillovers. One of the latest studies by the McKinsey Global Institute provides an analysis of AI technologies influences on the global economy. In particular, [1] analyzes the behavior of large companies and the dynamics of changes in various sectors of the economy in terms of developing approaches to the implementation and development of AI technologies within the digital economy. However, this analysis considers the probable costs that countries, companies, and workers may meet in the transition to AI. Therefore, based on these prerequisites, it becomes important and relevant to study the prospective impact of AI technologies on the digital economy.

2 Artificial Intelligence: Historical Aspect Many ideas appear and disappear very quickly. Some, like one-day butterflies, die almost immediately, others live for years, and still others for decades. But only very few of them determine the direction of the movement of human thought for many centuries. One of the phenomenal human qualities is the thirst for creativity. The inexplicable desire to reproduce oneself, to see one’s reflection in one’s creations, has its roots in the time of rock paintings. Even though our ancestors had no practical benefit from rock paintings, they decorated their own dwellings with sketches of themselves with enviable persistence. With the development of natural intelligence and the creation of more and more advanced tools and technologies of creativity, man recreated himself in clay, stone, metal, with amazing grace and, most importantly, accurately conveying forms. But how could a man stop there? Man has always dreamed of breathing life into his creations – the ability to think and feel. The period that replaced the thousand-year prehistory of human dreams was called “Dawn” by the famous scientist in the field of AI Patrick Winston. In work “AI in the 1980s and Beyond” (1987) he scaled the time axis as shown in Fig. 1. According to P. Winston, the prehistory of AI began in 1842, with the creation of an analytical (difference) engine by Charles Babbage, which largely anticipated the development of computer techniques. However, many researchers believe that the period of prehistory is not limited to the personality of Ch. Babbage but is rooted deep in the times of myths and legends. The period of prehistory lasted until 1960 (naturally, this and all other dates from Fig. 1 are conditional). By this time, supporters of the “top-down” computer approach to understanding AI had computers at their disposal and a lot of contextual ideas had accumulated. In 1953, American mathematician and philosopher Norbert Wiener had already offered the idea that the processes of control and communication in machines, living organisms and societies are similar. The processes of transmission, storage, and processing of information are common to them.

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Fig. 1. The evolution of approaches to the development of AI.

The “Dawn period” is characterized by excessive promises to make humanity happy with the creation of AI. The search for a semblance of a mechanism capable of displaying intellectual abilities in the logical basis of a computer was unsuccessful and, as a result, the period of the dawn of AI was replaced by stagnation. The revival of general interest in AI is associated with the emergence of applied modeling systems, such as expert systems MYCIN, Prospector, etc., as well as Soft Computing technology, formed based on Fuzzy Logic. The formation of Soft Computing technology became possible after the widespread use of Artificial Neural Networks, which are characterized by their adaptive and approximation abilities. If during the previous stages only specialists in cybernetics and computer technology were mainly engaged in the problems of AI, then the commonwealth period is characterized by the establishment of fruitful contacts between them and researchers from other fields of science, especially linguists and psychologists. Finally, P. Winston preferred to call the next period the time of entrepreneurship when work on AI should be put on a commercial basis and provide an economic synergistic effect from implementation. This idea was expressed a long time ago but remains very relevant.

3 Contribution of AI Technologies to Economic Activity According to [4], in the short term, AI technologies can significantly accelerate the pervasive development of the digital economy in the following five main areas: • Computer vision: [5]. • Natural language. • Intelligent virtual assistants as software agents that can solve problems and/or provide services based on commands given in natural language [6]. • Process automation with a high degree of robotization, as a form of business process automation technology based on bots (metaphorical software robots) or digital workers: [7]. • Advanced machine learning: [8]. According to the most conservative estimates, by 2030, about 70% of global companies can implement at least one of these areas of AI. However, less than half of them can fully reclaim all five categories of AI. At the same time, there are several barriers to the rapid adoption and reclaim of AI technologies. For example, it will be difficult for “laggard companies” to achieve the effect of the introduction of AI technologies, since by that time the leading companies will already have time to take advantage of

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the opportunities of AI, which will significantly reduce the ability to attract high-quality specialists from a limited number of talented people. It should be noted several factors that imply the introduction of innovations and specify a new level of competition under the use of AI technologies, which directly affect the growth of the economy in the context of its digitalization. Increase Productivity with Automation. AI technologies can provide a significant increase in productivity in enterprises that use automation industry. Automation of robotic and cognitive processes, machine learning and natural language processing, multi-agent systems of associativity enable companies to maximize their profits by increasing the synergies of investments (labor, capital, and assets). Capital-intensive industries such as manufacturing and transport are the main beneficiaries of productivity gains. Increase in Consumer Demand. As AI technologies adopt the consumer market, in the near future it is most probably may be visible the increase in consumer demand characterized by the availability of personalized and/or higher quality goods and services. Government revenue from consumer demand is projected to substantially outweigh productivity gains. Implementation of Innovations. By its very nature, AI can actively drive innovation because, when combined with BDA technology it can quickly analyze terabytes of data and create the new knowledge. The innovative activity of companies using AI technologies allows them to reduce the costs of ongoing research and development, as well as create favorable opportunities for conducting promising experiments. It is assumed that the affecting of AI on the global (or national) economy will be nonlinear, but over time it may increase at an increasing rate. By 2030, the contribution of AI to world economic growth could be three times or more higher than in the previous five years. A “sigmoid model” of AI adoption and reclaim is probably. As can be seen from Fig. 1, a slow start is predicted due to the significant costs and investments associated with study and implementing these technologies, and then an acceleration is expected due to the synergetic effect of competition and the emergence of additional opportunities along with the innovation process. It would be a mistake to interpret the “sigmoid model” as a “slow burning” phenomenon as argument that the effect of the introduction of AI technologies will be bounded. The volume of benefits for companies and/or countries that are the first to adopt and implement AI technologies will only grow in subsequent years and, first, at the expense of companies and/or countries that do not pay adequate attention to the development and implementation of AI. The capabilities of AI are significant, but there is no doubt that its infiltration can cause disruptions. AI productivity gains probably will not materialize right away. In time, its influence will increase at an accelerated pace. Therefore, the initial benefits of investing in the development and promotion of AI may not be noticeable in the short term. Laborious patience and long-term strategic thinking are needed (Fig. 2).

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Fig. 2. A “sigmoid model” of AI adoption and reclaim.

4 Projected Gap Between Countries, Companies and Workers According to statistical studies, the leaders in the implementation of AI, which are now post-industrial countries, can dramatically increase their undeniable advantage over developing countries. It is predicted that by the implementation of AI, these countries can receive an additional from 20% to 25% of net economic benefits compared to today, while developing countries can receive only about 5%−15%. Currently, in many economically and institutionally developed countries, where the proportion of the elderly population is quite high, there is a slowdown in GDP growth (recession). This is another very important stimulus for the adoption of AI as an additional option that can push the digital economy to higher growth by increasing the labor productivity. Moreover, over the past decades, high rates of remuneration have been established in industrializing countries. In essence, this is another additional incentive for the accelerated adoption of AI technologies that provide a replacement for manual labor and routine work. In developing countries, where there are relatively low rates of remuneration, other methods of increasing productivity are being used as the main factors in economic growth. First, this is the use of advanced experience of post-industrial countries and the restructuring of their industries. Therefore, these countries may have less incentive to implement AI, which, in any case, may offer them relatively less economic benefit than advanced economies. However, some developing countries may be an exception to this rule. For example, China has its own national strategy to become a global leader in the AI technologies supply chain and is already investing heavily in advancing AI. The other example is Azerbaijan speech technology market based on AI Azerbaijan Language Processing Systems will cover up to 60% of population by 2030 [9]. By 2030, the development of AI technologies may lead to a noticeable bundle between companies relative to productivity. A significant gap is predicted between companies that will fully implement AI tools in their enterprises over the next 5–7 years, and companies that have not adopted AI technologies. Companies that have a strong start-up IT base, are inclined to invest in AI, and have a positive view of the business case for

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AI will get benefit disproportionately. Potentially, these companies can double their net income and further to generate about 6% annual net income growth. Based on the exist cost and revenue model, companies that do not implement AI technologies are expected to experience a decrease in cash income of about 20%. One important factor in their predicted decline in profits will be the presence of strong competitive dynamics from companies using AI, which in turn will naturally provoke debate about the unequal distribution of AI benefits. The widening gap between countries and companies will also affect the level of individual workers. The demand for jobs may shift from routine (repetitive) industries to those associated with social and cognitive processes, which will require more digital skills. By 2030, jobs that perform repetitive manufacturing procedures or require low levels of digital skills could drop from 40% to 30% of total employment. On the contrary, the share of competencies in the field of non-repetitive industries that require digital skills will increase from about 40% to more than 50%. It is obvious that the transformation towards an increase in the share of digital skills in work competencies will affect the wages of workers. It is planned that about 13% of the total wage fund can move into categories requiring high digital skills in production with AI, where revenues will rise markedly. However, the share in the total wage fund for categories with low digital skills will decrease from 33% to 20%. Thus, because of the widening gap between competencies with low and high levels of digital skills, the competition for specialists in the development and use of AI tools will intensify. In addition, there is already an excess supply in the labor market for a relatively large proportion of people who lack cognitive and digital skills needed to interact with AI technologies. Under the current conditions, it is already necessary to pursue a decisive policy to overcome the discomfort of citizens from the impending threat of job loss soon as AI technologies are introduced within the digital transformation of the economy. Companies must also take part in find solutions to the challenge of training and retraining specialists to interact with AI tools. People will have to adapt to a new world, where staff turnover may be higher. They are probably must learn new professions and/or permanently update their skills to satisfy the needs of the dynamically changing labor market. Using historic experience of creating high-tech jobs on the base of exist ones and adjusting for lower labor-productivity ratios to account for the probably labor-saving nature of AI technologies by intelligent automation, new jobs created by investment in AI could increase employment by about by 5%. By 2030, the cumulative productivity effect is expected to have a positive effect on total employment of about 10%.

5 Conclusion In addition to the above factors of AI influence, the economy of Azerbaijan in the context of its digitalization will be influenced by micro factors, such as the pace of implementation of AI technologies, and macro factors, such as global connectivity or the structure of the labor market. To adopt the AI technologies within the Digital Strategy for the sectoral development of the Azerbaijan economy it is necessary to increase the domestic costs, primarily at the expense of all sources of public revenue in accordance with their shares in the GDP. Therefore, in the framework of the economy digitalization,

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it is also necessary to formulate a state strategy for the adoption of Artificial Intelligent, for which it is proposed to solve the following priority problems: • formation of an appropriate system for the legal regulation within the digital economy, based on a flexible approach in each area, and the adoption the digital technologies based civil circulation; • formation of a nationwide infrastructure for storing, processing and transmitting data mainly on the basis of competitive national engineering designs, including AI tools; • training highly qualified personnel in the development and use of AI tools with digital skills in management and production; • ensuring information security mainly on the basis of national developments in the storage, processing and transmission of data that guarantee the protection of the interests of the individual, business and the state; • creation of mainly national developments based end-to-end digital technologies; • adoption of digital technologies and platform decisions in the spheres of public management and rendering of services, including in the favors of the population and SME; • transformation of the socio-economic system of the state, including education, healthcare, agriculture, industry, construction, urban economy, transport and energy infrastructure, financial services by the adoption of digital technologies and platform decisions; • considering venture financing and other development institutions, the formation of a unified system for evaluating and financing projects relative to development and/or adoption of AI technologies and corresponding platform solutions.

References 1. Gillis, A.: What is internet of things (IoT)?. https://www.techtarget.com/iotagenda/definition/ Internet-of-Things-IoT 2. Dey, N., Hassanien, A.E., Bhatt, Ch., Ashour, A., Satapathy, S.Ch.: Internet of Things and Big Data Analytics Toward Next-generation Intelligence. Cham, Switzerland (2018) 3. What is Blockchain Technology and How Does It Work? https://www.simplilearn.com/tutori als/blockchain-tutorial/blockchain-technology 4. Notes from the AI frontier: Modeling the impact of AI on the world economy. McKinsey Global Institute. https://www.mckinsey.com/featured-insights/artificial-intelligence/notesfrom-the-ai-frontier-modeling-the-impact-of-ai-on-the-world-economy 5. Szeliski, R.: Computer Vision: Algorithms and Applications, 2nd edn. Springer, New York (2022) 6. What is an Intelligent Virtual Agent (IVA)? https://www.ultimate.ai/blog/ai-automation/whatis-an-intelligent-virtual-assistant-iva 7. AI interns: Software already taking jobs from humans. New Scientist. https://www.newscient ist.com/article/mg22630151-700-ai-interns-software-already-taking-jobs-from-humans/?ign ored=irrelevant#.VY2CxPlViko 8. Shalev-Shwartz, S., Ben-David, S.: Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press (2014) 9. Abbasov, A., Fatullayev, R., Fatullayev, A.: Speech technology market in Azerbaijan. American J. Manag. 21(3), 95–101 (2021). https://doi.org/10.33423/ajm.v21i3.4365

Evaluation of Logistics Services of Airlines in the Azerbaijan Passenger Transportation Market Sevil Imanova1,2(B) 1 Baku Engineering University, Khirdalan AZ010, Azerbaijan

[email protected] 2 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku AZ1010, Azerbaijan

Abstract. The high-quality and stable functioning of civil air transport contributes to the full development of the economy of any state and is one of the important indicators of the quality of people life. Nowadays development of the civil air transportation sector of the economy is characterized by excessively fierce competition, especially in the provision of services both directly at airports and during flights. At the same time, the quality of services for the transportation of passengers should, to the maximum extent, satisfy the constantly growing requirements of consumers. The article considers a combined approach to a multi-criteria assessment of the competitiveness of airlines operating in the passenger transportation market in Azerbaijan, based on expert data on the levels of services obtained in the course of surveys of different categories of passengers. Within the framework of this approach and the selected system of indicators of the airline’s competitiveness, a methodology for assessing and ranking airlines is applied, based on the adaptation of the considered expert-fuzzy analysis methods, as well as the methods of comparative analysis of Pareto and Borda. British Airways, Lufthansa, Turkish Airlines and AZAL, which are the most active in the passenger air transportation market in Azerbaijan, are considered as alternatives to be evaluated. Keywords: Airline · Logistic service · Competitiveness factor · Fuzzy set · Fuzzy inference

1 Introduction Information support for effective management and development of operational technologies to improve the quality of service meets the requirements of air passengers requires the use of new scientifically based (innovative) approaches to ensure the permanent growth of the airline’s competitiveness based on a multi-criteria assessment of the level of customer service quality. One of these approaches is the expert-fuzzy analysis of relevant data, which provides the solution of weakly structured problems and describes the behavior of a similar system of a humanistic type. The current level of development of the theory of fuzzy sets and fuzzy logic makes it possible to take into account an increasing number of not only metrizable (quantitative), but also non-metrizable (weakly © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 154–163, 2023. https://doi.org/10.1007/978-3-031-25252-5_24

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structured) parameters that significantly affect the quality of logistics services and offer a modern, more adequate and combined method for assessing the quality of service for air passengers. Based on these prerequisites, the relevance of developing methods for assessing the logistics services of airlines becomes obvious.

2 Statement of the Problem The competence requirements of approaches to the formation and assessment of the level of competitiveness of an airline consist in the study of multidimensional evaluated factors and their use in the formation of airline ratings. In other words, the assessment of the level of competitiveness of an airline is a multi-criteria procedure that implies the application of a compositional rule for aggregating the assessment for each of the selected influence factors. Nowadays, there is no single approach to the methodology for calculating the rating of an airline, as there are different points of view regarding the composition of factors that have a significant impact on the level of competitiveness of an airline. For example, some researchers consider the competitiveness of airlines at the level of airports and, in fact, the airlines themselves. In particular, at the levels of airports and airlines, various authors summarize and classify all external and internal factors that affect the competitiveness of airlines. Including in accordance with the requirements of the International Air Transport Association IATA. In the framework of this research the consumer assessment of the attractiveness of an airline is derived from the consideration that when choosing an airline (provided that there is equilibrium in terms of other indicators), the one with the ratio of the fare to the useful effect received by the passenger is less than in other airlines. However, in practice, the criteria by which a potential passenger evaluates and chooses the airline that suits him include a much larger number of indicators than the size of the air fare. Testing and comparative analysis of the adequacy of the proposed approaches will be carried out on a hypothetical example of a group of airlines, which we will conventionally denote as: a1 , a2 , . . . , a10 . From the point of view of making decisions on the subject of assessing attractiveness, these airlines are alternatives, the level or competitiveness of which is assessed by experts from among different categories of airline passengers according to the above variables: x1 , x2 , . . . , x5 . For evaluation the logistics services of British Airways, Lufthansa, Turkish Airlines and AZAL, we used the Fuzzy Delphi method, where the assessment data of Internet expertise obtained from different categories of air passengers were used as an information base. To evaluate airlines ak (k = 1 ÷ 4) using the Fuzzy Delphi method, the following variable indicators were chosen as the basis: x1 – air ticket price; x2 – airline reliability; x3 – frequency of flights; x4 – service on board; x5 – aircraft type. Based on these indicators as evaluation criteria, a questionnaire was compiled and experts were selected from among different categories of passengers who actively use the services of the listed airlines. Each of the independent experts was asked to individually evaluate each of these airlines on a 100-point scale for its satisfaction with respect to the criteria xi . After that, the expert assessments of the airlines were analyzed for their consistency (or inconsistency) according to the rule: the maximum allowable difference between

156

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two expert opinions on the airline’s satisfaction with respect to the criterion xi (i = 1 ÷ 5) should not exceed 50 units. In particular, by applying the Fuzzy Delphi method with respect to the criterion “Reliability of the airline” for these airlines, evaluation concepts are formed in the form of corresponding fuzzy sets by means of the identified membership functions in a triangular form, which are shown in Fig. 1. British

Lutfhansa

1,2

1,2

1

90

1

0,8

91

0,8

0,6

Series1

0,6

0,4

0,4

0,2

0,2

0

80 0

20

40

60

100 100

80

Series1

0

120

80 0

20

40

60

Turkish

80

100 100

120

Azal

1,2

1,2

82

1

1

0,8

80

0,8

Series1

0,6

0,6

0,4

0,4

0,2

0,2

0 0

20

40

60

70 80

100 100

Series1

0

120

60 0

20

40

60

80

95 100

Fig. 1. Membership functions of the fuzzy set “Reliability” for airlines.

Based on the application of the Fuzzy Delphi method in [1], for all criteria, aggregated expert estimates of airline logistics services were established, which are summarized in Table 1. Table 1. Aggregated expert assessments of airline logistics services. Airlines

Competitiveness factors Ticket price

Reliability

Frequency

Service

Type of aircraft

x1

x2

x3

x4

x5

a1 – British airways

86

90

88

87

89

a2 – Lufthansa

90

91

92

93

90

a3 – Turkish airlines

92

82

86

89

86

a4 – Azal Avia

85

80

84

86

88

Based on the preliminary results, it is necessary to develop a combined approach to the evaluation of logistics services, taking into account non-metrizable indicators of the competitiveness of airlines in the air transportation market.

3 Estimation of Airlines Using a Fuzzy Inference System Before creating an analytical model for a multi-criteria assessment of the levels of competitiveness of airlines, it is advisable to build an appropriate reasonable gradation scale.

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To build a fuzzy inference system (FIS) regarding the assessment of the satisfaction of airlines ak (k = 1 ÷ 4) for their compliance with the criteria x i (i = 1 ÷ 5) a verbal model was chosen as the basis, formulated in the form of the following information fragments: d 1 : “If the price of the ticket and the reliability of the airline are acceptable, then it is satisfactory”; d 2 : “If, in addition to the above, the frequency of air transportation is acceptable - May, then the airline is more than satisfactory”; d 3 : “If the price of the ticket, the reliability and frequency of air transportation, the maintenance service, and the fleet of airliners are acceptable, then such an airline is impeccable”; d 4 : “If the ticket price, reliability, service, and the fleet of airliners are acceptable, then this airline is very satisfactory”; d 5 : “If an airline’s ticket price, reliability, fleet are acceptable, but the service it offers is unacceptable, then the airline is still satisfactory”; d 6 : “If the price of the ticket, the frequency of air transportation and the fleet of airliners are unacceptable, then the airline is unsatisfactory.” Assuming the set of airlines U = {a1 , a2 , a3 , a4 } to be a universal set, fuzzification of input qualitative characteristics can be carried out using fuzzy sets of the form Ai = {μAi (a1 )/a1 , μAi (a2 )/a2 , μAi (a3 )/a3 , μAi (a4 )/a4 }

(1)

where μAi (ak ) (k = 1 ÷ 4) are the values of the membership functions of the corresponding fuzzy sets Ai , reflecting the qualitative criteria for assessing the satisfaction of airlines. As a membership function that determines the ratio of the airline ak (k = 1 ÷ 4) to the qualitative assessment criterion Ai , a Gauss function of the form is chosen: μAi (ak ) = exp{−[ei (ak ) − 100]2 /σi2 }

(2)

where ei (ak ) is the consolidated assessment of experts regarding the airline ak , made on a 100-point scale for the satisfaction of the airline in terms of the i -th feature x i (i = 1 ÷ 5) (see Table 1); σ i 2 = 1089 is the density chosen empirically, which is the same for all cases of term fuzzification. Taking into account this formulation, based on the verbal model d 1 ÷ d 6 FIS in symbolic form looks like this: d 1 : (x 1 = A1 ) & (x 2 = A2 ) ⇒ (y = S); d 2 : (x 1 = A1 ) & (x 2 = A2 ) & (x 3 = A3 ) ⇒ (y = MS); d 3 : (x 1 = A1 ) & (x 2 = A2 ) & (x 3 = A3 ) & (x 4 = A4 ) & (x 5 = A5 ) ⇒ (y = P); d 4 : (x 1 = A1 ) & (x 2 = A2 ) & (x 4 = A4 ) & (x 5 = A5 ) ⇒ (y = VS); d 5 : (x 1 = A1 ) & (x 2 = A2 ) & (x 4 = ¬A4 ) & (x 5 = A5 ) ⇒ (y = S); d 6 : (x 1 = ¬A1 ) & (x 3 = ¬A3 ) & (x 5 = ¬A5 ) ⇒ (y = YS), where ∀j ∈ J = {0, 0.1, 0.2, …, 1} fuzzy sets from the right parts of the rules are restored by means of the corresponding membership functions [2]: S = satisfactory

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(airlines),M S (j) = j; MS = more than satisfactory, M MS (j) = j(1/2) ; P = perfect, 1, j = 1, VS = very satisfactory, M VS (j) = j2 ; US = unsatisfactory, μP (j) = 0,j < 1; M S (j) = 1 − j. The implementation of the rules using the Lukasiewicz implication μU×J (u, j) = min{1, 1 − μU (u) + μJ (j)} gave the desired functional solution in the matrix form

a1 R = a2 a3 a4

0 0.1647 0.0877 0.2573 0.3074

0.1 0.1647 0.0877 0.2573 0.3074

0.2 0.1647 0.0877 0.2573 0.3074

0.3 0.1647 0.0877 0.2573 0.3074

0.4 0.1647 0.0877 0.2573 0.3074

0.5 0.1647 0.0877 0.2573 0.3074

0.6 0.1647 0.0877 0.2573 0.3074

0.7 0.1647 0.0877 0.2573 0.3074

0.8 0.1647 0.0877 0.2573 0.3074

0.9 0.1647 0.0877 0.2573 0.3074

1 0.1647 0.9429 0.9429 0.8761

,

where, according to [3], the elements of the k-th line, as the values of the membership function of the fuzzy subset of the discrete universe J, form a fuzzy conclusion regarding the satisfaction of the k airline (k = 1 ÷ 4) in the context of consolidated expert assessments for its compliance factors x i (i = 1 ÷ 5). After defuzzification of these conclusions, numerical estimates of the logistics services of airlines were obtained, which are summarized in Table 6.

4 Identification of Weights of Evaluation Criteria The assessment of the attractiveness of an airline is made by experts based on the analysis and comparison of specific values of the criteria of the companies under study. This assessment will be the more accurate, the better the experts know the needs of consumers in this segment of the transportation market. Assume that by independent questioning of 15 passengers from different categories who make permanent trips on certain routes, expert assessments of the degree of importance of airline attractiveness factors x i (i = 1 ÷ 5) are determined. Each expert-passenger is provided with a questionnaire, where he is asked to place the variable xi according to the principle: the most important variable is designated by the number “1”, the next less important - by the number “2” and then in descending order of importance. After checking the rank scores for consistency, in the process of Internet expertise, the values of the normalized scores of the generalized weights of the airline attractiveness variables x i (i = 1 ÷ 5) are set, which are summarized in Table 2. To calculate the average value α i for the i group of normalized estimates of variables x i , an iterative equality of the form [4] weighted by the degrees of expert competence is used: m αi (t + 1) = wj (t)αij (3) j=1

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Table 2. Expert normalized estimates of generalized variable weights x i . Experts

Estimated variables x i (i = 1 ÷ 5) and their normalized values (α ij ) x1

x2

x3

x4

x5

01

0.300

0.250

0.225

0.150

0.075

02

0.300

0.250

0.225

0.075

0.150

14

0.300

0.225

0.250

0.075

0.150

15 

0.300

0.250

0.150

0.225

0.075

4.350

3.550

2.800

2.325

1.975

…

where wj (t) is the weight characterizing the degree of competence of the j expert (j = 1 ÷ m) at time t. For each iteration step, the weights that determine the degrees of expert competence are established based on the following equalities: n ⎧ ⎨ wj (t) = [1/η(t)] αi (t) · αij (j = 1, m − 1), i=1 m m ⎩ wm (t) = 1 − wj (t), wj (t) = 1, j=1

j=1

where η(t) is a normalizing factor that ensures the transition to the next iteration step, which is determined by the formula n m η(t) = αi (t)αij . i=1

j=1

The process of determining group estimates of normalized values is iterative in nature, which ends when the following condition is met: {|αi (t + 1) − αi (t)|} ≤ ε, where ε is the allowable accuracy of calculations, which is set in advance by the user. Thus, using (3) in the 3rd approximation, normalized estimates of the generalized weights for groups i = 1 ÷ 5: α 1 (3) = 0.28995, α 2 (3) = 0.23760, α 3 (3) = 0.18721, α 4 (3) = 0.15449, α 5 (3) = 0.13075. The conclusion of the integral assessment of the consumer index, located in the range from 0 to 100, was carried out using the evaluation criterion [4]: R = 100 ×

5 i=1

αi (3)ei /[max{

5 i=1

αi (3)ei }]

(4)

where ei is an expert assessment of the airline’s satisfaction with respect to the i-th factor x i . At the same time, the minimum value of the R index reflects the minimum level of attractiveness of the airline, and vice versa, the maximum value of the index indicates the highest level of its competitiveness. As a result of applying (4), total values were obtained, which are summarized in Table 6.

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S. Imanova

5 Estimating Airlines Using the Fuzzy Maximin Convolution Method As criteria for assessing the satisfaction of airlines ak (k = 1 ÷ 4), we use the evaluation concepts “ACCEPTABILITY” as one of the possible terms of linguistic variables x i (i = 1 ÷ 5). Based on (1) and (2), these terms are reflected by the corresponding fuzzy sets of the form Ai on a finite set of estimated airlines {a1 , a2 , a3 , a4 } in the following: • • • • •

ACCEPTABILITY (ticket price): A1 = {0.8353/a1 , 0.9123/a2 , 0.9429/a3 , 0.8133/a4 }; ACCEPTABILITY (reliability): A2 = {0.9123/a1 , 0.9283/a2 , 0.7427/a3 , 0.6926/a4 }; ACCEPTABILITY (frequency): A3 = {0.8761/a1 , 0.9429/a2 , 0.8353/a3 , 0.7905/a4 }; ACCEPTABILITY (service): A4 = {0.8563/a1 , 0.9560/a2 , 0.8948/a3 , 0.8353/a4 }; ACCEPTABILITY (type of aircraft): A5 = {0.8948/a1 , 0.9123/a2 , 0.8353/a3 , 0.8761/a4 }.

Next, a set of optimal alternatives [5–10] A is established by intersecting fuzzy sets containing airline scores according to the ACCEPTABLE criterion in the form:A = A1 ∩ A2 ∩ A3 ∩ A4 ∩ A5 , where the airline with the maximum degree of belonging to the fuzzy set A is considered satisfactory. In this case, the operation of crossing fuzzy sets corresponds to the choice of the minimum value for the alternative ak (k = 1 ÷ 4): μA (ak ) = min{μAi (ak )}. As a result, the set of optimal alternatives is formed as follows: i

A = {min{0.8353, 0.9123, 0.8761, 0.8563, 0.8948}, min{0.9123, 0.9283, 0.9429, 0.9560, 0.9123}, min{0.9429, 0.7427, 0.8353, 0.8948, 0.8353}, min{0.8133, 0.6926, 0.7905, 0.8353, 0.8761}} = {0.8353, 0.9123, 0.7427, 0.6926}. The most competitive airline is determined from the vector of priorities relative to alternative airlines: max{μA (ak )} = max{0.8353, 0.9123, 0.7427, 0.6926, the market of passenger air transportation in Azerbaijan is the airline a2 (Lufthansa), which corresponds to the value of 0.9123. The subsequent ranking of airlines is built in descending order: a1 (British Airways) → 0.8353, a3 (Turkish Airlines) → 0.7427, a4 (AZAL) → 0.6926. In the case of different degrees of importance of indicators x i (i = 1 ÷ 5), defined above as weights α i (3) (i = 1 ÷ 5), the set of optimal alternative airlines {a1 , a2 , a3 , a4 } is determined by intersecting fuzzy sets Ai : A = Aα1 1 ∩ Aα2 2 ∩ Aα3 3 ∩ Aα4 4 ∩ Aα5 5 , where the k-th airline (k = 1 ÷ 4) is considered to be the best, for which the condition: μA (ak ) = max{μA (ak )} Then, taking into account the weighted criteria Ai (a), the set of optimal alternatives is: A = {min{0.83530.28995 , 0.91230.23760 , 0.87610.18721 , 0.85630.15449 , 0.89480.13075 }; min{0.91230.28995 , 0.92830.23760 , 0.94290.18721 , 0.95600.15449 , 0.91230.13075 }; min{0.94290.28995 , 0.74270.23760 , 0.83530.18721 , 0.89480.15449 , 0.83530.13075 }; min{0.81330.28995 , 0.69260.23760 , 0.79050.18721 , 0.83530.15449 , 0.87610.13075 } = {0.94915, 0.97373, 0.93175, 0.91643}. As in the previous case, the most satisfactory airline is found from the expression: max{μA (ak )} = {0.94915, 0.97373, 0.93175, 0.91643}. Among the components of this

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vector, 0.97373 is the largest, which corresponds to the alternative a2 . This means that the best airline in terms of consumer appeal is Lufthansa. The subsequent ranking of airlines is built in descending order as: a1 (British Airways) → 0.94915, a3 (Turkish Airlines) → 0.93175, a4 (AZAL) → 0.91643.

6 Evaluation of Airlines by Pareto Rules and Bord Method The Pareto rule provides for the ranking of alternatives by determining pairwise preferences regarding evaluation criteria. For airlines ak (k = 1 ÷ 4) the results of the comparative analysis are summarized in Table 3. The most preferred airline is a2 , which contains 2 columns that do not contain the “−” character: columns a1 and a4 . Airline a1 contains only one column that does not contain a “−” character: column a4 . The remaining two airlines, namely a3 and a4 , do not contain any columns with a “+” symbol at all. This means that airline a2 is preferred over airlines a1 , a3 and a4 . It is followed by the airline a1 , which includes only one column a4 that does not contain the “−” symbol, which determines the preference for a1 over a3 and a4 . To compare a3 and a4 , the Pareto rule is again applied, which, due to its triviality, quite easily establishes the advantage of a3 over a4 . Table 3. Preference table based on pairwise comparisons of airlines. a1 a2 a3 a4 a3 a1 a2 a4 x1 − − + x1 + + + x2 − + + x2 − − + x3 − + + x3 − − + x4 − − + x4 + − + x5 − + + x5 − − − a2 a1 a3 a4 a4 a1 a2 a3 x1 + − + x1 − − − x2 + + + x2 − − − x3 + + + x3 − − − x4 + + + x4 − − − x5 + + + x5 − − +

Next, Bord’s selective rule is applied, according to which airlines are ranked by each factor x i (i = 1 ÷ 5) in descending order with the assignment of appropriate ranks to them (Table 4) and then the total rank is calculated for each decision (Table 5). The airline with the highest total rank is considered the best. As can be seen from Table 5, Lufthansa received the highest total score, which positions it as the best airline in the five-factor assessment of the selected alternatives.

162

S. Imanova Table 4. Airline ranking in descending order.

Ranking

Airline benchmark x1

x2

x3

x4

x5

4

a4

a4

a4

a4

a3

3

a1

a3

a3

a1

a4

2

a2

a1

a1

a3

a1

1

a3

a2

a2

a2

a2

Table 5. Airline ranking using the Borda Method. Airlines

Project comparative evaluation indicators

British airways

x1

x2

x3

x4

x5

3

2

2

3

2

Total points

Order

12

2

Lufthansa

2

1

1

1

1

6

1

Turkish airlines

1

3

3

2

4

13

3

AZAL

4

4

4

4

3

19

4

Table 6. The results of the assessment of airlines in the air transportation market in Azerbaijan. Airlines

Fuzzy Delphi

FIS

Estimate

Estimate

Order

MaxMin convolution: Order

For the For the homogeneous case inhomogeneous case Estimate

Order

Estimate

Order

British Airways

87.87

2

0.9080

2

0.8353

2

0.9492

2

Lufthansa

91.08

1

0.9535

1

0.9123

1

0.9737

1

Turkish Airlines

87.25

3

0.8635

3

0.7427

3

0.9318

3

AZAL

84.17

4

0.8246

4

0.6926

4

0.9164

4

7 Conclusion As a result of applying the Fuzzy Delphi, FIS method, as well as the fuzzy maximin convolution method, integral satisfaction scores for British Airways, Lufthansa, Turkish Airlines and AZAL were obtained for the entire set of criteria x i (i = 1 ÷ 5). A comparative analysis of the results obtained by the three methods is presented in Table 6, from which it can be seen that the results completely coincide with respect to the positions

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of airlines. Moreover, this ranking is also confirmed by the results of evaluating these airlines using the rather trivial Pareto rule and the Borda Method.

References 1. Imanova, S.N.: Application of fuzzy Delphi method for evaluation of service quality of airlines in Azerbaijan. In: Forth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, Turkey (2007) 2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1965) 3. Rzaev, R.R.: Analytical Decision Support in Organizational Systems. Saarbruchen Palmerium Academic Publishing, 306 p. (2016). (in Russian), (in German) 4. Mardanov, M., Rzayev, R.: One approach to multi-criteria evaluation of alternatives in the logical basis of neural networks. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F. (eds.) ICAFS 2018. AISC, vol. 896, pp. 279–287. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_38 5. Andrejchikov, A.B., Andrejchikova, O.H.: Analysis, synthesis, planning of decisions in the economy. Finance and statistics, 368 p. (2000). (in Russian) 6. Aliev, R.A., Aliev, B.F., Gardashova, L.A., Huseynov, O.H.: Selection of an optimal treatment method for acute periodontitis disease. J. Med. Syst. 36(2), 639–646 (2012). https://doi.org/ 10.1007/s10916-010-9528-6 7. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., et al. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_10 8. Aliev, R.A., Pedrycz, W., Kreinovich, V., Huseynov, O.H.: The general theory of decisions. Inform. Sci. 327(10), 125–148 (2016). https://www.sciencedirect.com/science/article/abs/pii/ S0020025515005885 9. Aliev, R.A., Pedrycz, W., Alizadeh, A.V., Huseynov, O.H.: Fuzzy optimality based decision making under imperfect information without utility. Fuzzy Optim. Decis. Mak. 12(4), 357– 372 (2013). https://doi.org/10.1007/s10700-013-9160-2 10. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000Research 11(310), 1–24 (2022). https://doi.org/10.12688/f1000r esearch.109709.1

Customer Characteristics in Digital Marketing Model Gunay E. Imanova1(B)

and Gunel Imanova1,2

1 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku, Azerbaijan

[email protected], [email protected] 2 Azerbaijan State University of Economics, Istiglaliyyat Street 6, AZ1001 Baku, Azerbaijan

Abstract. Growth in e-commerce marketing and customers’ interest toward online shopping have changed the traditional way of ‘try and buy’ to online ordering of products. As a result, most of the brick and mortar companies and startups tend to strengthen their digital marketing strategies by creating e-commerce sites that appeal to customers. Online seller companies can understand their customers’ needs, wants, and preferences by analyzing the customer characteristics that influence their purchase decisions. In this research, personal characteristics that affect the consumer buying decision in online shopping are identified, weighted and analyzed using triangular fuzzy numbers and fuzzy AHP method. Investigated criteria are provided as customer’s age, occupation, economic situation, lifestyle, and personality and self-concept. Furthermore, based on the research it is identified that personal characteristics of customers have a significant impact in online retailing. Keywords: Digital marketing · Fuzzy AHP · Decision making · Consumer buying behavior · E-commerce

1 Introduction Today, marketing practices are highly affected by the global events such as pandemic, lockdown, economic crisis and following inflation, advanced and accessible technology, digital marketing and so forth. Therefore, dynamic marketing environment makes competition even fiercer, and companies become more customer-oriented. As a result, acquiring timely and relevant information about customer needs, wants and preferences, potential opportunities and threats, and competitive intelligence, need digitalization in marketing. Digitalization offers advantages such as reaching broader customer base and segments without; space restrictions for selling products, and country borders [1]. E-commerce marketing as part of digital marketing is the transaction of product and services and realized through B2B, B2C, B2E, G2C, C2C variations [2]. B2C or business to customer variant is the most popular one in e-commerce, where the companies such as Amazon, Alibaba, eBay, or Spotify sell products and services to the customers. Use of online shopping gained even more popularity after pandemic and lockdowns. Online seller companies should be aware of the several characteristics of customers that © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 164–171, 2023. https://doi.org/10.1007/978-3-031-25252-5_25

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can affect the consumer buying behavior and decision. Main characteristics that affect the consumer behavior can be classified as cultural, social, personal and psychological characteristics [3, 4]. Cultural factors involve sub topics such as culture and social classes [3]. Culture is reflected on customers’ needs and wants through the learned set of beliefs and values. Social factors comprised of factors such as family, groups, social roles and status [3]. Personal factors involve the influences such as customer’s age, occupation, economic situation, lifestyle and personality (and self-concept) [3]. Personal factors and their influence on online shopping behavior will be discussed throughout the research. Psychological factors comprised of factors such as perception, motivation, learning, beliefs and attitudes that further influence the consumer buying decision [3]. In this paper, main aim is to analyze and identify the relative importance of each pair of criteria based on triangular fuzzy numbers and fuzzy AHP method to understand the effect of several customer characteristics on consumer behavior during online shopping. Unfortunately, there are limited number of research about this subject and uncertainty and reliability is not always taken into account. The remaining part of the paper is structured as following. In Sect. 2, preliminary information is presented, and it is followed by the statement of the MCDM problem. In Sect. 4, solution method of the MCDM problem with an illustrative case is provided. Finally, conclusion points for the study are presented in Sect. 5.

2 Preliminaries Definition 1. Fuzzy numbers [5, 6]: Decision making process tends to be uncertain within the real-world environment, regarding the possibility of the given values. Besides, possible degrees of uncertainty or impreciseness related to given values remain unknown to the decision maker, because of the ill-defined data. In a fuzzy set, for each possible value of x, the assigned degree is given as μ(x)  [0.1]. x0 ∈ R, where μM (x0 ) = 1

(1)

  for any 0 ≤ α ≤ 1, Aα = x, μAα (x) ≥ α is a closed interval, where F(R) Definition 2. Random variables [5]: Random variables can be classified into two groups as continuous random variables and discrete random variables. Continuous variable which can be shown by X, can take infinite numerical outcomes of possible values of x. However, a discrete random variable, X can only be presented with countable distinct values. ˜ l , am , au ) is used to indicate Definition 3. Triangular fuzzy numbers [7] : Triplet A(a the triangular fuzzy number, where the membership is assigned using the formula (2). ⎧ 0, x ∈ (−∞, al ) ⎪ ⎪ ⎪ ⎨ x−al , x ∈ [a , a ] l m al (2) μA˜ (x) = am− c−x ⎪ , x ∈ [a m , au ] ⎪ au− am ⎪ ⎩ 0, x ∈ (au , +∞)

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Definition 4. Fuzzy MCDM model [8]: For multi-criteria decision-making process, DM makes assessments under fuzzy environment, and decisions are made based on multiple criteria in order to select the optimal alternative. Fuzzy sets theory provides the needed flexibility for the evaluation of data under the uncertainty.

3 Statement of the Problem The main aim of this research is to analyze and identify the relative importance of each pair of factors of personal characteristics that influence the online shopping behavior of customers, based on triangular fuzzy numbers and fuzzy AHP method. Companies can use the results of this evaluation to understand their customers in a better way. Moreover, sellers can utilize the results in their digital marketing strategies to increase the traffic in their website. Analyzed research indicate the most important factors that affect the consumer behavior [9] and consumer buying decisions in online markets [4, 10, 11]. Our research is characterized by 5 main criteria C = {c1 , c2 , c3 , c4 , c5 }. After analyzing the related literature, we suggest criteria to be feed based on the personality characteristics of the customers as the following: C1: Age: Age is an important factor that affects the purchase decision. Younger customers tend to use more online shopping than older generations. They are more interested in using the technology and evaluating the products and available information about offers [10]. In the research [4], it is found that age is positively correlated to online buying. C2: Occupation: Occupation is another important factor that affect the consumer buying decision. Customers with different jobs tend to need and want different products and services. For instance, white-collar employees need to wear suits, while workers in the construction sector need distinct apparel and may buy durable phones such as CAT smartphones [3]. C3: Income/Economic situation: Higher income consumers, who earn higher than $75.000 annually, tend to shop more online than lower income earner customers. The main reasons can be stated as the availability of internet, technology, medium for purchase such as computers and higher education levels of customers [4, 10, 11]. On the other hand, nowadays, customers use online shopping for acquiring the same products in the stores with the discounted prices. Therefore, lower income consumers can also prefer online shopping. C4: Lifestyle: Lifestyle is the other personality factor that affects the consumer behavior. Customers’ interests (about fashion, food, shopping), opinions (about business, products, events) and activities (sports, social activities) shape how he/she will act in the society [3, 9]. In the research [10], it is shown that there is a relationship between consumer online buying behavior and lifestyle.

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C5: Personality and self-concept: A customer’s distinct and unique personality affects his or her purchasing decision. Customer characteristics such as self-confidence, defensiveness, sociability, aggressiveness decide what the consumer buy and consume [3]. It can be defined as the complete behavior of an individual in different situations [9]. Consumers tend to buy products/services that match their own self-concept [3]. Decision makers provide the weights for the above given criteria and pairwise comparison matrix is created as it is shown in Table 1, which are defined in triangular fuzzy numbers. Table 1. Pairwise comparison matrix C1

C2

C3

C4

C5

C1

(1.1.1)

(2,3,4)

(1/3.1/2.1/1)

(1,2,3)

(1,2,3)

C2

(1/4, 1/3, 1/2)

(1.1.1)

(1/4.1/3.1/2)

(1/3.1/2.1/1)

(1/3.1/2.1/1)

C3

(1,2,3)

(2,3,4)

(1.1.1)

(1,2,3)

(1,2,3)

C4

(1/3.1/2.1/1)

(1,2,3)

(1/3.1/2.1/1)

(1.1.1)

(1,2,3)

C5

(1/3.1/2.1/1)

(1,2,3)

(1/3.1/2.1/1)

(1/3.1/2.1/1)

(1.1.1)

4 Solution of the Problem In this paper, we analyze the importance of criteria based on triangular fuzzy numbers and suggest the use of fuzzy AHP method [12] for pairwise comparison of the provided criteria and deriving consistency ratio. Step 1: Through evaluating the priority values in fuzzy numbers c˜ ij = (cij,l , cij,m , cij,u ), (i, j = 1, 2, ..., n), pair-wise comparison reciprocal fuzzy matrix indicated as C˜ is created for the given criteria C1 ,C2 ,…,Cn . Three crisp matrices Cl , Cm , Cu are obtained by dividing the fuzzy matrix C˜ as it is given below [13–16].

(3)

Step 2: The acquired matrices are used in order to calculate the system of fuzzy linear homogeneous equations (Tables 2, 3 and 4). Cl wl + Cm wm + Cu wu − λl wl − λm wm − λu wu = 0

(4)

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where: Cl = 2Cl + Cm = 3

Cm = Cl + 4Cm + Cu = 6

Cu = Cm + 2Cu = 3

Table 2. Cl 1

2

0

1

1

0.25

1

0

0

0

1.00

2.00

1

1

1

0.33

1.00

0.33

1

1

0.33

1.00

0.33

0.33

1

Table 3. Cm 1

3

0.5

2

2

0.33

1

0.33

0.5

0.5

2

3

1

2

2

0.5

2

0.5

1

2

0.50

2

0.5

0.5

1

Table 4. Cu 1

4

1

3

3

0.5

1

0.5

1

1

3

4

1

3

3

1

3

1

1

3

1

3

1

0.024

1

Next, we compute the following matrices: Cl = 2Cl + Cm Cm = Cl + 4Cm + Cu Cu = Cm + 2Cu The matrices are given in Tables 5, 6 and 7.

(5)

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Table 5. Cl 3.00

7.00

1.17

4.00

4.00

0,83

3.00

0,83

1.17

1.17

4.00

7.00

3.00

4.00

4.00

1.17

4.00

1.17

3.00

4.00

1.17

4.00

1.17

1.17

3.00

Table 6. Cm 6.00

18.00

3,33

12.00

12.00

2.08

6.00

2.08

3,33

3,33

12.00

18.00

6.00

12.00

12.00

3,33

12.00

3,33

6.00

12.00

3,33

12.00

3,33

2,36

6.00

Table 7. Cu 3.00

11.00

2,50

8.00

8.00

1.33

3.00

1,33

2,50

2,50

8.00

11.00

3.00

8.00

8.00

2,50

8.00

2,50

3.00

8.00

2,50

8.00

2,50

0.55

3.00

Step 3: Eigenvalues λl , λm, λu of Cl , Cm and Cu are acquired using MATLAB software program: λl = 1.49 λm = 5.29 λu = 5.3 Moreover, to obtain consistency index and consistency ratio, the following formulas are used: CI =

λmax − n n−1

(6)

CI RI

(7)

CR =

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5 Conclusion Increasing demand and interest of consumers towards using digital marketing and buying online have changed the marketing and retailing strategies of many companies. Brickand-mortar stores also become online sellers by developing their e-commerce websites to target broader customer base. For effective and efficient online retailing, sellers should also know about the characteristics of customers that influence their online purchase decisions. There are several characteristics of customers, and the main subject of this research is related to personal characteristics. Personal characteristics involve customer’s age, occupation, economic situation, lifestyle, and personality and self-concept. In this research, main aim is to analyze and identify the relative importance of each pair of the mentioned criteria based on triangular fuzzy numbers and fuzzy AHP method. The proposed method can also be applied for different decision-making problems related to consumer behavior and other marketing practices, regarding the uncertainty.

References 1. Teo, T.S., Yeong, Y.D.: Assessing the consumer decision process in the digital marketplace. Omega 31(5), 349–363 (2003) 2. Piñeiro-Otero, T., Martínez-Rolán, X.: Understanding digital marketing—basics and actions. In: Machado, C., Davim, J. (eds.) MBA. Management and Industrial Engineering, pp. 37–74. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-28281-7_2 3. Kotler, P., Armstrong, G., Opresnik, O.M.: Harlow: Principles of Marketing. England, Pearson (2018) 4. Kanchan, U., Kumar, N., Gupta, A.: A study of online purchase behaviour of customers in India. ICTACT J. Manag. Stud. 1(3), 136–142 (2015). https://doi.org/10.21917/ijms.2015. 0019 5. Aliev, R.A., Alizadeh, A., Aliyev, R.R., Huseynov, O.H.: Arithmetic of Z-Numbers, the: Theory and Applications. World Scientific (2015) 6. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I and Part II - Singapore: World Sci., 692 p. (2018, 2019) 7. Aliev, R.A., Aliev, R.R.: Soft Computing and Its Application. World Scientific (2001) 8. Dalalah, D., Hayajneh, M., Batieha, F.: A fuzzy multi-criteria decision making model for supplier selection. Expert Syst. Appl. 38(7), 8384–8391 (2011). https://doi.org/10.1016/j. eswa.2011.01.031 9. Gajjar, N.B.: Factors affecting consumer behavior. Int. J. Res. Hum. Soc. Sci. 1(2), 10–15 (2013) 10. Li, N., Zhang, P.: Consumer online shopping attitudes and behavior: an assessment of research. In: AMCIS 2002 Proceedings, vol. 74 (2002). https://aisel.aisnet.org/amcis2002/74 11. Lohse, G.L., Bellman, S., Johnson, E.J.: Consumer buying behavior on the Internet: findings from panel data. J. Interact. Mark. 14(1), 15–29 (2000). https://doi.org/10.1002/(SICI)15206653(200024)14:1%3c15::AID-DIR2%3e3.0.CO;2-C 12. Mehdiyev, N.: Application of fuzzy AHP-TOPSIS method for software package selection. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 827–834. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_109

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13. Dovlatova, K.J.: Estimation of benchmarking influence in buyer’s decision-making process by using fuzzy AHP. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 173–182. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_26 14. Prašˇcevi´c, N., Prašˇcevi´c, Ž.: Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. Tehniˇcki vjesnik/Techn. Gaz. 23(1), 57–64 (2016). https://doi.org/10.17559/TV-20140212113942 15. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 16. Aliyeva, K.R.: Demand forecasting for manufacturing under Z information. Procedia Comput. Sci. 120, 509–514 (2017). https://doi.org/10.1016/j.procs.2017.11.272

Estimation of Countries’ Economic Development by Using Z-Number Theory Rafig R. Aliyev(B) Azerbaijan State Oil and Industry University, Azadlyg Avenue, 20, AZ1010 Baku, Azerbaijan [email protected]

Abstract. The economic development level of countries or regions is main indicator for measuring progress in their economy. This problem has increased attention of the scientists and practitioners in the recent past. The level of countries’ economic development mainly is characterized by the level of GDP. GDP per capita, unemployment rate and others. Both in classical and fuzzy modeling of economic development level of countries unfortunately reliability of available information is not taken into consideration. In this paper Z-rule based method for estimation of economic development level of countries which takes into account bimodal information processing is suggested. The numerical example including six Z-rules is tested. Keywords: Z-set · Z-number · Similarity of Z-sets and Z-numbers · Z-approximate reasoning · Economic development · GDP

1 Introduction In the literature economic development level of countries is considered as a function of macroeconomic factor such as GDP, GDP per capita, population size, unemployment, and others. In [1] economic development of countries is considered. Neural network model is used for predicting the country’s development level. This model describes relationship between economic development and different economic, governance indicators. Also, sensitivity analysis for estimation of relative importance of these factors in prediction is investigated. Local economic development problem is investigated in [2]. Objective analysis of the economic development level of countries is given in [3]. Classifying countries in optimal number of groups which characterizes different level of economic development is performed. Authors propose a composite index for estimation of the level of economic development of countries. Classification of countries into specific groups is based on this suggested index. In [4] authors investigate economic development level of regions and countries with finance and growth nexus. Clustering for dividing countries into groups for identification of the level of development also is considered in [5]. This clustering approach is based on hierarchical clustering using Euclidean distance. Classification of countries into specific group is investigated. In [6] identification of main factors that can be influenced to economic level of countries is considered. Different socio-economic indicators were investigated for construction of relationship between dependent and independent variables. As model of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 172–179, 2023. https://doi.org/10.1007/978-3-031-25252-5_26

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relationship statistical regression model is used. In the paper [7] author presents powerful approach to model for evaluating the level of economic development of countries and regions. Main advantage of the proposed model is fact that it is based on fuzzy logic and it takes into account vagueness and uncertainty of existing information declared by experts. It is shown that economic division of countries is consequence of the level of different indicators, such as GDP, GDP per capita, unemployment rate, industrial growth, etc. Authors suggest If-Then fuzzy model in which antecedent variables are GDP, GDP per capita, and unemployment rate and consequent variable is economic development level of countries. By using approximate reasoning algorithm country’s economic development level is calculated. Both in classical and fuzzy modeling of economic development level of countries unfortunately reliability of available information is not taken into consideration. To deal with real-life problems that are characterized not only crisp or fuzzy values of variable of interest same time with reliability of them prof. L. Zadeh suggested Znumber conception. Basic objective of this paper is to develop the Z-information-based model to predict the country’s economic level by using some macroeconomic indicators such as GDP, GDP per capita, and unemployment rate (for medium population). The paper is structured as follows: Sect. 2 includes some preliminaries on Z-number theory. In the Sect. 3 statement of the problem is given. In Sect. 4 new approach to solution of stated problem is considered. The final section offers some conclusions.

2 Preliminaries Definition 1. Continuous Z-number. [8–10]. A continuous Z-number is an ordered pair Z = (A, B) where A is a continuous fuzzy number playing a role of a fuzzy constraint on values that a random variable X may take: X is A, B is a continuous fuzzy number with a membership function μB : [0, 1] → [0, 1], playing a role of a fuzzy constraint on the probability measure of A:  P(A) = μA (x)p(x)dx is B. R

Definition 2. A discrete Z-number [8, 9]. A discrete Z-number is an ordered pair Z = (A, B) where A is a discrete fuzzy number which describes a fuzzy constraint on values that a random variable X may take – “X is A”, and B is a discrete fuzzy number with a membership function μB : {b1 , ..., bn } → [0, 1], {b1 , ..., bn } ⊂ [0, 1], which describes a fuzzy constraint on the probability measure of A : P(A) is B Definition 3. Z-rules [11]. Rule 1: If X1 is ZX1 ,1 = (AX1 ,1 , BX1 ,1 ) and , … , and Xm is ZXm ,1 = (AXm ,1 , BXm ,1 ) then Y is ZY = (AY ,1 , BY ,1 ).

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Rule 2: If X1 is ZX1 ,2 = (AX1 ,2 , BX1 ,2 ) and , … , and Xm is ZXm ,2 = (AXm ,2 , BXm ,2 ) then Y is ZY = (AY ,2 , BY ,2 ). . . Rule n: If X1 is ZX1 ,n = (AX1 ,n , BX1 ,n ) and , … , and Xm is ZXm ,n = (AXm ,n , BXm ,n ) then Y is ZY = (AY ,n , BY ,n ). Definition 4. Similarity of Z-numbers. Similarity of Z-numbers Z1 , Z2 is computed as follows: S(Z1 , Z2 ) =

1 (S(A1 , A2 ) + S(B1 , B2 ) + S(G1 , G2 )) 3

(1)

where S(A1 , A2 ) and S(B1 , B2 ) are values of Jaccard similarity of fuzzy numbers. S(G1 , G2 ) is similarity of the sets of probability distributions. Definition 5. Jaccard similarity measure [11, 12]. Jaccard similarity measure between Z-number valued vectors is represented as ⎛ m    ⎜ 1  ⎜ w Jsi = Z Aw ×⎜ j , Bj K ⎝2  j=1 k=1 K 

+

1 K 2  k=1

K 

μAi (xk )

2

+

μAi (xk ) · μAid (xk )

k=1 K  k=1

μAid (xk )

2

K 

−

k=1

μAi (xk ) · μAid (xk )

(2)

⎞

μBi (xk ) · μBid (xk )

⎟ ⎟ k=1 ⎟ K K ⎠

2

2   μBi (xk ) · μBid (xk ) μBi (xk ) + μBid (xk ) − k=1

k=1

Definition 6. Similarity between probability distributions. 1 , S(G1 , G2 ) = 1 + Dset (G1 , G2 ) n 

Dset (G1 , G2 ) =

i=1

αi Dset (G1αi , G2αi ) n 

(3) αi

i=1

Dset (G1αi , G2αi ) = max{maxp1 ∈Gαi (minp2 ∈Gαi D(p1 , p2 )), maxp2 ∈Gαi (minp1 ∈Gαi D(p1 , p2 ))} 1

2

2

1

αi ∈ (0, 1] D(p1 , p2 ) is computed as 1 (D(p1 , p) + D(p2 , p)), 2 p1 (x) + p2 (x) ,x ∈ X. p(x) = 2

D(p1 , p2 ) =

(4)

Estimation of Countries’ Economic Development by Using Z-Number Theory

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3 Statement of the Problem Given the following Z-rules:

1. If (GDP is (low, very sure)) and (per capita is (low, very sure)) and (unemployment rate is (medium, very sure)), then (the level of economic development is (low, sure)) 2. If (GDP is (medium, very sure)) and (per capita is (medium, very sure)) and (unemployment rate is (low, very sure)), then (the level of economic development is (medium, sure)). 3. If (GDP is (high, very sure)) and (per capita is (medium, very sure)) and (unemployment rate is (medium, very sure)), then (the level of economic development is (medium, sure)). 4. If (GDP is (medium, very sure)) and (per capita is (medium, very sure)) and (unemployment rate is (high, very sure)), then (the level of economic development is (low, sure)). 5. If (GDP is (high, very sure)) and (per capita is (high, very sure)) and (unemployment rate is (low, very sure)), then (the level of economic development is (high, sure)). 6. If (GDP is (medium, very sure)) and (per capita is (high, very sure)) and (unemployment rate is (medium, very sure)), then (the level of economic development is (high, sure)). 7. If (GDP is (low, very sure)) and (per capita is (high, very sure)) and (unemployment rate is (high, very sure)), then (the level of economic development is (medium, sure)).

(5)

and investigated country indicators (GDP, per capita and unemployment rate) find the Z-value of level of economic development of the country. Corresponding to the rules (5) reliability linguistic terms are sure = {0.7, 0.8, 0.9}; very sure = {0.8, 0.85, 0.9}. Codebooks of linguistic terms in (5) are shown in Figs. 1, 2, 3, 4 and 5.

Low

Medium

1

High

0.8 0.6 0.4 0.2 0 -1

1

3

5

7

9

Fig. 1. Membership functions for the level of economic development

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1

Medium

Low

High

0.8 0.6 0.4 0.2 0 0

10000 20000 30000 40000 50000

Fig. 2. Membership functions for GDP per capita

1 Low

Medium

High

0.8 0.6 0.4 0.2 0 0

10

20

30

40

Fig. 3. Membership functions for Unemployment

1

VL

L

ME

H

VH

0.8 0.6 0.4 0.2 0 0

100000 200000 300000 400000 500000 600000 700000 Fig. 4. Membership functions for GDP (Million USD)

Estimation of Countries’ Economic Development by Using Z-Number Theory

Very sure

Sure

1

177

0.8 0.6 0.4 0.2 0 0.7

0.75

0.8

0.85

0.9

Fig. 5. Membership functions for reliability of Z-numbers

4 Solution of the Problem The problem is solved as follows: For each rule in (5) similarity of current observation Z = (ZX 1 , ZX 2 , ZX 3 ) and vector of rule antecedents is computed as a minimum similarity: Sv (Z , Zj ) = mini=1,...,3 S(ZX i ZXi ,j ), j = 1, ..., 6,

(6)

S(ZX i ZXi ,j ) is similarity of Z-numbers. Resulting output (level of economic development) is computed as ZY =

n 

wj ZY ,j ,

(7)

j=1

where ZY ,j is the Z-valued consequent of the j-th rule, Sv (Z , Zj ) , wj = n  k=1 Sv (Z , Zk )

(8)

j = 1, ..., 6; k = 1, ..., 6 are coefficients of linear interpolation. Taking into account Codebooks given in Figs. 1, 2, 3, 4 and 5 rules can be presented as 1. If (GDP is ((100, 100, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 0, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 10, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0, 0, 10), (0.7, 0.8, 0.9))) 2. If (GDP is ((100, 300, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 15, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 0, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0, 5, 10), (0.7, 0.8, 0.9))). 3. If (GDP is ((100, 700, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 15, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 10, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0,5,10), (0.7,0.8,0.9))). 4. If (GDP is ((100, 300, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 15, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 20, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0, 0, 10), (0.7, 0.8, 0.9))).

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5. If (GDP is ((100, 700, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 30, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 0, 10), (0.8, 0.85, 0.9))), then (the level of economic development is ((5, 10, 10), (0.7, 0.8, 0.9))). 6. If (GDP is ((100, 300, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 30, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 10, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((5, 10, 10), (0.7, 0.8, 0.9))). 7. If (GDP is ((100, 100, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 30, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 20, 20),(0.8, 0.85, 0.9))), then (the level of economic development is ((0, 5, 10), (0.7, 0.8, 0.9))). Assume that economic development level of the investigated country is characterized by following information GDP is ((100, 200, 700), (0.8, 0.85, 0.9)) per capita is((0, 20, 30), (0.8, 0.85, 0.9)) unemployment rate is ((0, 5, 15), (0.75, 0.8, 0.85)) In accordance with Sect. 4 similarity between the given data and antecedent vector of rules in (5) is calculated as S(Z , Z1 ) = 0.44, S(Z , Z2 ) = 0.49, S(Z , Z3 ) = 0.44, S(Z , Z4 ) = 0.33, S(Z , Z5 ) = 0.39, S(Z , Z6 ) = 0.44, S(Z , Z7 ) = 0.33. By using (8) interpolation weights are calculated for activated rules. Here threshold level for similarity is 0.4. w1 = 0.24, w2 = 0.27, w3 = 0.24, w6 = 0.24 . Finally resulting information economic development level of considered country is calculated by using (7) Z = w1 Z1 + w2 Z2 + w3 Z3 + w6 Z6

Z = ((1.22, 5, 10), (0.37, 0.44, 0.53))

So economic development level of the considered country is “about 5” with reliability about 45%.

5 Conclusion The estimation of economic development level of regions and countries is challenging problem in the evaluation of their sizes. In existing literature general approach to analysis of this problem is based on statistical and rarely on fuzzy logic methods. Unfortunately, both in statistical and fuzzy approaches to evaluation of countries’ or regions’ economic development level reliability of decision relevant information in existence is not taken into account. Basic objective of this paper was to develop the Z-information-based [13, 14] model to predict the country’s economic level by using some macroeconomic indicators such as GDP, GDP per capita, and unemployment rate (for medium population). The

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suggested method is based on Z-number similarity-based approximate reasoning taking into consideration ambiguity and uncertainty described both fuzzy and probabilistic measures. Numerical example given in the study shows validity of proposed method of evaluation of economic development level of countries.

References 1. Ahmad, Z., Saleem, A.: Predicting level of development for different countries. J. Sustain. Dev. 5(11), 15–31 (2012). https://doi.org/10.5539/jsd.v5n11p15 2. Greenwood, D.T., Holt, R.P.F.: Local Economic Development in the 21st Century: Quality of Life and Sustainability, 232 p. (2014) 3. Nastu, A., Stancu, S., Dumitrache, A.: Characterizing the level of economic development of countries. In: Proceedings of the International Conference on Applied Statistics, vol. 1(1), pp. 343–354 (2019). https://doi.org/10.2478/icas-2019-0030 4. Nguyena, Y.N., Brownb, K., Skullyb, M.: Economic development levels and the finance and growth nexus (2016). https://doi.org/10.13140/RG.2.1.5126.5684 5. Vazquez, S.T., Sumner, A.: Beyond low and middle income countries: what if there were five clusters of developing countries? Poverty and inequality research cluster, p. 404 (2012) 6. Popa, D.I.: Influence factors of the economic development level across European countries. Rom. Stat. Rev. 64(2), 3–16 (2016) 7. Stojic, G.: Using fuzzy logic for evaluating the level of countries’ (regions’) economic development. Panoeconomicus 3, 293–310 (2012). https://doi.org/10.2298/PAN1203293S 8. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181(14), 2923–2932 (2011) 9. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers: Theory and Applications. World Scientific, Singapore (2015). https://doi.org/10.1142/9575 10. Aliev, R.A., Huseynov, O.H., Zeinalova, L.M.: The arithmetic of continuous Z-numbers. Inf. Sci. 373, 441–460 (2016). https://doi.org/10.1016/j.ins.2016.08.078 11. Aliyev, R.R.: Fuzzy logic’s Z-extension-based decision tools and their applications. dissertation work for the degree of Doctor of Philosophy, Baku, Azerbaijan, 104 p. (2021) 12. Aliyev, R.R.: Similarity based multi-attribute decision making under Z-information. bQuadrat Verlag, Germany, pp. 33–39 (2015) 13. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 14. Nuriyev, A., Baysal, A.B.: Z-Numbers-based approach to hotel service quality assessment. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 85–94. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-92127-9_15

Fuzzy Approach to Explainable Artificial Intelligence Alexey Averkin1,2

and Sergey Yarushev3(B)

1 Federal Research Centre of Informatics and Computer Science of RAS, Moscow, Vavilova,

42, Moscow, Russia 2 Educational and Scientific Laboratory of Artificial Intelligence, Neuro-technologies and

Business Analytics, Plekhanov Russian University of Economics, Stremyanny Lane, 36, Moscow, Russia 3 Departments of Informatics, Plekhanov Russian University of Economics, Stremyanny Lane, 36, Moscow, Russia [email protected]

Abstract. The widespread introduction of artificial intelligence systems in all areas of human activity imposes requirements of responsibility on these systems. Systems operating in critical areas such as healthcare, economics, and security systems based on artificial neural network models should have an explanatory apparatus to be able to evaluate not only the recognition, prediction, or recommendation accuracy familiar to everyone, but also to show the algorithm for getting result of neural network working. In this paper, we investigate methods of explainable artificial intelligence for rules extraction from artificial neural networks, which are based on the fuzzy logic. Keywords: Fuzzy logic · Machine learning · Explainable artificial intelligence · Neural networks · Decision tree

1 Introduction Research in the field of explanatory artificial intelligence has been actively conducted since the mass introduction and application of artificial intelligence methods, in particular artificial neural networks, began. The reason was the inability of Artificial neural networks (ANN) to give an answer to a simple question – how was the result achieved? ANN, including deep learning networks, already surpass human capabilities in many tasks, for example, the task of image recognition or the search for regularities. But the mass introduction of such technologies was followed by a few problems, because for the result to be trusted, it is necessary to determine based on which factors ANN made a particular decision. From a legal point of view, restrictions are also imposed, because it is impossible to justify legally accepted decisions by artificial intelligence. To solve these problems, scientists around the world are working on the creation of explanatory artificial intelligence (XAI). One of the approaches to creating models based on ANN is to extract rules from them based on fuzzy logic methods, genetic algorithms, or decision © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 180–187, 2023. https://doi.org/10.1007/978-3-031-25252-5_27

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trees. In this paper, we will consider the operation of decision trees in the problem of extracting rules from ANN. One of the most important fields of application neural networks is the time series forecasting. And here this is extremely important to understand how an artificial neural network made a particular decision. And one of the variations of solving this problem is fuzzy logic theory application. To begin with, let’s say a few words about the time series and importance of rules extraction from ANN when working with time series. The time series is controlled by two main forces - time and events that affect the change in the values of the time series over time. Most of these events are characterized by some uncertainty. Each time series point can be correlated with a fuzzy variable with a certain membership function. Lotfi Zadeh has suggested the fuzzy logic theory in 1965, thanks to which it is possible to describe qualitative fuzzy concepts and knowledge about the surrounding world, and later operate with them to obtain new information. The use of this concept allows us to formalize linguistic information for the construction of mathematical models. The concept of a fuzzy set is based on the proposition that the elements that make up this fuzzy set, as well as having common properties, can possess it and, therefore, belong to this set to varying degrees. Nowadays, XAI is a prominent and fruitful research field where many of Zadeh’s contributions can become crucial if they are carefully considered and thoroughly developed. It is worth noting that about 30% of publications in Scopus related to XAI, dated back to 2017 or earlier, came from authors well recognized in the Fuzzy Logic field. This is mainly due to the commitment of the fuzzy community to produce interpretable fuzzy systems since interpretability is deeply rooted in the fundamentals of Fuzzy Logic. Since 2011, L. Zadeh (Father of Fuzzy Logic, co-inventor of Z-Transform, and AI Hall-of-Fame inductee) had been involved in Z Advanced Computing, Inc. (ZAC) and was one of the ZAC’s inventors. ZAC is the pioneer Cognitive Explainable-AI (Artificial Intelligence) (Cognitive XAI) technologies. The Cognitive Explainable-AI (Artificial Intelligence) approach use the results of Prof. Rafic Aliev, Prof. Ronald Yager, Prof. Mo Jamshidi [1].

2 Review of Fuzzy Rules Extraction Algorithms Research in the development of explanatory systems has been going on for a long time. The current state of research in the development of explanatory artificial intelligence systems can be divided into three stages: the first stage (since 1970) - the development of expert systems, the second stage (mid-1980s) - the transition from expert systems to knowledge-based systems, and the third (since 2010) - the study of deep architectures of artificial neural networks, which required new global research on the construction of explainable systems. The most interesting direction in the development of explanatory AI models is rule extraction using neuro-fuzzy models. Fuzzy rule-based systems (FRBS) developed with fuzzy logic have become a field of active research over the past few years. These algorithms have proven their strengths in tasks such as managing complex systems, creating fuzzy controls. The relationship between both approaches (ANN and FRBS) has been carefully studied and shown to be equivalent. This leads to two important conclusions.

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First, you can apply what was found for one of the models to another. Second, we can translate the knowledge embedded in the neural network into a more cognitively acceptable language - fuzzy rules. In other words, we get a semantic interpretation of neural networks [2, 3]. To get a semantic interpretation of the deep learning black box, neural networks can be used instead of the last fully connected layer. For example, ANFIS (Adaptive Neural Fuzzy System) is a multi-layer feedforward network. This architecture has five layers such as a fuzzy layer, a production layer, a normalization layer, a defuzzification layer, and an output layer. ANFIS combines the advantages of a neural network and fuzzy logic. Below is a classification of the most well-known neuro-fuzzy approaches. There are three techniques for combining artificial neural networks (ANNs) and fuzzy models: [4, 5]: 1. neuro-FIS, in which ANN is used as a tool in fuzzy models. 2. fuzzy ANNs, in which the classical ANN models are fuzzified. 3. neuro-fuzzy hybrid systems, in which fuzzy systems and ANN are combined into hybrid systems. Based on these techniques, neuro-fuzzy models can be divided into three classes [6, 7]. Cooperative neuro-fuzzy models. In this case, part of the ANN is initially used to define fuzzy sets and/or fuzzy rules, where only the resulting fuzzy system is subsequently executed. In the learning process, membership functions are determined, and fuzzy rules are formed based on the training sample. Here the main task of the neural network is to select the parameters of the fuzzy system. Parallel neuro-fuzzy models. The neural network in this type of model works in parallel with the fuzzy system, providing input to the fuzzy system or changing the output of the fuzzy system. A neural network can also be a post-processor of the output data from a fuzzy system. Hybrid neuro-fuzzy models. The fuzzy system uses a training method, as does the ANN, to adjust its parameters based on the training data. Among the presented classes of models, models of this class are most popular, as evidenced by their application in a wide range of real problems [8–11]. Among the most popular hybrid models are the following architectures. Fuzzy Adaptive Learning Control Network (FALCON) [12], which has a five-layer architecture. There are two linguistic nodes per one output variable. The first node works with a training sample (training pattern), the second is the input for the entire system. The first hidden layer labels the input sample according to membership functions. The second layer defines the rules and their parameters. Training takes place based on a hybrid unsupervised algorithm to determine the membership function, the rule base and uses the gradient descent algorithm to optimize and select the final parameters of the membership function. The adaptive neuro-fuzzy inference system ANFIS [13] is a well-known neuro-fuzzy model that has been applied in many applications and research areas [14]. Moreover, a comparison of the architectures of neural fuzzy networks showed that ANFIS shows

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the minimum error in the prediction task. The main disadvantage of the ANFIS model is that it places heavy demands on computing power [15]. The Generalized Approximate Intelligent Reasoning Control (GARIC) [16] system is a neuro-fuzzy system using two neural network modules, an action selection module, and a state assessment module, which is responsible for assessing the quality of the action selection by the previous module. GARIC is a five-layer feedforward network. The Neural Fuzzy Controller (NEFCON) [17] was developed to implement a Mamdani-type fuzzy inference system. Links are defined using fuzzy rules. The input layer is a fuzzifier, and the output layer solves the defuzzification problem. A network is trained based on a hybrid reinforcement learning algorithm and an error backpropagation algorithm. The fuzzy inference and neural network system in fuzzy inference software (FINEST) [18] is a parameter setting system. Tuning of fuzzy predicates, implication function and combinatorial function is performed. The system for automatically building a neural network of fuzzy inference (SONFIN) [19] is in essence like the NEFCON controller, but instead of implementing fuzzy inference of the Mamdani type, it implements the inference of the Takagi-Sugeno type. In this network, the input sample is processed using the aligned clustering algorithm. When identifying the structure of the precondition part, the input space is divided in a flexible manner according to an algorithm based on aligned clustering. The tuning of system parameters is partially implemented using the least squares method, the preconditions are tuned using the backpropagation method. Dynamically developing fuzzy neural network (dmEfuNN) and (EFuNN) [20]. In EFuNN, all nodes are created in the learning process. The first layer passes the training data to the second, which calculates the degree of fit with a predefined membership function. The third layer contains sets of fuzzy rules, which are prototypes of input-output data, which can be represented as hyperspheres of fuzzy input and output spaces. The fourth layer calculates the degree to which the output membership function has labeled the input, and the fifth layer defuzzifies and calculates the numerical values of the output variable. DmEfuNN is a modified version of EFuNN. The main idea is that for all input vectors a set of rules is dynamically selected, the activation values of which are used to calculate the dynamic parameters of the output function. While EFuNN implements Mamdani-type fuzzy rules, dmEFuNN uses Takagi-Sugeno type.

3 Rule Extraction Algorithm Based on Decision Trees The most well-known disadvantage of ANN is that it is impossible to determine how the neural network achieved the result. ANN basically work according to the principle: received a training sample, trained, received input data, processed, and gave the result. What happens inside the neural network and how the neural network makes this or that decision is unclear. Accordingly, as mentioned in previous chapters, these problems impose significant restrictions on the use of artificial intelligence algorithms in real tasks, especially if these tasks are critically important for a person or his health. To solve the problem of extracting knowledge from neural networks, many algorithms have been developed, mainly they work with ANN weights and impose significant restrictions on the neural network architecture.

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In this paper, we will consider an algorithm for extracting rules based on decision trees, which does not impose specific requirements on the neural network architecture. This algorithm builds decision trees from a trained ANN. The advantage of this algorithm is that it can work with absolutely any artificial neural network of any architecture, regardless of the presence of feedbacks, training methods or types of input and output data. The decision tree obtained from the neural network will be a classification tree. 3.1 Rule Extraction Algorithm Using decision trees to extract rules from ANN allows you to extract a humanunderstandable structure from a neural network and convert the output result of the network into a hierarchical sequence of IF-THEN rules. The algorithm classifies the input data in the neural network and analyzes the network itself, thereby extracting classification rules from it separately for each class. The algorithm for constructing a decision tree approximating the operation of a trained artificial neural network looks like this: 1. Build and train the original neural network - “oracle”. 2. Calculate the value q = max (0, minSamples − S), where minSamples is the minimal number of training examples used in each node of the tree, S is the current training sample (respectively S is its volume). Thus, q is the number of additional examples that need to be generated. 3. Based on the evaluation of the distribution of features from S, q new training examples are randomly generated. 4. The “oracle” recognizes that both new examples and old examples from the set S belong to one or another class. 5. Add the generated examples to the set S. 6. We are splitting up a set of buildings as a free algorithm for building buildings. 7. For each of the resulting subsets – recursion from step 2 until the local or global completion criterion of the algorithm is met. The maximum allowable depth of the generated tree is used as a global criterion for the completion of the algorithm. The local stopping criterion is met, if there are examples in this node of the tree that belong to only one class, or the signs that allow further separation to have ended or the test for the consistency of this division has not been passed. After reading the description of the algorithm, the question may arise: why, in fact, use the “oracle”? After all, you can simply build a decision tree based on the available training sample, which already contains an exact indication of which class each example belongs to. Moreover, such an “oracle” as a neural network, no matter how well trained it is, will still make mistakes. The point here is the generalizing ability of artificial neural networks, which allows us to obtain simpler decision trees. In addition, the use of “oracle” makes it possible to compensate for the lack of data, which is observed when constructing decision trees at lower levels. Thus, it is possible to extract structured knowledge not only from extremely simple neural networks, but also from arbitrary classifiers, which makes it possible to apply the described algorithm in a wide range of practical tasks.

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3.2 Rules Extraction from ANN Based on the Decision Trees A thinned tree is much more compact and simpler than an untreated one. In addition to this, the thinned tree has greater classification accuracy. In this regard, we will draw all meaningful conclusions based on a thinned tree. The first meaningful conclusion that can be drawn at first glance is that the work of Sergei Dovlatov is very clearly different in style (here, by style we will understand the frequency response of sentence lengths) from three other writers, and for making such a decision there was enough data that in the text fragment under study there are less than 2 sentences 34 words long and less than 4 sentences 48 words long. Linguistics experts will have to judge why exactly such figures turned out, and such data may be of great value to them. In contrast to the work of S. Dovlatov, the work of A.I. Kuprin is the least clearly distinguished from others. We can see this by the way a lot of records describing his works gradually disintegrate into parts, often close in size. However, such a feature can be caused not only by the peculiarities of the writer’s work, but also by the small number of works (18 in total) that participated in the study. It can be noted that the resulting decision tree does not include all the attributes that were present in the training sample. This leads to an important conclusion that decision trees also allow you to select the most significant characteristics and discard unnecessary ones. This observation is very important for further research in the field of choosing the characteristics most relevant to the individual author’s style. Having made sure that thinning gives a more compact decision tree, it would be interesting to find out: and what threshold level of significance gives the most compact decision tree, without reducing the accuracy of prediction? To answer this question, various threshold levels of significance were checked. Threshold levels of significance from the range [0; 1] were checked, and the threshold level of significance 0 corresponds to the «strictest» thinning, and level 1 corresponds to the complete absence of thinning From this graph after thinning, with a successful choice of the threshold level of significance (the choice can be made using the same technique as was used during testing), the percentage of errors is significantly reduced. In the presented algorithm, there is an additional parameter reflecting the minimum number of training data for each node. Classical algorithms based on decision trees are not capable of achieving such accuracy.

4 Discussion In this paper, the possibility of using algorithms for extracting rules from an artificial neural network based on decision trees was demonstrated. As an example, the task of determining the authorship of classical works of Russian writers based on ANN and decision trees was chosen. Decision trees based on the trained network built its structure. Two more approaches to the extraction of rules and the development of explanatory artificial intelligence systems, such as fuzzy cognitive maps and a mining clustering algorithm, were also considered. Briefly, it should be noted that all the presented algorithms require additional testing and research of their effectiveness as meth odes of extracting rules and knowledge from neural networks, but they can be considered as possible ways of developing explanatory artificial intelligence systems.

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Acknowledgement. The paper is partially supported be the grants RFBR 20-7-00770 “Facing Fundamental Problems of Constructing “Understanding” Cognitive Agents, Multi-Agent Systems and Artificial Societies on the Basis of Synergetic Artificial Intelligence Approaches, Information Granulation Techniques, Dynamic Bipolar Scales and Dialogical Worlds” and RSCF 22-7110112 “Hybrid Decision Support Models Based on Augmented Artificial Intelligence, Cognitive Modeling and Fuzzy Logic in Problems of Personalized Medicine”.

References 1. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I And Part II. World Scientific (2018). https://doi.org/10.1142/10936 2. Averkin, A., Yarushev, S.: Hybrid neural networks for time series forecasting. In: Kuznetsov, S., Osipov, G., Stefanuk, V. (eds.) RCAI 2018. CCIS, vol. 934, pp. 230–239. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00617-4_21 3. Pilato, G., Yarushev, S.A., Averkin, A.N.: Prediction and detection of user emotions based on neuro-fuzzy neural networks in social networks. In: Abraham, A., Kovalev, S., Tarassov, V., Snasel, V., Sukhanov, A. (eds.) IITI’18 2018. AISC, vol. 875, pp. 118–125. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-01821-4_13 4. Jin, X.-H.: Neurofuzzy decision support system for efficient risk allocation in public-private partnership infrastructure projects. J. Comput. Civ. Eng. 24(6), 525–538 (2010). https://doi. org/10.1061/(ASCE)CP.1943-5487.0000058 5. Jin, X.-H.: Model for efficient risk allocation in privately financed public infrastructure projects using neuro-fuzzy techniques. J. Constr. Eng. Manag. 137(11), 1003–1014 (2011). https://doi.org/10.1061/(ASCE)CO.1943-7862.0000365 6. Mitra, S., Hayashi, Y.: Neuro-fuzzy rule generation: survey in soft computing framework. IEEE Trans. Neural Netw. 11(3), 748–768 (2000). https://doi.org/10.1109/72.846746 7. Kim, J., Kasabov, N.: HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Netw. 12(9), 1301–1319 (2004). https://doi.org/10. 1016/s0893-6080(99)00067-2 8. Shihabudheen, K.V., Pillai, G.N.: Recent advances in neuro-fuzzy system: a survey. Knowl. Based Syst. 152, 136–162 (2018). https://doi.org/10.1016/j.knosys.2018.04.014 9. Lin, C.T., Lee, C.S.G.: Neural network based fuzzy logic control and decision system. IEEE Trans. Comput. 40(12), 1320–1336 (1991). https://doi.org/10.1109/12.106218 10. Viharos, Z.J., Kis, K.B.: Survey on neuro-fuzzy systems and their applications in technical diagnostics and measurement. Measurement 67, 126–136 (2015). https://doi.org/10.1016/j. measurement.2015.02.001 11. Naderpour, H., Mirrashid, M.: Shear failure capacity prediction of concrete beam-column joints in terms of ANFIS and GMDH. Pract. Period. Struct. Des. Constr. 24(2) (2019). https:// doi.org/10.1061/(ASCE)SC.1943-5576.0000417 12. Fan, L.: Revisit fuzzy neural network: demystifying batch normalization and ReLU with generalized hamming network. In: 31st International Conference on Neural Information Processing Systems, Long Beach California, USA, pp. 1920–1929 (2017). https://doi.org/10. 48550/arXiv.1710.10328 13. Bherenji, H.R., Khedkar, P.: Learning and tuning fuzzy logic controllers through reinforcements. IEEE Trans. Neural Netw. 3, 724–740 (1992). https://doi.org/10.1109/72. 159061 14. Nauck, D., Kruse, R.: Neuro-fuzzy systems for function approximation. Fuzzy Sets Syst. 101(2), 261–271 (1999). https://doi.org/10.1016/S0165-0114(98)00169-9

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15. Juang, C.F., Lin, C.T.: An online self constructing neural fuzzy inference network and its applications. IEEE Trans. Fuzzy Syst. 6(1), 12–32 (1998). https://doi.org/10.1109/91.660805 16. Nürnberger, A., Nauck, D., Kruse, R.: Neuro-fuzzy control based on the NEFCON-model: recent developments. Soft Comput. 2(4), 168–182 (1999). https://doi.org/10.1007/s00500005 0050 17. Tano, S., Oyama, T., Arnould, T.: Deep combination of fuzzy inference and neural network in fuzzy inference. Fuzzy Sets Syst. 82(2), 151–160 (1996). https://doi.org/10.1016/0165-011 4(95)00251-0 18. Prasad, M., Lin, C., Li, D.: Soft-boosted self-constructing neural fuzzy inference network. IEEE Trans. Syst. Man Cybern. Syst. 47(3), 584–588 (2017). https://doi.org/10.1109/TSMC. 2015.2507139 19. Kasabov, N.: Evolving fuzzy neural networks for supervised/unsupervised on-line knowledgebased learning. IEEE Trans. Syst. Man Cybern. 31(6), 902–918 (2001). https://doi.org/10. 1109/3477.969494 20. Aliev, R.A., et al.: Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization. Inf. Sci. 181(9), 1591–1608 (2011). https://doi.org/10.1016/j.ins.2010. 12.014

Z-Numbers Based Evaluation of Expert Opinions on Agricultural Structure G. Imanov1

, A. Aliyev1(B)

, and R. Mikayilova2,3

1 Institute of Control Systems of Azerbaijan National Academy of Sciences, Baku AZ1141,

Azerbaijan [email protected] 2 Azerbaijan State University of Economics, Baku AZ1001, Azerbaijan [email protected] 3 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku AZ1010, Azerbaijan

Abstract. This article sets out the methodology for evaluation of expert opinions on agricultural structure of sown areas that is one of main factors constituting food security. For this purpose, the theory and instruments of fuzzy Z-numbers have been employed. The Z-number theory opened a new window of opportunities for many applications, especially in the areas of computation with probabilities and events stated in natural language. From this perspective, Z-numbers theory is an effective tool to make synthesis and analysis of expert opinions. In this paper, we try to determine the best case among expert opinions. Firstly, on the basis of subjective expert evaluations, corresponding Z-numbers are constructed. Then, in order to establish the medium version of expert opinions, addition and averaging operations on Z-numbers have been carried out. As a result, the intermediate of the expert opinions is assessed, then the best case is selected which may be accepted as the desired agricultural structure of sown areas of cereal and leguminous plants in Azerbaijan for the upcoming years. Keywords: Food security · Agricultural structure of sown areas · Z-numbers · Z-average · Z-t-conorm

1 Introduction The world is passing through a very turbulent and challenging time. If you have a look at today’s scene of our planet, you cannot see any pleasant pictures. A pandemic continuing more than two years, conflicts and wars bursting out from time to time, the results of climate change, humanitarian and economic crises attracted attentions on food security problems of world countries. Worsening international relations and trade, increasing risk factors require a new approach to food security problems. Food security is an agenda at public and political debates in many countries, for its urgency in national security, rural and agricultural development, general welfare of the society, poverty reduction, and more. Food security concept is defined as the condition in which people all the time have economic, social and physical access to sufficient and nutritious food that meeting their © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 188–195, 2023. https://doi.org/10.1007/978-3-031-25252-5_28

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dietary needs for a healthful and active life. Built on this definition addressed in the 1996 World Food Summit, the Global Food Security Index takes into account the main issues of Affordability, Availability, Quality and Safety, Natural Resources & Resilience within a group of 113 countries. The index is a dynamic quantitative and qualitative scoring model, generated from 28 particular indicators, that measures different aspects of food security over both developed and developing countries. The general goal of the study is to measure which countries are most and least susceptible to food insecurity based on the categories of Affordability, Availability, Quality and Safety, and Natural Resources & Resilience [1]. Food security index in 2021 was 62.6 with global ranking 56 in Azerbaijan. Affordability sub index was 82.3, availability was 82.3, Quality & Safety was 62.0, and Natural Resources & Resilience was 50.7. Today Azerbaijan meets its wheat demand at 59–60% level [2]. The main factor influencing Availability sub index is considered to be agricultural structure of sown areas. In this paper by application of fuzzy Z-number tools to define optimal agricultural structure two expert opinions are evaluated.

2 Statement of the Problem Two expert opinions have been used in order to outline the current state of agricultural structure of sown areas use. First expert opinion describes the current situation of the agricultural structure of sown areas in Azerbaijan. The second expert opinion as a proposal of an agricultural scientist takes into account liberated areas after II Karabakh war, which is given in Table 1 [3, 4]. Table 1. Structure of sown areas in Azerbaijan №

All categories of farmlands

Expert I

Expert II

X (Thnd. ha.)

P

X (Thnd. ha.)

P

1

Wheat

588.4

0.5949

740

0.64

2

Maize

33.7

0.0341

36

0.03

3

Barley

345

0.3488

350

0.31

4

Rye

0.3

0.0003

0.5

0.00

5

Wild oat

5.8

0.0059

6.0

0.00

6

Spelt

0.0

0.0000

0.0

0.00

7

Millet

0.1

0.0001

0.2

0.01

8

Rice

3.0

0.0030

4.0

0.00

9

Sorghum grain

0.1

0.0001

0.2

0.00

Leguminous

12.7

0.0128

15.0

0.01

10

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The Table 1 illustrates that the wheat and barley are main grown products. They are followed by maize and leguminous plants. The remaining categories of farmland have insignificant percentage (converted to probability (denoted as p) as a proxy). In this paper by employing fuzzy Z-numbers instruments two expert opinions are analyzed and the best structure is selected.

3 The Algorithm and Solution of the Problem In this paper the main purpose is to determine the best case for the structure of sown areas in Azerbaijan taking into account all categories of farmlands. In this regard the algorithm is developed consisting of five steps. The solution procedure includes subjective conversion of crisp data into fuzzy Z-numbers, addition, averaging and t-conorm operations on fuzzy Z-numbers. The algorithm of solution consists of following steps: Step 1. Based on statistical information provided in Table 1 expert opinions on agricultural structure of sown areas can be presented in fuzzy Z-numbers subjectively as following: A1 = 0.63/588.4 + 0.92/33.7 + 0.13/345 + 0/0.3 + 0/5.8 + 0/0.1 + 1/0.1 + 0.95/3.0 + 1/0.1 + 0.58/12.7 B1 = 0.15/0.5949 + 0.02/0.0341 + 0.1/0.3488 + 0.001/0.0003 + 0.01/0.0059 + 0.0001/0 + 0.0001/0.0001 + 0.002/0.003 + 0.0001/0.0001 + 0.001/0.0128 A2 = 0.59/740 + 0.57/36 + 0.24/350 + 0/0.5 + 0/6.0 + 0/0.1 + 1/0.2 + 0.6/4.0 + 1/0.2 + 0.29/15.0 B2 = 0.92/0.6424 + 0.62/0.0313 + 0.008/0.3038 + 0.08/0.0004 + 0.1/0.0052 + 1/0 + 0.33/0.0002 + 0.36/0.0035 + 0.33/0.0002 + 0.09/0.0130 The support of fuzzified data and probabilities have been built based on historical data [4]. Step 2. In this stage, expert opinions converted to fuzzy Z-numbers are added in order to find the average Z-number. For this purpose, the following adding rules as one of binary operations on fuzzy Z-numbers [5, 6] are carried out: Let us consider some binary arithmetic operations (+, −, ×, ÷) on two discrete Znumbers. If we denote * as binary operations, and Z1 = (A1 , B1 ) and Z2 = (A2 , B2 ), + = (Z1+ ∗ Z2+ ) should be estimated: then first Z12 Z1+ ∗ Z2+ = (A1 ∗ A2 , R1 ∗ R2 )

(1)

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The operations on the first part A1 ∗A2 are carried out according to arithmetic rules on fuzzy numbers. R1 ∗R2 is a convolution p12 = p1 ◦ p2 of discrete probability distributions defined as following:  p1 (x1 )p2 (x2 ) p12 (x) = (2) x=x1 +x2 + + as Z12 = (A1 ∗A2 , p12 ), which is the first stage in computation As a result, we have Z12 with discrete fuzzy Z-numbers. By definition, a fuzzy Z+ number carries more information than a fuzzy Z-number. This is the reason why it is labelled a fuzzy Z+ number. As will be seen in the sequel, computation with fuzzy Z+ numbers is a portal to computation with fuzzy Z-numbers [7]. In the next stage, it gets obvious that the probability distributions of p1 and p2 are not exactly known for data given as Z-numbers. So fuzzy restrictions on p1 and p2 are taken into account: n1 μA1 (x1k )p1 (x1k ) is B1 , (3) k=1

n2 k=1

μA2 (x2k )p2 (x2k ) is B2 ,

(4)

Thus, Bj , j = 1, 2 is a discrete fuzzy number,   that is a soft constraint on probability measure of Aj . Thus, values of bjl ∈ supp Bj , j = 1, 2; l = 1, . . . , m of the discrete fuzzy number of Bj , j = 1, 2 are probability values of Aj , bjl = P(Aj ). In order to evaluate pj the following goal-programming problem must be solved:             (5) μAj xj1 pjl xj1 + μAj xj2 pjl xj2 + . . . + μAj xjn pjl xjn → bj Subject to        pjl xj1  + pjl xj2 + · · · + pjl xjn = 1 pjl xj1 , pjl xj2 , · · · , pjl xjn ≥ 0

(6)

n j Taking into account the fuzzy restrictions i=1 μAj (xji )pj (xji ) is Bj , probability distributions pj , j = 1, 2 are obtained by solution of the goal programming problems given below: c1 v1 + c2 v2 + · · · + cn vn → bj

(7)

Subject to v1 + v2 + · · · + vn = 1 v1 , v2 , · · · , vn ≥ 0

 (8)

where, ck = μAj (xjk ), vk = pj (xjk ), k = 1, . . . , nj It must be noted that to guarantee a unique solution for goal programming problem (7)–(8) the compatibility conditions have to be employed.

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  As a result, pjl xjk , k = 1, . . . , n is obtained. Then, solving n linear goal programming problems the fuzzy set of probability distribution pjl is constructed. Membership function values of fuzzy set of convolutions p12s , s = 1, . . . , m2 is found as following:   μp12 (p12 ) = max μp1 (p1 ) ∧ μp2 (p2 ) (9) p1 ,p2

Subject to.

nj        μAj xjk pj xjk , j = 1, 2 μpj pj = μBj p12s (x) =

(10)

k=1



p1 (x1 )p2 (x2 ), ∀x12 ∈ X12 ; x1 ∈ X1 ; x2 ∈ X2

(11)

x=T (x1 ,x2 )

 In the final step P(A12 ) = nk=1 μA12 (x12k )p12 (x12k ) turning into B12 taking into account the membership function μB12 that induces fuzziness, is found as below:   μB12 (b12s ) = sup μp12s (p12s ) (12) Subject to b12s =



p12s (xk )μA12 (xk )

(13)

k

Finally, Z12 = Z1 + Z2 = (A12 , B12 ) is obtained. The summing of Z-numbers have been carried out by a special program coded and added as an additional tool in Matlab by the authors of “The arithmetic of Z-numbers” [5]. Step 3. Afterward of addition, the average Z Average = (A, B) of Z1 , Z2 is computed, that is given in Table 2. Step 4. Further, the averaged Z-number is defuzzified according the following rules: The A part of averaged Z-number is defuzzified referring [8] employing the formula given below: μa˜ =

l+m+u (25) 3

where a˜ = (l, m, u) – is a triangular fuzzy number In this stage according to Kang’s method [9], the reliability part B of obtained Z-number is converted into crisp number as given below:  xμR˜ (x)dx α= (36) μ∗˜ (x)dx R

˜ is reliability part, μ ˜ (x)- is membership values, x-probability values, μ∗ (x)where RR R˜ is minimum membership function values for B part of Z-numbers (expert I and expert II).

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Table 2. Average of Z-numbers №

Z Average = (A, B)

1

[(568.43, 664.2, 883.7) (0.1368, 0.1516, 0.1928)]

2

[(31.78, 34.85, 39.75) (0.0036, 0.0041, 0.0063)]

3

[(171.63, 347.5, 363.5) (0.0531, 0.0871, 0.1048)]

4

[(0.075, 0.40, 0.4505) (0.00036, 0.000431, 0.000434)]

5

[(1.525, 5.9, 6.1) (0.000397, 0.000537, 0.002184)]

6

[(0, 0.055, 0.11) (0, 0, 0)]

7

[(0.05, 0.15, 0.25) (0, 0, 0)]

8

[(2.1, 3.5, 5.6) (0.000317, 0.000384, 0.000594)]

9

[(0.05, 0.15, 0.25) (0, 0, 0)]

10

[(10, 13.85, 27.15) (0.000356, 0.000427, 0.000753)]

Table 3. Averaged expert opinions №

All categories of farmlands

Average structure of sown areas X (Thnd. ha.)

P

1

Wheat

705,44

0.64

2

Maize

35,46

0.02

3

Barley

294,21

0.30

4

Rye

0,31

0.01

5

Wild oat

4,51

0.01

6

Spelt

0,06

0.00

7

Millet

0,15

0.00

8

Rice

3,73

0.00

0,15

0.00

9 10

Sorghum grain Leguminous

17,0

0.01

Subsequently, the expert opinions given in Z- numbers combined as an average of Z-numbers that is broken down in Table 3 as an optimal structure of sown areas taking into account both expert evaluations. Step 5. Finally, to distinguish expert opinions in Z-numbers, t-conorm operation on the base of rule: T(Z1 , Z2 , Z Average ) = max(Z1 , Z2 , Z Average ) is performed [10–12]. The selected expert opinion as a best case is introduced in Table 4. To sum up, it can be inferred that t-conorm operation on expert opinions (Expert II, and Average version) allows selecting the best case. The selected best case puts forward the highest possible and optimal structure over the all categories of farmlands.

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№

All categories of farmlands

The selected expert opinion X (Thnd. ha.)

P

1

Wheat

740

0.64

2

Maize

36

0.03

3

Barley

350

0.31

4

Rye

0.5

0.01

5

Wild oat

6.0

0.01

6

Spelt

0.06

0.00

7

Millet

0.2

0.00

8

Rice

4.0

0.00

Sorghum grain

0.2

0.00

Leguminous

17

0.01

9 10

4 Conclusions In this paper, we carried out evaluation of expert opinions with the application of the theory and instruments of fuzzy Z-numbers. Concept of Z-numbers is suitable to generalize expert opinions into a single one, on that account we applied Z-number average and t-conorm operator. Taking into consideration that Z-numbers based reasoning is suitable to deal with partially reliable information in economics, it has an advantage over the traditional fuzzy methods in evaluation and selection of expert opinions. The proposed approach can be a piece of help for decision-makers in application to the different aspects of socio-economic systems.

References 1. https://www.unccd.int/resources/knowledge-sharing-system/global-food-security-index 2. https://impact.economist.com/sustainability/project/food-security-index/Index 3. Ibrahimov, I.: Development perspectives of regions and liberated areas. Cooperation, Baku, 240 p. (2022) 4. www.azstat.gov.az 5. Aliyev, R., Huseynov, O., Aliyev, R., Alizadeh, A.: The Arithmetic of Z-numbers. Theory and Applications, 301 p. World Scientific Publishing Co. (2015) 6. Aliyev, R., Huseynov, O., Aliyev, R., Alizadeh, A.: The arithmetic of discrete Z-numbers. Inf. Sci. 290(1), 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 7. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181, 2923–2932 (2010) 8. Rahmani, A., Lotfi, H., Rostami, M., Allahviranloo, T.: A new method for defuzzification and ranking of fuzzy numbers based on the statistical beta distribution. Adv. Fuzzy Syst. 2016, Article ID 6945184, 8 p. https://doi.org/10.1155/2016/6945184 9. Kang, B., Wei, D., Li, Y., Deng, Y.: Amethod of converting Z-number to classical fuzzy number. J. Inf. Comput. Sci. 9(3), 703–709 (2012)

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10. Aliyev, R.R., Huseynov, O.H., Aliyeva, K.R.: Z-valued t-norm and and t-conorm operatorsbased aggregation of partially reliable information. Procedia Comput. Sci. 102, 12–17 (2016). https://doi.org/10.1016/j.procs.2016.09.363 11. Gardashova, L.A.: Using fuzzy probabilistic implication in Z-set based inference. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 33–39. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_5 12. Aliev, R.A., Pedrycz, W., Eyupoglu, S.Z., Huseynov, O.H.: Approximate reasoning on a basis of Z-number-valued ıf-then rules. IEEE Trans. Fuzzy Syst. 25(6), 1589–1600 (2017). IEEE Computational Intelligence Society, USA. https://ieeexplore.ieee.org/document/7572935

Pareto-Optimality-Based Investigation of Quality of Fuzzy IF-THEN Rules Nigar E. Adilova(B) Joint MBA Program, Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku AZ1010, Azerbaijan [email protected]

Abstract. In recent times, fuzzy IF-THEN rules have been successfully applied to construct conditional statements in decision making, decision analysis etc. The specification of quality criteria of fuzzy IF-THEN rules provides a better model to be used, created alternative cases, and selected one of the important cases among alternatives. Therefore, great number of works have been dedicated to define preferable case of rule base. However, obtaining Pareto-optimality solutions is still considered an important matter to improve quality criteria. In this paper, the author proposes Pareto-optimality-based investigation of quality of IFTHEN rules. As the main part of this work, the mentioned approach is solved by considering the importance of quality criteria. An experimental analysis is carried out regarding the quality criteria assessment for different cases of If-Then model. Keywords: Pareto-optimality · Fuzzy IF-THEN rules · Quality criteria · Complexity · Coverage · Partition · Inconsistency · Accuracy

1 Introduction The existence of imprecise information in multi-criteria decision making is an actual problem, which has been widely spread. It can be concluded with the lack of certainty or distinctness. The usage of optimization methods, or in wide sense, the updating If-Then model can be a reason to apply a better model even in an ambiguous environment. Fuzzy Pareto-optimality is a fundamental theory to obtain Pareto-optimal cases among all possible variants. The main theoretic goal of this method is to define the lowest degree as Pareto optimality case and the highest degree as a strong definition of optimality. Respectively, the lowest degree can be identified with 0, and the highest one can be accepted as 1. A set of these points categorizes as an optimal solution, a small subset points are considered as Pareto front. This classification demonstrates dominance relation among objectives. For the first principle the number of objectives in a solution must be identified to improve the other solution. The second principle is to define the size of each improvement. As a result, “less” and “more” optimal solutions are individualized [1–5]. Widely developed theories on this field with the combination of fuzzy logic tools, multi-objective optimization and decision-making methods are available in the following resources [6–10]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 196–202, 2023. https://doi.org/10.1007/978-3-031-25252-5_29

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This paper examines an optimal method known as Pareto-optimality to any kind of IF-THEN model. The motivation of the paper is about the investigation of multicriterial optimization problem for fuzzy If-Then rules [11]. An optimal solution can be acquired with the assistance of Pareto-optimality method. Therefore, the rest of the paper is structured as follows: Section 2 offers fuzzy IF-THEN rules and Pareto-optimality-related some preliminary information. Section 3 covers the general description of the problem. The solutional approach based on Pareto-optimality investigation on the specific case is exemplified in Sect. 4. Eventually, Sect. 5 is devoted to the concluding marks.

2 Preliminaries Definition 1. Fuzzy Fuzzy If-Then rules [12]: Fuzzy IF-THEN rules comprehensively identify conditional statements. Considering multi-input case fuzzy IF-THEN rules are shown as below: If (X1 is A1 ), (X2 is A2 ), . . . , (Xn is An ) Then Y is B where Ai determines information granules. Definition 2. Quality criteria of Fuzzy If-Then rules [13, 14]: The quality criteria of Fuzzy If-Then rules must be noticed in: – – – – –

Complexity (comp); Partition (part); Coverage (cov); Inconsistency (Incons); Accuracy (RMSE).

Although the assessment of quality criteria is widely discussed in [13], overall, their measuring formulas are as (1)–(5). r  comp = m/ nk

(1)

k=1

parti = 1/(pi − 1)

(2)

⎧ pi ⎪ ⎨ hi (x) =  µ(k) (x), if 0 ≤ hi (x) ≤ 1 Xi hi (x)dx i covi = where hi (x) = k=1 ⎪ Ni pi −hi (x) ⎩ otherwise pi −1 , 

Incons(i) =

∑ [1.0 − Cons( R (i), R (k ))] + ∑ 1

1≤ k ≤ N k ≠i

1

[1.0 − Cons( R1 (i), R 2 (l ))],

1≤ l ≤ L i =1,2,..., N



n

1  RMSE =  (yi − yi )2 n

(3)

(4)



i=1

(5)

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Definition 3. Pareto-optimality [15]. Assume that two solutions are given: A1 , A2 ∈ A; (A1 is considered to dominate A2 in the Pareto sense for the given conditions) nbF, neF, and nwF are evaluated by the membership degrees of predefined fuzzy sets “greater than 0”, “equal to 0”, “less than 0” respectively. These three parameters are defined as follows: nbF(A1 , A2 ) =

M 

µib (fi (A1 ) − fi (A2 )),

(6)

µie (fi (A1 ) − fi (A2 )),

(7)

µiw (fi (A1 ) − fi (A2 )).

(8)

i=1

neF(A1 , A2 ) =

M  i=1

nwF(A1 , A2 ) =

M  i=1

In the following step, any couple of alternatives do(A1 , A2 ) is obtained as:

0, if nbF ≤ M −neF 2 do(A1 , A2 ) = 2·nbF+neF−M , otherwise nbF

(9)

do(A1 , A2 ) = 1 shows that A1 Pareto dominates A2 ; do(A1 , A2 ) = 0 shows that A1 does not Pareto dominant A2 . Membership functions for i-th objective of “” cases are described in the following (Fig. 1)

=




0

Fig. 1. Membership functions for i-th objective of “ ” cases

3 Statement of the Problem Consider that FRBS (Fuzzy Rule-based System) consists of n number of rules, m number of antecedents and a consequent as given below:

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If X1 is High, X2 is Low, …., Xm is Low, Then Y is Small If X1 is High, X2 is Low, …., Xm is Medium, Then Y is Medium If X1 is High, X2 is Low, …., Xm is High, Then Y is High … n. If X1 is Low, X2 is High, …., Xm is High, Then Y is High The problem is designed to improve FRBS by using multi-criteria optimization method. The solution of the problem must be realized by considering constraints on fuzzy terms, collection of the rules, collection of the terms, quality criteria [14]. To develop FRBS goal functions for 5 quality criteria must be emphasized: comp → max, cov → max, part → max, fincons → min, RMSE → min.

4 Solution of the Problem by Using Numerical Example We will illustrate the main features of the problem by means of a numerical example. The general problem mentioned in the previous section is concretely being solved with the aid of the given rules. The main objective is to find an optimal version of FRBS by applying Pareto-optimality method. Thus, as an experimental analysis, FRBS is a mixture of the following rules and is formed by 3 antecedents and a consequent part (Table 1): Table 1. An example for fuzzy rule-based system Rules

Antecedents

№

X1

X2

X3

Y

Consequent

1

H

L

L

S

2

H

L

M

M

3

H

L

H

H

4

H

M

L

M

5

H

M

M

M

6

H

M

H

H

7

H

H

L

H

8

H

H

M

H

9

H

H

H

H

10

M

L

L

S

…

…

…

…

…

25

L

H

L

S

26

L

H

M

M

27

L

H

H

H

where the mnemonics H, L, M, S represent “High”, “Low”, “Medium”, “Small” linguistic terms which have been marked with triangular fuzzy numbers, respectively. We consider the problem of how to improve FRBS for the quality criteria. Optimal version of FRBS may be obtained as the result of Pareto-Optimality investigation method.

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More extensively, the actuality of multi-criterial optimization matter for the given FRBS regarding to the competitive parameters has been proposed in [11]. However, in this work we have tried to make our contribution to find Pareto-Optimality solutions to this problem. For the current statement of rule base, the calculational result of quality criteria is characterized in Case-1. Other cases are formulated by updating FRBS. The main purpose of the usage of multi-cases is related to the multi-criteria optimization problem solution. Consequently, evaluation of quality criteria using (1)–(5) for the obtained 4 cases is reflected in Table 2. Table 2. Measures of quality criteria for FRBS Cases

Complexity

Coverage

Partition

Inconsistency

RMSE

Case-1

0,045

0,588

0,5

0,0153

8,704

Case-2

0,045

0,584

0,5

0,0178

6,578

Case-3

0,045

0,592

0,5

0,0184

8,824

Case-4

0,045

0,617

0,5

0,017

34,92

First, experiments are initiated with normalizing the parameters described in Table 2. The application of constraints on quality criteria given in [11] helps to construct a better model. For the normalization of positive parameters in the goal function, we will use formula (10), for negative indices formula (11) will be applied. = xinorm j xinorm j

=

xi j − xjmin xjmax − xjmin

,

(10)

xjmax − xi j

(11)

xjmax − xjmin

Correspondingly, a result of normalizing values is summarized in Table 3. Table 3. Normalized values of quality criteria Cases

comp

cov

part

fincons

RMSE

Case-1

0

0.121212121

0

1

0.924988

Case-2

0

0

0

0.193548387

1

Case-3

0

0.242424242

0

0

0.920754

Case-4

0

1

0

0.451612903

0

Then the realization of Pareto-optimality-based investigation will be activated with the given program code:

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201

After that the degree of optimality (do) is automatically calculated for (6)–(9) equations. Hereby, do result for the given FRBS will be as follows (Table 4): Table 4. The degree of optimality for 4 cases Cases

do

Case-1

1

Case-2

0.0809

Case-3

0.1207

Case-4

0.5965

Diversified series of cases are described as below: Case − 1  Case − 4  Case − 3  Case − 2 It is obvious that the best solution is Case-1 as it has the maximal optimality degree.

5 Conclusion In this paper a method based on the principle of pareto-optimality for optimizing the quality of fuzzy If-Then rules has been investigated and a rule base close to the optimal case has been obtained. Numerical example given in the study reveals validity of proposed investigation method. Results extracted from the experimental analysis reflects Pareto-optimality-based solution to the problem.

References 1. Farina, M., Amato, P.: A fuzzy definition of “optimality” for many-criteria optimization problem. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 34(3), 315–326 (2004) 2. Farina, M., Amato, P.: On the optimal solution definition for many-criteria optimization problems. In: Proceedings of the NAFIPS-FLINT International Conference, New Orleans, pp. 233–238. IEEE Service Center (2002) 3. Carlsson, C., Fuller, R.: Multiobjective optimization with linguistic variables. In: Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing, EUFIT 1998, Aachen, Verlag Mainz, Aachen, vol. 2, pp. 1038–1042 (1998)

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4. Alizadeh, A.V.: Application of the fuzzy optimality concept to decision making. In: 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions, pp. 373–382 (2020) 5. Alizadeh, A.V., Musayev, A.A., Aliyev, R.R.: Application of the fuzzy optimality concept to decision making with imprecise probabilities. In: Sixth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, ICSCCW 2011, b-Quadrat Verlag, pp. 373–382 (2012) 6. Aliev, R.A.: Decision making theory with imprecise probabilities. In: Proceedings of the Fifth International Conference on Soft Computing and Computing with Words in System Analysis, Decision and Control (ICSCCW 2009), Famagusta, North Cyprus, p. 1 (2010). https://doi. org/10.1109/ICSCCW.2009.5379425 7. Jabbarova, K.I.: Application of expected utility to business decision making under U-number valued information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 716–723. Springer, Cham (2019). https://doi.org/10. 1007/978-3-030-04164-9_94 8. Jabbarova, K., Hasanova, N.: An application of the VIKOR method to decision making in investment problem under Z-valued information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 499–506. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_67 9. Gardashova, L.A., Guirimov, B.G.: Decision making problem of a single product dynamic macroeconomic model on base of fuzzy uncertainty. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 237–245. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_30 10. Imanova, G.E., Imanova, G.: Some aspects of fuzzy decision making in digital marketing analysis. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 465–473. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_63 11. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy IF-THEN rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/ 10.1007/978-3-030-64058-3_10 12. Novák, V., Lehmke, S.: Logical structure of fuzzy IF-THEN rules. Fuzzy Sets Syst. 157(15), 2003–2029 (2006) 13. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_7 14. Adilova, N.E.: Specificity of fuzzy rule bases. Dissertation work for the degree of Doctor of Philosophy, Baku, Azerbaijan, 160 p. (2022) 15. Aliev, R.A.: Uncertain Computation-Based Decision Theory, 521 p. World Scientific, Singapore (2017)

Predicting Solar Power Generated by Grid-Connected Two-Axis PV Systems Using Various Empirical Models Youssef Kassem1,2,3,4(B) , Hüseyin Gökçeku¸s2,3,4 , Marilyn Hannah Godwin2,4 James Mulbah Saley2,4 , and Momoh Ndorbor Mason2,4

,

1 Faculty of Engineering, Mechanical Engineering Department, Near East University,

Nicosia 99138, North Cyprus [email protected] 2 Faculty of Civil and Environmental Engineering, Near East University, Nicosia 99138, North Cyprus [email protected], {20215601,20213832, 20213467}@std.neu.edu.tr 3 Energy, Environment, and Water Research Center, Near East University, Nicosia 99138, North Cyprus 4 Engineering Faculty, Kyrenia University, Kyrenia 99138, North Cyprus

Abstract. The main goal of this paper is to predict the mean monthly electricity generation (EG) produced by Two-axis solar systems using the Adaptive-Neuro Fuzzy Inference System (ANFIS) and Response Surface Methodology. The Twoaxis solar systems are located in 25 coastal Mediterranean cities. Accordingly, in this study, the geographical coordinates (latitude, longitude, and altitude) and climate conditions (global solar radiation, air temperature, and clearance index) were collected and used as input variables for the models. The results showed that all proposed models were suitable for EG prediction. The results demonstrated that the RSM model has produced the highest value of R-squared (0.956) and lowest value of RMSE (42.672 kWh) compared to the ANFIS model. Keywords: Electricity generation · ANFIS · RSM · Climate conditions · Geographical coordinates

1 Introduction The growth of population and energy demand has led to an increase in the consumption of fossil fuels [1]. Moreover, climate change has forced countries for finding an alternative sources for generating electricity and reducing greenhouse gas emissions [2]. Therefore, utilizing renewable energy as an alternative energy source will help to reduce environmental problems, essentially greenhouse gas emissions and air pollution due to increasing fossil fuel consumption [3, 4]. Renewable energy including solar energy is rapidly increasing due to economically viable and limited environmental impacts [5]. Recently, several studies have investigated the utilization of renewable energy as a clean © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 203–210, 2023. https://doi.org/10.1007/978-3-031-25252-5_30

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energy source in different locations [6–8]. For example, Mansouri et al. [7] estimated the potential of rooftop PV electricity in Lethbridge, Canada using LiDAR data and ArcGIS. The results showed that the developed system has huge potential to offset the energy demand of the city. Generally, geographic location and climate conditions are most factors that affect the performance of the solar system particularly power generated [9]. In recent years, machine learning and mathematical models have been employed to predict the performance of the solar system [9–11]. In this regard, the present paper aims to predict the power generation for Two-axis grid-connected solar system using ANFIS and RSM models. To this aim, the geographical coordinates (latitude, longitude, and altitude) and climate conditions (global solar radiation, air temperature, and clearance index) were collected and used as input variables for the models.

2 Material and Methods 2.1 Study Area and Data In this research, 25 coastal Mediterranean cities located in Libya, Lebanon, Syria, Palestine, Tunisia, and Algeria are taken as a case study for predicting the mean monthly electricity generation produced by a small-scale Two-axis grid-connected solar system. The mean monthly climate parameters and electricity generation of the solar system are collected from Ref. [12]. The statistics summary of the selected variables is tabulated in Table 1. Table 1. Statistical parameters of the collected data. Variable

Unit

Explanation

Lat

◦

Mean

SD

Min.

Max.

Latitude

33.92

2.02

31.19

36.91

Long

◦

Longitude

18.30

11.55

−0.64

36.00

Alt

m

Altitude

31.92

42.23

3.00

204.00

GSR

kWh/m2

Global solar radiation

5.15

1.91

2.01

8.50

AT

◦C

Air temperature

5.15

1.91

2.01

8.50

Cl

–

Clearance index

0.60

0.07

0.46

0.74

EG

kWh

Electricity generation

735.30

188.50

390.40

1125.40

SD: Standard deviation; Min: Minimum; Max: Maximum

2.2 Adaptive-Neuro Fuzzy Inference System (ANFIS) In 1993, Jang has developed the ANFIS as a hybrid of artificial neural network (ANN) and fuzzy inference system (FIS) [13]. ANFIS combines the advantage of ANN learning

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ability and reasoning ability of rule-based FIS that can include past observation in the classification process [14]. In this model, the fuzzy logic definition is used to build the system and the neural network automatically optimizes the system parameters as opposed to manual optimization in building a system in FIS [13–15]. The flexibility and adaptability of the ANFIS model make it a proven approach to dealing with uncertainty that is in addition to its high ability to handle large noisy data from dynamic and complex systems [13–15]. The description of the MFFNN and CFNN models was given in Ref. [16, 17]. In this research, the training (60%), checking, and testing data (other parts) were used to develop and validate the model, respectively. The results of the ANFIS are compared with observed data. 2.3 Response Surface Methodology The RSM is a mathematical and statistical method polynomial model as expressed below [18, 19]. Y = β0 +

n  i=1

βi xi +

n  i=1

βii xi2 +

n n−1   i

βij xi xj

(1)

i=i+1

where Y is the predicted response, β0 , βi , are related to the main effects and βii and βij to interaction, x i and x j are the independent variables. The main goal of this model is to show the interaction between the input variables and output variables as shown in Eq. (2) EG = f (Lat, Long, Alt, GSR, AT , CL)

(2)

3 Results and Discussion In this study, two models are developed and evaluated to find the suitable model for the mean monthly EG prediction Then, the results of the proposed models are compared with each other. These models are ANFIS and RSM. In this study, the training was done using the mean monthly data for Al khums, Al Ladhiqiyah, Alexandria, Algiers, Annaba, Az Zawiyah, Beirut, Bejaia, Benghazi, Djerba Modoun, Gabes, Gaza Strip, Matrouh, Misratah, and Oran. For checking, mean monthly data for Surt, Sousse, Skikda, Sfax, and Port Said were utilized for checking/validating the model. The developed model was used to predict the monthly EG for Tartus, Tripoli-Lebanon, Tripoli-Libya, Tunis, and Turbruq. 3.1 Modeling with ANFIS ANFIS algorithm is used to estimate the relationship between the EG as geographical coordinates (Lat, Long, and Alt) and climate conditions (GSR, AT, and Cl). In this work, the trial and error method was utilized to determine the number of membership functions, and type of membership for input and output. Table 2 lists ANFIS information.

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Information

Value

Number of nodes

161

Number of linear parameters

64

Number of nonlinear parameters

36

Total number of parameters

100

Number of training data pairs

180

Number of checking data pairs

60

Number of fuzzy rules

64

Number of membership functions for each input

2

Membership grades for input

Triangular-shaped

The output port of each rule use

Linear defuzzifier

Moreover, the hybrid algorithm with the least square method and the backpropagation gradient descent method is employed in ANFIS learning. Figure 1 shows the structure (rules) of the tuned FIS. Furthermore, the rule viewers, which indicate the value of different inputs to the ANFIS model and determining output are shown in Fig. 2. Additionally, Fig. 2 shows the scatter diagram that compared the observed data with the estimated ones by the ANIFS model in the training phase.

Fig. 1. Structure of the ANFIS model

3.2 Modeling with RSM The mathematical equation that was developed using RSM (Eq. (3)) for predicting the EG is expressed as shown below.

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EG = −71317 + 409(Lat) + 59.2(Long) + 17.03(Alt) + 76(GSR) − 931(Cl)           + 4.96 Lat 2 − 0.0746 Long 2 + 0.02952 Alt 2 + 7.34 GSR2 + 5067 Cl 2 − 1.473(Lat)(Long) − 0.555(Lat)(Alt) + 2.87(Lat)(GSR) − 86.3(Lat)(Cl) − 0.1038(Long)(GSR) − 0.017(Long)(GSR) − 7.3(Long)(Cl) + 0.0252(Alt)(GSR)

(3)

+ 0.61(Alt)(Cl) − 292(LGSR)(Cl)

EsƟmated data [kWh]

Figure 3 compares the scatter plots of the RSM model versus the observed data in the training and checking phase. It can be noticed that the estimated values are closed to the measured data.

1

Training phase

0.8 0.6 0.4 y = 0.9489x + 0.029 R² = 0.9346

0.2 0 0

0.2

0.4

0.6

0.8

1

Observed data [kWh]

EsƟmated data [kWh]

Fig. 2. Correlation between the observed and predicted data using the ANFIS model.

1 0.8 0.6 0.4 0.2

y = 0.951x + 0.028 R² = 0.9493

0 0

0.2

0.4

0.6

0.8

1

Observed data [kWh] Fig. 3. Correlation between the observed and predicted data using RSM in the training phase.

3.3 Performance Evaluation of ANFIS and RSM The ANFIS’s performance is compared with the RSM to evaluate the performance of the proposed models. The values of R-squared and root mean squared error (RMSE) are listed in Table 3. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the RSM model. Figure 4 illustrates the time series plot for each location used in the testing phase.

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Fig. 4. Time series plot for the locations used in the testing phase

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Table 3. Overall performance evaluation of the models. Statistical indicator R-squared RMSE [kWh]

ANFIS

RSM

0.949

0.956

47.358

42.672

4 Conclusions The prediction of electricity generation from the solar system is very important for the power grid’s secure, stable, and economical operation. Therefore, ANFIS and RSM models were designed and developed to predict the mean monthly electricity generation from the Two-axis solar system located in 25 coastal Mediterranean cities The results showed that all proposed models were suitable for estimating the EG of the solar system. Among the developed models, the RSM model presented significantly better prediction performance based on the value R2 and RMSE.

References 1. Kassem, Y., Çamur, H., Aateg, R.A.F.: Exploring solar and wind energy as a power generation source for solving the electricity crisis in Libya. Energies 13(14), 3708 (2020). https://doi. org/10.3390/en13143708 2. Ghazouani, A., Jebli, M.B., Shahzad, U.: Impacts of environmental taxes and technologies on greenhouse gas emissions: contextual evidence from leading emitter European countries. Environ. Sci. Pollut. Res. 28(18), 22758–22767 (2021). https://doi.org/10.1007/s11356-02011911-9 3. Kassem, Y., Gökçeku¸s, H., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 7(3), 1475–1502 (2020). https://doi.org/10.1007/s40808-020-00866-y 4. Kassem, Y.: Computational study on vertical axis wind turbine car: static study. Model. Earth Syst. Environ. 4(3), 1041–1057 (2018). https://doi.org/10.1007/s40808-018-0461-x 5. Shahsavari, A., Akbari, M.: Potential of solar energy in developing countries for reducing energy-related emissions. Renew. Sustain. Energy Rev. 90, 275–291 (2018). https://doi.org/ 10.1016/j.rser.2018.03.065 6. Yadav, S.K., Bajpai, U.: Performance evaluation of a rooftop solar photovoltaic power plant in Northern India. Energy Sustain. Dev. 43, 130–138 (2018). https://doi.org/10.1016/j.esd. 2018.01.006 7. Mansouri Kouhestani, F., Byrne, J., Johnson, D., Spencer, L., Hazendonk, P., Brown, B.: Evaluating solar energy technical and economic potential on rooftops in an urban setting: the city of Lethbridge, Canada. Int. J. Energy Environ. Eng. 10(1), 13–32 (2018). https://doi.org/ 10.1007/s40095-018-0289-1 8. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Economic assessment of renewable power generation based on wind speed and solar radiation in urban regions. Glob. J. Environ. Sci. Manag. 4(4), 465–482 (2018). https://doi.org/10.22034/gjesm.2018.04.007 9. Kassem, Y., Othman, A. A.: Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models. Model. Earth Syst. Environ., 1–26 (2022). https://doi.org/10.1007/s40808-022-01413-7

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10. da Silva Fonseca, J.G., Jr., Oozeki, T., Takashima, T., Koshimizu, G., Uchida, Y., Ogimoto, K.: Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu, Japan. Prog. Photovolt. 20(7), 874–882 (2012). https://doi.org/10.1002/pip.1152 11. Kumar, P.M., Saravanakumar, R., Karthick, A., Mohanavel, V.: Artificial neural networkbased output power prediction of grid-connected semitransparent photovoltaic system. Environ. Sci. Pollut. Res. 29(7), 10173–10182 (2021). https://doi.org/10.1007/s11356-021-163 98-6 12. Kassem, Y., Gökçeku¸s, H., Lagili, H.S.A.: A techno-economic viability analysis of the twoaxis tracking grid-connected photovoltaic power system for 25 selected coastal Mediterranean cities. Eng. Technol. Appl. Sci. Res. 11(4), 7508–7514 (2021). https://doi.org/10.48084/etasr. 4251 13. Tabbussum, R., Dar, A.Q.: Performance evaluation of artificial intelligence paradigms— artificial neural networks, fuzzy logic, and adaptive neuro-fuzzy inference system for flood prediction. Environ. Sci. Pollut. Res. 28(20), 25265–25282 (2021). https://doi.org/10.1007/ s11356-021-12410-1 14. Zaman, M., Hassan, A.: Improved statistical features-based control chart patterns recognition using ANFIS with fuzzy clustering. Neural Comput. Appl. 31(10), 5935–5949 (2018). https:// doi.org/10.1007/s00521-018-3388-2 15. Yue, X., Chen, Y., Chang, G.: Accurate modeling of biodiesel production from castor oil using ANFIS. Energy Sour. Part A Recover. Utili. Environ. Eff. 40(4), 432–438 (2018). https://doi. org/10.1080/15567036.2017.1422058 16. Kassem, Y., Çamur, H., Bennur, K.E.: Adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) for predicting the kinematic viscosity and density of biodieselpetroleum diesel blends. Am. J. Comput. Sci. Technol. 1(1), 8–18 (2018). https://doi.org/10. 11648/j.ajcst.20180101.12 17. Kassem, Y., Çamur, H., Esenel, E.: Adaptive neuro-fuzzy inference system (ANFIS) and response surface methodology (RSM) prediction of biodiesel dynamic viscosity at 313 K. Procedia Comput Sci 120, 521–528 (2017). https://doi.org/10.1016/j.procs.2017.11.274 18. Kassem, Y., Çamur, H.: Prediction of biodiesel density for extended ranges of temperature and pressure using adaptive neuro-fuzzy inference system (ANFIS) and radial basis function (RBF). Procedia Comput. Sci. 120, 311–316 (2017). https://doi.org/10.1016/j.procs.2017. 11.244 19. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Prediction of kinematic viscosity and density of biodiesel produced from waste sunflower and canola oils using ANN and RSM: comparative study. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 880–887. Springer, Cham (2020). https:// doi.org/10.1007/978-3-030-35249-3_117

Z-Preferences in Consumer Buying Behavior Khatira J. Dovlatova(B) Joint MBA Program, Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, Baku AZ1010, Azerbaijan [email protected]

Abstract. In recent years one of the main topics in the marketing environment advancing consumer behavior and their decision making process. The research paper focuses on the analysis of variables influence on consumers’ buying behavior and their decision in marketing. Marketing is the process which begins with the consumers’ needs, desires, demands and ends with consumer purchasing decision making. Professional marketing managers attempt to clarify consumers and their feedback, therefore they analyze the main features of their behavior. As the process customer buying behavior comes from identifying needs, collecting information, ranking alternatives and realizing the decision making process. All these steps taken by consumer before making a purchase start the formation of the buyer’s desire to make a purchase. Research papers are related to consumer behavior. Marketers initiate to affect to each marketing decisions by providing information which may form the consumer evaluation. The research paper is dedicated to clarifying the various variables of customer purchasing behavior, which are analyzed by using Z numbers. Decision making process and customer behavior are usually subordinated to uncertainties associated with influences of different determinants. In research paper, the Z-number theory is applying to regulate ambiguous situations in investigating the consumer buying behavior. This paper is useful for marketers to analyze and understand the customers’ interests. Research can also help support their marketing tactics and strategy for clarifying different criteria in buying process. Keywords: Customer buying behavior · Marketing strategy · Consumer decision-making · Purchase decision · Z-numbers · Preferences

1 Introduction For being successful in marketing place one of the main rules is to clarify consumer behavior. Consumer attitudes and marketing strategy are in very closely relationship. Most companies focus on realizing the behavior of their target market. Consumer behavior comprises the psychological processes which consumers go through in clarifying their needs, discovering ways to solve these needs, making buying decision. Research process of consumer behavior initiates not only to understand purchase as the process but also to clarify purchasing motives and reasons. Analyzing consumer behavior is the process of how individually consumers make decision to use their accessible resources © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 211–217, 2023. https://doi.org/10.1007/978-3-031-25252-5_31

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for consumption process. This operation combines the study of different factors and determinants influencing customers buying behavior in Z-environment. There are various uncertainty handling models that are improved the analysis of uncertain data. In marketing fuzzy logic approaches, managerial decision, market segmentation are founded and applied [1–3]. Research papers on consumer buying practices have mainly focused on statistical and fuzzy approach. But modern research information is described by integration of fuzzy and incomplete information. Prof. Zadeh established the Z-number conception as new approach in uncertain computation. Z-number concept can be applied for different sectors, especially in marketing, consumer behavior, risk assessment processes.

2 Preliminaries Definition 1. The Z-number [4, 5]: A couple of two fuzzy numbers A and B is represented by Z = (A, B). The value A is a limitation on the values which the uncertain value characterizes as a real value and the second B component measures the degree of ambiguity of the first A component. Definition 2. A discrete Z-number: A fuzzy number depicts a fuzzy limitation on the values which the random variable Y may take and characterizes first component Z = (A, B). B is a discrete fuzzy number with a membership function μB : {b1 , ..., bn } → [0, 1] that depicts a fuzzy limitation on the probability of A: P(A) is B. Definition 3. Operations using for Discrete Z-numbers: Data Y1 and Y2 are discrete Z-numbers depicting the information concerning values of Z12 = MIN (Z1 , Z2 ) and Z12 = MAX (Z1 , Z2 ). Take into consideration calculation of Z12 = Z1 ∗ Z2 , ∗ ∈ {+, −, ·, /}. The first step is calculation of A12 = A1 * A2 . The next step included obtaining of B12 . As a defining result, Z12 = Z1 * Z2 is constructed as Z12 = (A12 , B12 ). A, Z = (λA1 , B1 ) is defined from the scalar multiplication Z = λZ1 , λ ∈ R [6–8]. Definition 4. Finding a distance between Z-numbers: A Z-number Z = (A, B) is described by fuzzy number A, fuzzy number B and an underlying set of probability distributions G. We offer to determine distance between Z-numbers D(Z1 , Z2 ) as mentioned below: Distance between A1 and A2 is computed as D(A1 , A2 ) = supα∈(0,1] D(Aα1 , Aα2 ), D(Aα1 , Aα2 )

  α  A11 + Aα12 Aα21 + Aα22   − = . 2 2

(1) (2)

Aα1 and Aα2 denote α-cuts of A1 and A2 relevantly, Aα11 , Aα12 indicate lower and upper borders of Aα1 (Aα21 , Aα22 are those of Aα2 ). Distance between B1 and B2 is calculated analogously.

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3 Statement of the Problem In the decision-making process, consumer purchasing behavior is influenced by various variables. The aim of this study is to analyze the preference of attributes which influence the consumer buying behavior and choose the best alternative for buying process. By using MCDM problem given 4 criteria and 4 alternatives are involved: C1 - hedonism, C2 - shopping experience, C3 - brand perception, C4 - purchasing intention. A1 , A2 , A3 , A4 , Problem of decision making is Z-preference in consumer buying behavior. Four decision criteria are considered: hedonism, shopping experience, brand perception, purchasing intention. Hedonism is an important variable which directly influences consumer buying behavior, represents emotional qualifications and focuses on implementing emotional satisfaction. Shopping experience is defined as customer internal and subjective response to direct and indirect interconnection with the company’s service, product or other offers. One of the main consumers’ ability-brand perception is the process which consumers can define the brand under different situations, as expressed by brand identification or recall performance. Purchasing intention is one of the main variable which marketers use to predict prospective sales and to clarify how the operations they take will influence consumers’ buying process. The given criteria are used for comparing 4 alternatives during uncertainty environment, the decision-appropriate information is described by partial reliability and fuzziness. In this paper we use incompletely dependable preference degrees of the Saaty scale to characterize relative importance of attribute in Table 1. ˜ Table 1. Z matrix of the attribute (A) Criteria (C1 )

(C2 )

(C1 )

(0.99 1 1)(0.99 1 1)

(7 8 9)(0.7 0.8 9)

(C2 )

(0.11 0.13 0.14)(0.7 0.8 0.9) (0.99 1 1)(0.99 1 1)

(C3 )

(0.14 0.17 0.2)(0.8 0.9 1)

(0.2 0.3 0.3)(0.6 0.7 0.8)

(C4 )

(0.33, 0.5, 1)(0.1 0.2 0.3)

(0.14, 0.16, 0.2)(0.5 0.6 0.7)

Criteria (C3 )

(C4 )

(C1 )

(5 6 7)(0.8 0.9 1)

(1 2 3)(0.1 0.2 0.3)

(C2 )

(3 4 5)(0.6 0.7 0.8)

(5 6 7)(0.5 0.6 0.7)

(C3 )

(0.99 1 1)(0.99 1 1)

(2 3 4)(0.7 0.8 0.9)

(C4 )

(0.25, 0.33, 0.5)(0.7 0.8 0.9) (0.99 1 1)(0.99 1 1)

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A 4 × 4 pairwise comparison matrix of Z-numbers with triangular fuzzy numbers (TFNs)-formed on elements is represented below: So, we need to define the best alternative in the given Z-valued information on criteria assessment and significance: Find a∗ ∈ {a1 , ..., a9 } such that a∗  ai , i = 1, ..., 9, where  denotes preference. Then we depict the explanation way for issue. Firstly, we will check elements of matrix for constructing a consistent pairwise comparison matrix. Constructed a consistent pairwise comparison matrix, we will calculate its Zvalued eigenvectors to estimate significance weights of criteria. In the following step an ideal alternative will be defined which weight is the highest one between criteria values. As a final solution, alternatives will be compared by using distance results that defined by using (1–2).

4 Solution of the Problem Defined optimal matrix is described by the results of the constraint and objective function [9, 10] (Table 2). Table 2. For original and optimal matrices results of limitations Constraints and objective function

Original matrix

Equal-to-Unity consistency check, constraint

0.0001

Reciprocity consistency check, constraint

9.725

Transitivity consistency check, constraint Overall inconsistency value, objective function

11207.86 1.3836

Optimal matrix 3.2887 16.084 281.09 0.173

We should clarify whether the value of K for the defined matrix (Zij ) exceeds a predefined threshold θK = 0.1. The calculated value of K is K((Zij )) = 0.33 that does not get over θK . So, the defined matrix can be computed as consistent. Then, we normalized the criteria values of the alternatives. The decision table (Table 3) is shown below: In the next step, we defined the weighted values of attribute by using the arithmetic of Z-numbers [11, 12]: Zwj Cij = Zwj ZCij , i = 1, ..., 9, j = 1, ..., 4 (Table 4). We should define the best alternative which is with the highest values of the Z-valued weighted attribute. For this reason, Z-numbers (values of the Z-valued weighted attribute) are converted to fuzzy numbers by using the method suggested by Kang et al. For each weighted criterion, the defined fuzzy numbers are compared to define the highest one. As result, the Z-number, from that the highest fuzzy number was previously defined, is used. The determined ideal alternative a∗ = (Z1∗ , ..., Z4∗ ) is shown in Table 5:

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Table 3. Z-valued criteria evaluations (C1 )

(C2 )

(C3 )

(C4 )

(C1 )

(1.03, 1.04, 1.5) (0.43, 0.44, 0.77)

(1.82, 1.83, 4.01) (0.01, 0.82, 0.83)

(2.16, 2.17, 6.24) (0.93, 0.94, 0.98)

(2.08, 2.28, 4.33) (0.46, 0.51, 0.52)

(C2 )

(0.43, 0.59, 0.6) (0.097, 0.099, 0.1)

(1.061, 1.063, 1.068) (0.49, 0.51, 0.52)

(1.41, 1.44, 1.46) (0.09, 0.76, 0.77)

(1.32, 1.33, 4.03) (0.62, 0.63, 0.99)

(C3 )

(0.2, 0.45, 0.46) (0.98, 0.99, 1)

(0.36, 0.72, 0.73) (0.68, 0.69, 0.99)

(1.03, 1.04, 1.24) (0.14, 0.73, 0.74)

(1.08, 1.09, 2.25) (0.87, 0.93, 0.94)

(C4 )

(0.24, 0.48, 0.49) (0.19, 0.5, 0.51)

(0.38, 0.81, 0.82) (0.38, 0.56, 0.57)

(0.89, 0.95, 0.96) (0.25, 0.85, 0.86)

(0.95, 0.96, 0.963) (0.24, 0.89, 0.895)

Table 4. The weighted attribute values (C1)

(C2)

(C3)

(C4)

(C1)

(0 0.41 1.11) (0 0.43 0.76)

(0 0.44 1.16) (0 0.76 0.77)

(0 0.39 1.25) (0.0013 0.7706 0.7709)

(0 0.41 0.82) (0 0.31 0.48)

(C2)

(0 0.24 0.44) (0 0.097 0.099)

(0 0.26 0.31) (0 0.47 0.489)

(0 0.26 0.29) (0 0.69 0.7)

(0 0.24 0.76) (0 0.37 0.76)

(C3)

(0 0.18 0.34) (0 0.87 0.88)

(0 0.17 0.21) (0 0.65 0.83)

(0 0.19 0.25) (0 0.67 0.68)

(0 0.19 0.43) (0 0.45 0.76)

(C4)

(0 0.19 0.36) (0 0.48 0.51)

(0 0.19 0.23) (0 0.53 0.534)

(0 0.17 0.19) (0 0.77 0.78)

(0 0.17 0.18) (0 0.46 0.81)

Table 5. The ideal alternative

a∗

A

B

A

B

A

B

A

B

0, 0.4, 0.74

0, 0.98, 1

0, 0.24, 0.29

0, 0, 1

0, 0.18, 0.2

0, 0.99, 1

0, 0.18, 0.19

0, 0.5.1

Then, we calculate values of distance between each alternative ai = (ZCi1 , ..., ZCi4 ) (Table 6) and the ideal one a∗ = (Z1∗ , ..., Z4∗ ). The distance is defined as below:   4  ∗ D(ai , a ) =  D2 (Zij , Z ∗ ) (3) j=1

, Z ∗ ) is depicted in Definition 4. The determined results are given in Table 6.

where D(Zij As a final solution, at the 4th stage, we compare the alternatives as ai  ak if D(ai , a∗ ) ≤ D(ak , a∗ ). ∼ So, the results are given as follow: a3  a2  a4  a1

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K. J. Dovlatova Table 6. The values of distance Alternative

D(ai , a∗ )

α1

0.61

α2

0.46

α3

0.44

α4

0.55

5 Conclusion This research paper is dedicated to creating the comparison between criteria as hedonism, shopping experience, brand perception and purchasing intention in consumer buying practice by using the Z-number approach. In research paper we offered method to decision making on consumer buying behavior under Z-valued information. Four alternatives (determinants) are determined. The expressed problem comprises PCM with Z-valued degrees of relative significance of attribute. Pairwise comparison matrix is described by a low degree of consistency. The eigenvector is defined to yield Z-valued importance weights of the criteria. Having defined these significance weights and Z-valued attribute estimates of alternatives (variables), the multi-attribute decision problem is solved. The offered way permits to deal with Z-valued information straightly (by applying essential arithmetic of Z-numbers and the different techniques lately offered by the researches). The suggested method can be used for different areas of Marketing Management and consumer behavior to solve different decision-making problems.

References 1. Kumar, A.A.: Factors influencing customers buying behavior. J. Mark. Consum. Res. Int. Peer Rev. J. 27, 30–34 (2016) 2. Sadikoglu, G.: Modeling of consumer buying behaviour using Z-number concept. IASC 24(1), 173–178 (2018). https://doi.org/10.1080/10798587.2017.1327159 3. Dovlatova, K.J.: Estimation of benchmarking influence in Buyer’s decision-making process by using fuzzy AHP. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 173–182. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_26 4. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_7 5. Aliev, R.A., Huseynov, O.H., Serdaroglu, R.: Ranking of Z-numbers and its application in decision making. Int. J. Inf. Technol. Decis. Mak. 15(6), 1503–1519 (2016). https://doi.org/ 10.1142/S0219622016500310 6. Zadeh, L.A.: Methods and systems for applications for Z-numbers. US Patent, 8311973 B1 (2012)

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7. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers. Theory and Applications. World Scientific, Singapore (2015) 8. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inf. Sci. 290, 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 9. Aliev, R.A.: Uncertain Computation-Based Decision Theory. World Scientific, Singapore (2017) 10. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices 18(4), 37–49 (2021). https:// doi.org/10.22111/IJFS.2021.6028 11. Shen, K., Wang, J.: Z-VIKOR method based on a new comprehensive weighted distance measure of Z-number and its application. IEEE Trans. Fuzzy Syst. 26(6), 3232–3245 (2018) 12. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: Country selection problem for business venturing in Z-information environment. Inf. Sci. 597(6), 230–243 (2022). https:// doi.org/10.1016/j.ins.2022.03.049

Prediction of the Power Output of a 4.5 kW Photovoltaic System Using Three Empirical Models: A Case Study in Nahr El-Bared, Lebanon Hüseyin Çamur1

, Youssef Kassem1,2,3,4(B) , Mustapha Tanimu Adamu1 and Takudzwa Chikowero1

,

1 Faculty of Engineering, Mechanical Engineering Department, Near East University,

Nicosia 99138, North Cyprus {huseyin.camur,yousseuf.kassem}@neu.edu.tr, {20215363, 20215146}@std.neu.edu.tr 2 Faculty of Civil and Environmental Engineering, Near East University, Nicosia 99138, North Cyprus 3 Energy, Environment, and Water Research Center, Near East University, Nicosia 99138, North Cyprus 4 Engineering Faculty, Kyrenia University, Kyrenia 99138, North Cyprus

Abstract. In this paper, Multilayer Feed-Forward Neural Network (MFFNN) and Cascade Feed-forward Neural Network (CFNN) have been used to predict the electricity production (EP) from a 4.5 kW PV system located in Nahr ElBared, Lebanon. Moreover, the accuracy of the proposed models is compared with the response surface methodology (RSM). For this aim, the hourly data of beam irradiance (BI), diffuse irradiance (DI), reflected irradiance (RI), sun height (SH), air temperature (AT), and wind speed (W) were collected and used as input parameters for the proposed models. The results showed that all proposed models were suitable for predicting the EP of the PV system. Among the developed models, the CFNN model presented significantly better prediction performance based on the value R2 and RMSE. Keywords: Nahr El-Bared · Lebanon · PV system · RSM · MFFNN · CFNN

1 Introduction The growth of energy demand, global warming, climate change, and increasing consumption of fossil fuels has led to the transition from conventional fuel to renewable energy resources [1, 2]. According to [3], utilizing renewable energy as an alternative energy source will help to reduce the environmental problems, essentially greenhouse gas emissions and air pollution due to increasing fossil fuel consumption. Renewable energy including solar energy is rapidly increasing due to economically viable and limited environmental impacts [4]. In recent years, many studies have evaluated solar energy’s potential as a clean power source for electricity generation. For instance, Çamur © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 218–225, 2023. https://doi.org/10.1007/978-3-031-25252-5_32

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et al. [5] evaluated the performance of a 5 kW rooftop photovoltaic (PV) system in Nahr El-Bared, Lebanon. The results indicated that the annual generation of electricity could cover the energy demand and reduce the electricity bill in the selected location. Kassem and Abdalla [6] estimated the potential of rooftop PV electricity in the Red Sea State in Sudan. The results showed that the developed system has huge potential to cover the energy demand of households. According to [7], weather parameters, geographic location, and the PV system’s orientation angles are the essential factors that influenced the energy output of the PV system. Moreover, several studies have used machine learning models to predict the power of PV systems as a function of climate parameters [7–9]. Therefore, it needs to develop a model for estimating the output power of PV systems based on the climate parameters. In this regard, the performance of the MFFNN, CFNN, and RSM are developed to estimate the EP of PV system located in Nahr El-Bared, Lebanon. In this study, the hourly data of beam irradiance (BI), diffuse irradiance (DI), reflected irradiance (RI), sun height (SH), air temperature (AT), and wind speed (W) were collected and utilized as input parameters for the developed models. Additionally, the hourly data of the EP from the 4.5 kW PV system was measured using a data logger. The overall flowchart of the current study is illustrated in Fig. 1.

Fig. 1. Flowchart of the current study

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2 Material and Methods 2.1 Study Area and Data One of the largest Palestinian camps in north Lebanon is the Nahr El-Bared camp. It is located near Tripoli city. The climate of Nahr El-Bared is a solid Mediterranean climate with full seasons and a significant difference in temperature in the seasons and regard to rain and the weather in general. In this study, a 4.5 kW PV system is constructed for generating electricity for the residential building located in Nahr El-Bared. For building the system, mono-Si - CS6X-300M manufactured by Canadian Solar and with efficacy of 15.63% is used. In addition, an inverter with a capacity of 5 kW is selected for converting the direct current into alternating current. The hourly data of BI, DI, RI, SH, AT, W, and EP are collected from 01 January 2020–31 December 2020. Table 1 listed the summary statistics of the used parameters. Table 1. Statistical parameters of mean hourly data during 2020. Variable

Unit

Mean

Standard deviation

Coefficient of variation

Minimum

Maximum

PV-power

W

886.3

1284.1

144.88

0

4378.2

BI

W/m2

156.64

258.68

165.14

0

965.47

DI

W/m2

74.85

98.19

RI

W/m2

SH

◦

16.761

AT

◦C

20.33

WS

m/s

2.8104

2.2451

131.19

0

464.61

4.027

143.29

0

13.81

21.981

131.15

0

77.38 37.68

7.01

34.48

0.97

1.2882

57.38

0

8.21

2.2 Machine Learning Models (MLMs) MLMs are utilized as a tool to describe a complex system [10, 11]. Wide ranges of ML models are utilized to solve complex problems in a variety of fields [10, 11]. In this study, MFFNN and CFNN are developed to determine the PV-power of a 4.5 kW PV system. MFFNN is one of the most popular artificial neural network approaches for modeling nonlinear and complex processes in the real world [12, 13]. The description of the MFFNN and CFNN models was given in [14]. The training (70%) and testing data (30%) were used to develop and validate the models, respectively. The results of the MFFNN and CFNN models are compared with observed data.

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2.3 Response Surface Methodology The RSM is a mathematical and statistical method polynomial model as expressed below [15, 16]. Y = β0 +

n i=1

βi xi +

n i=1

βii xi2 +

n−1 n i

i=i+1

βij xi xj

(1)

where Y is the predicted response, β0 , βi , are related to the main effects and βii and βij to interaction, x i and x j are the independent variables. The main goal of this model is to show the interaction between the input variables and output variables as shown in (2) PV − power = f (Bi, DI , RI , SH , AT , W )

(2)

3 Results and Discussion 3.1 Estimating the PV-Power Using MFFNN and CFNN Aforementioned, two machine learning models were utilized to estimate the PV-power of a 4.5 kW PV system. Thus, BI, DI, RI, SH, AT and W are used as input parameters. The best network configuration was found by trial and error method and selected based on the lowest value of mean squared error (MSE). The best function is selected through several trials in the training phase. The training function was TRAINLM. The backpropagation algorithm was used to reduce the MSE value between the measured and predicted values. Table 2 summarizes the best configuration for MFFNN and CFNN. Moreover, the scatter plots of the developed models compared to the observed data is presented in Fig. 2. Table 2. Optimal configuration for MLMs MLM

Configuration

Transfer Function

Number of neurons

MSE

MFFNN

6:1:1

TANSIG

8

3.77 × 10–7

CFNN

6:1:1

LOGSIG

10

9.116 × 10–8

H. Çamur et al.

Predicted data [W]

222

4000 3500 3000 2500 2000 1500 1000 500 0

MFFNN

y = 0.9982x + 0.3245 R² = 0.999996

0

1000

2000

3000

4000

Observed data [W]

Predicted data [W]

4000

CFNN

3000 2000 y = 0.9999x + 0.2064 R² = 0.999997

1000 0 0

1000

2000

3000

4000

Observed data [W] Fig. 2. Comparison of the estimated data with the observed data for PV-power using different MLM models

3.2 Estimating the PV Power Using RSM The mathematical equation that was developed using RSM formula (3) for predicting the PV-power is expressed as shown below. PV − power = −16.18 + 4.9334 · BI + 4.916 · DI − 48.15 · RI − 3.022 · SH + 1.225 · AT + 3.34 · W − 0.001582 · BI 2 + 0.001913 · DI 2 − 17.96 · RI 2 + 0.05164 · SH 2 − 0.03118 · AT 2 − 0.504 · W 2 − 0.000954 · BI · DI + 0.4213 · BI · RI − 0.0702 · BI · SH − 0.012406 · BI · AT + 0.07749 · BI · W + 0.2575 · DI · RI − 0.06495 · DI · SH − 0.01975 · DI · AT + 0.0276 · DI · W + 3.997 · RI · SH − 0.0958 · RI · AT − 2.367 · RI · W − 0.00105 · SH · AT + 0.1215 · SH · WS − 0.0987 · AT · W

(3)

Figure 3 compares the scatter plots of the RSM model versus the observed data in testing phase. It can be noticed that the estimated values are closed to the measured data.

Predicted data [W]

Prediction of the Power Output of a 4.5 kW Photovoltaic System

4000 3500 3000 2500 2000 1500 1000 500 0

223

RSM

y = 0.9993x + 0.8529 R² = 0.99973

0

1000

2000

3000

4000

Observed data [W] Fig. 3. Comparison of the estimated data with the observed data for RSM.

3.3 Performance Evaluation of MFFNN, CFNN, and RSM The performance of MFFNN and CFNN is compared with the RSM to evaluate the performance of the proposed models. The values of R-squared and root mean squared error (RMSE) are listed in Table 3. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the CFNN model. Table 3. Performance evaluation of the models. Statistical indicator RSM

MFFNN

CFNN

R-squared

0.99973 0.999996 0.999997

RMSE*

0.00455 0.00076

0.00049

*RMSE for normalized data

4 Conclusions The PV output power estimation is essential for the power grid’s secure, stable, and economical operation. Therefore, three models, namely, MFFNN, CFNN, and RSM, were developed to determine the EP of a 4.5 kW PV system. The results showed that all proposed models were suitable for estimating the PV-power of the PV system. Among the developed models, the CFNN model presented significantly better prediction performance based on the value R2 and RMSE. In future work, various models with various combinations of parameters including rainfall, relative humidity, and wet-bulb temperature should propose to categorize the most influencing input parameters for predicting the PV-power output value of the PV system.

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References 1. Tercan, E., Eymen, A., Urfalı, T., Saracoglu, B.O.: A sustainable framework for spatial planning of photovoltaic solar farms using GIS and multi-criteria assessment approach in Central Anatolia, Turkey. Land Use Policy 102, 105272 (2021). https://doi.org/10.1016/j.landusepol. 2020.105272 2. Shorabeh, S.N., Firozjaei, M.K., Nematollahi, O., Firozjaei, H.K., Jelokhani-Niaraki, M.: A risk-based multi-criteria spatial decision analysis for solar power plant site selection in different climates: a case study in Iran. Renew. Energy 143, 958–973 (2019). https://doi.org/ 10.1016/j.renene.2019.05.063 3. Neupane, D., Kafle, S., Karki, K.R., Kim, D.H., Pradhan, P.: Solar and wind energy potential assessment at provincial level in Nepal: geospatial and economic analysis. Renew. Energy 181, 278–291 (2022). https://doi.org/10.1016/j.renene.2021.09.027 4. Kassem, Y., Gökçeku¸s, H., Güvensoy, A.: Techno-economic feasibility of grid-connected solar PV system at Near East University hospital, Northern Cyprus. Energies 14(22), 7627 (2021). https://doi.org/10.3390/en14227627 5. Çamur, H., Kassem, Y., Alessi, E.: A techno-economic comparative study of a grid-connected residential rooftop PV panel: the case study of Nahr El-Bared, Lebanon. Eng. Technol. Appl. Sci. Res. 11(2), 6956–6964 (2021). https://doi.org/10.48084/etasr.4078 6. Kassem, Y., Abdalla, M.H.A.: Modeling predictive suitability to identify the potential of wind and solar energy as a driver of sustainable development in the Red Sea State, Sudan. Environ. Sci. Pollut. Res., 1–22 (2022). https://doi.org/10.1007/s11356-022-19062-9 7. Kassem, Y., Othman, A.A.: Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models. Model. Earth Syst. Environ., 1–26 (2022). https://doi.org/10.1007/s40808-022-01413-7 8. da Silva Fonseca, J.G., Jr., Oozeki, T., Takashima, T., Koshimizu, G., Uchida, Y., Ogimoto, K.: Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu, Japan. Prog. Photovolt. Res. Appl. 20(7), 874–882 (2012). https://doi.org/10.1002/pip.1152 9. Kumar, P.M., Saravanakumar, R., Karthick, A., Mohanavel, V.: Artificial neural networkbased output power prediction of grid-connected semitransparent photovoltaic system. Environ. Sci. Pollut. Res. 29(7), 10173–10182 (2021). https://doi.org/10.1007/s11356-021-163 98-6 10. Berjawi, A.H., Najem, S., Faour, G., Abdallah, C., Ahmad, A.: Assessing Solar PV’s Potential in Lebanon. Issam Fares Institute for Public and International Affairs (2017) 11. Kassem, Y., Gökçeku¸s, H., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 7(3), 1475–1502 (2020). https://doi.org/10.1007/s40808-020-00866-y 12. Kassem, Y., Gökçeku¸s, H., Maliha, M.R.M.: Identifying most influencing input parameters for predicting chloride concentration in groundwater using an ANN approach. Environ. Earth Sci. 80(7), 1–16 (2021). https://doi.org/10.1007/s12665-021-09541-6 13. Kassem, Y., Gökçeku¸s, H., Alassi, E.: Identifying most influencing input parameters for predicting Cereal production using an artificial neural network model. Model. Earth Syst. Environ. 8(1), 1157–1170 (2021). https://doi.org/10.1007/s40808-021-01148-x 14. Kassem, Y., Gokcekus, H.: Do quadratic and Poisson regression models help to predict monthly rainfall? Desalin. Water Treat. 215, 288–318 (2021). https://doi.org/10.5004/dwt. 2021.26397 15. Kassem, Y., Çamur, H.: Prediction of biodiesel density for extended ranges of temperature and pressure using adaptive neuro-fuzzy inference system (ANFIS) and radial basis function (RBF). Procedia Comput. Sci. 120, 311–316 (2017). https://doi.org/10.1016/j.procs.2017. 11.244

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16. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Prediction of kinematic viscosity and density of biodiesel produced from waste sunflower and canola oils using ANN and RSM: comparative study. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 880–887. Springer, Cham (2020). https:// doi.org/10.1007/978-3-030-35249-3_117

Z-Decision Making for the Selection of IT Engineers Gunay A. Huseynzada(B) Joint MBA Program, Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, Baku AZ1010, Azerbaijan [email protected]

Abstract. The paper deals with IT engineer selection problem in decision making to have comprehensive results for every business. Existing works are devoted to solving this issue through the diverse decision making methods under fuzzy information. In this research we suggest new method for solving ˙IT engineer selection process under fuzzy and partially reliable information formalized by using Z-numbers. The proposed approach that is being described is based on general pairwise matrix on criteria including the distance between Z-vectors and the positive and negative ideal solutions of alternatives. A numerical example is provided to illustrate validity of the proposed approach on multi-attribute decision making for employee selection problem. Final decision alternative is selected according to degree of membership of candidates belonging to the optimal solution. Keywords: Decision making · Z-number · Ideal solution · Distance between Z-vectors · IT engineer selection

1 Introduction Personnel selection is procedure for choosing a candidate from a group of applicants who each satisfy the requirements to perform a particular job in the best possible manner [1]. The advancement of every firm requires the recruitment of skilled staff and their selection The ability of an organization to produce a high-quality product at a fair price and according to schedule is significantly influenced by the abilities of its employees [2]. The most important consideration when hiring new employees is matching the right person with the appropriate position [3]. There are several approaches to the issue of personnel selection problem using Fuzzy logic and various MCDM [4]. Some of these methods are the Analytical Hierarchy Process (AHP) [5, 6] Analytic Network Process (ANP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) [5], Multi-criteria Optimization and Compromise Solution (VIKOR) [7], Simple Additive Weighting Method (SAW), Elimination Et Choice Translating Reality (ELECTRE), Preference Ranking Organization METHODS for Enrichment Evaluations (PROMETHEE) [8], Fuzzy expert systems.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 226–233, 2023. https://doi.org/10.1007/978-3-031-25252-5_33

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The literature on employee selection has been analyzed in numerous researches[9]. In paper [10] the issue is simplified to a multicriteria decision-making process taking place in a fuzzy environment. Authors provide a technique for estimating the criteria that allows for the regulation and selection of the best option in accordance with the scenario that best suits the decision-needs maker’s at the moment. Research [11] refers to ANOVA single factor theory. The study’s conclusions demonstrated a link between improved organizational productivity and efficiency and recruiting and selection practices. Article [12] examines modeling of supply and demand dynamics in the employment of information technology experts (IT professionals). On the basis of a fuzzy unbalance scale, methodologies are presented for measuring the structural mismatch in the IT professional labor market and the degree of supply and demand disparity. The fuzzy state classification algorithm of imbalance can assist a variety of parties in making judgments about how to handle the differentiation in the demand for IT workers. Unfortunately, up today there are rare multi-attribute decision-making research under Z-environment. Taking into consideration actual concerns, the Z-number idea was presented by Professor Zadeh. A Z-number is made up of two fuzzy numbers, A and B, where A is a soft constraint on the value of an interest variable and B is a soft constraint on the value of a probability measure of A, acting as a reliability factor for A [13]. In this paper, we suggest a novel strategy called consistency-driven partially reliable preferences. For IT engineer selection using Z-number-valued entries in multi-attribute decision analysis. The paper is set up as follows. We present some background information in Sect. 2, such as definitions of discrete Z-numbers, the distance between Z-numbers, operations over Z-numbers, etc. In Sect. 3 we state the problem of employee selection using information with a Z-number value. The suggested approach to resolving the issue described in Sect. 3 is illustrated in Sect. 4 of this article. Section 5 is conclusion.

2 Preliminaries Definition 1. Z-number [14]. The value of a variable X is expressed as an ordered pair of fuzzy numbers termed a “Z-number,” where A is an imperfect restriction on the values of X and B is an imprecise assessment of the reliability of A and is taken into account as a value of probability measure of A. Z = (A, B) Definition 2. Discrete Z-number Discrete Z-number [15]. An ordered pair Z = (A, B) is referred to as a discrete Z-number if A is a discrete fuzzy number that represents a fuzzy constraint on the possible values of a random variable X: X is A, and B is a discrete fuzzy number with a membership function μB : {b1 , ..., bn } → [0, 1], which describes a fuzzy constraint on the probability measure of A: P(A) is B

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Definition 3. Operations over Discrete Z-numbers [16, 17]: Assume X1 and X2 be discrete Z-numbers describing information about values of X1 and X2 . Whether taking into consideration of the calculation Z12 = Z1 ∗ Z2 , ∗ ∈ {+, −, ·, /}. A12 = A1 ∗ A2 is initial stage. The second stage concerns construction B12 . We identify that in Z-numbers Z1 and Z2 , the ‘true’ probability distributions p1 and p2 are not exactly known. When compared, fuzzy restrictions represented in terms of the membership functions are available   n n 1 2   μA1 (x1k )p1 (x1k ) , μp2 (p2 ) = μB2 μA2 (x2k )p2 (x2k ) μp1 (p1 ) = μB1 k=1

k=1

Probability distributions pjl (xjk ), k = 1, .., n probabilistic uncertainty over X12 = X1 + X2 . Given any possible pair p1 , p2 , the convolution p12 = p1 ◦ p2 is computed as  p12 (x) = p1 (x1 )p2 (x2 ), ∀x ∈ X12 ; x1 ∈ X1 , x2 ∈ X2 . x1 +x2 =x

Given p12s , the value of probability measure of A12 is computed: P(A12 ) =

n 

μA12 (x12k )p12 (x12k ).

k=1

However, p1 and p2 are presented by fuzzy restrictions which coerce fuzzy set of convolutions: μp12 (p12 ) = max{p1 , p2 :p12 =p1 ◦p2 } min{μp1 (p1 ), μp2 (p2 )} Fuzziness of information on p12 induces fuzziness of P(A12 ) as a discrete fuzzy number B12 . The membership function μB12 is described as μB12 (b12 ) = max μp12 (p12 ) according to b12 =

n 

μA12 (xi )p12 (xi )

i=1

Consequently, Z12 = Z1 ∗ Z2 is obtained as Z12 = (A12 , B12 ). Definition 4. A distance between Z-numbers [17, 18].

Z-Decision Making for the Selection of IT Engineers

D(Z1 , Z2 ) =

229

n m         1   L     L L  +  R − aR  + 1 − bL2α  + bR − bR  a   a1αk − a2α b 1α 2α 1α 1α 2α k k k k k k k n+1 m+1 k=1

k=1

where aαL = min Aα , aαR = max Aα , bLα = min Bα , bRα = max Bα

3 Statement of the Problem Construction of Pairwise Matrix on Criterion for 1st , 2nd , 3rd Experts Take the challenge of selecting an IT engineer using multi-attribute decision-making with information that is valued at a Z-number. Let’s say the firm wants to bring on a new engineer. Three individuals were selected after preliminary screening. A1 , A2, A3 remain for the next evaluation. Three specialists on a committee for the purpose of conducting the interview and choosing the best applicant, E1, E2, and E3 have been developed. The following five criteria are considered [19]. C1 C2 C3 C4 C5

- Emotional steadiness - Oral Communication - Personality - Past experience - Self confidence

Z-numbers analyze all three options in this scenario based on five criteria. As preliminary step there formalized pairwise matrixes on considerations of each expert. Triangle fuzzy numbers and scaled decision matrices are used in Tables 1 and 2 to depict these Z-numbers’ components below. Table 1. First expert’s decision matrix (C1–C5 compared to C1–C3) C1

C2

C3

C1

(0.9 1 1) (0.7 0.8 0.9)

(1.9 2 2.1) (0.7 0.8 0.9)

(2.9 3 3.1) (0.7 0.8 0.9)

C2

(1/2.1 1/2 1/1,9) (0.7 0.8 0.9)

(0.9 1 1) (0.9 1 1)

(1.9 2 2.1) (0.7 0.8 0.9)

C3

(1/3.1 1/3 1/2.9) (0.7 0.8 0.9)

(1/2.1 1/2 1/1,8) (0.7 0.8 0.9)

(0.9 1 1) (0.9 1 1)

C4

(1/4.1 1/4 1/3.9) (0.7 0.8 0.9)

(1/4.1 1/4 1/3.9) (0.7 0.8 0.9)

(1/3.1 1/3 1/2.9) (0.7 0.8 0.9)

C5

(1/5.1 1/5 1/4.9) (0.7 0.8 0.9)

(1/5.1 1/5 1/4.9) (0.7 0.8 0.9)

(1/2.1 1/2 1/1,9) (0.7 0.8 0.9)

230

G. A. Huseynzada Table 2. First expert’s decision matrix (C1–C5 compared to C4–C5) C4

C5

C1

(3,9 4 4,1) (0.7 0.8 0.9)

(4.9 5 5.1) (0.7 0.8 0.9)

C2

(3,9 4 4,1) (0.7 0.8 0.9)

(4.9 5 5.1) (0.7 0.8 0.9)

C3

(2.9 3 3.1) (0.7 0.8 0.9)

(1.9 2 2.1) (0.7 0.8 0.9)

C4

(0.9 1 1) (0.9 1 1)

(2.9 3 3.1) (0.7 0.8 0.9)

C5

(1/3.1 1/3 1/2.9) (0.7 0.8 0.9)

(0.9 1 1) (0.9 1 1)

Analogous matrices were constructed for 2nd and 3rd experts.

4 Solution of the Problem As the next stage, we calculate appropriate values of each experts’ matrixes. Obtained results have been expressed in Tables 3 and 4 presented below [20, 21]. Table 3. Average of obtained Z-numbers (C1–C5 compared to C1–C3) C1

C2

C3

C1

(0.99 1 1) (0.99 1 1)

(0.9 1 1.3) (0.2 0.4 0.5)

(1.6 1.7 1.8) (0.3 0.4 0.5)

C2

(1 1/1.3 1/0.9) (0.2 0.4 0.5)

(0.99 1 1) (0.99 1 1)

(2.4 2.4 2.5) (03. 0.4 0.5)

C3

(1/1.8 1/1.7 1/1.6) (0.3 0.40.5)

(1/2.5 1/2.4 1/2.4) (03. 0.4 0.5)

(0.99 1 1) (0.99 1 1)

C4

(1/1.8 1/1.7 1/1.7) (0.3 0.40.5)

(1/3.1 1/3 1/2.9) (0.6 0.6 0.7)

(1/2.6 1/2.5 1/2.4) (0.5 0.5 0.6)

C5

(1/2.4 1/2.4 1/3.1) (0.3 0.4 0.5)

(1/2.8 1/2.7 1/2.6) (0.3 0.4 0.5)

(1/1.2 1/1.17 1/1.07) (0.3 0.4 0.5)

Z-Decision Making for the Selection of IT Engineers

231

Table 4. Average of obtained Z-numbers (C1–C5 compared to C4–C5) C4

C5

C1

(1.7 1.7 1.8) (0.3 0.4 0.5)

(3.1 2.4 2.4) (0.3 0.4 0.5)

C2

(2.9 3 3.1) (0.6 0.6 0.7)

(2.6 2.7 2.8) (0.3 0.4 0.5)

C3

(2.4 2.5 2.6) (0.5 0.5 0.6)

(1.07 1.17 1.2) (0.3 0.4 0.5)

C4

(0.99 1 1) (0.99 1 1)

(1.3 1.36 1.4) (0.3 0.4 0.5)

C5

(1/1.4 1/1.36 1/1.3) (0.3 0.4 0.5)

(0.99 1 1) (0.99 1 1)

Tables 5 contains the Z-valued data on the criteria evaluated for the options [22–24]. Table 5. Z-valued criteria evaluations (C1)

(C2)

(C3)

(C4)

(C5)

A1 (1.26 1.48 1.48) (1.87 1.87 5.11) (1.48 1.48 1.62) (1.28 2.43 4.84) (2.02 3.05 6.25) (0.12 0.34 0.36) (0.85 0.88 0.88) (0.12 0.69 0.78) (0.82 0.82 0.83) (0.29 0.81 0.84) A2 (1.47 2.17 2.17) (1.64 1.64 2.20) (1.33 2.57 2.57) (1.44 2.30 2.30) (271 2.71 2.72) (0.57 0.78 0.78) (0.17 0.17 0.86) (0.91 0.91 0.93) (0.27 0.47 0.47) (0.20 0.20 0.79) A3 (2.62 2.62 7.75) (1.83 1.83 5.29) (1.29 1.68 4.10) (1.38 1.38 3.23) (3.45 3.45 4.17) (0.27 0.78 0.88) (0.04 0.87 0.87) (0.12 0.88 0.88) (0.20 0.67 0.67) (0.13 0.34 0.89)

Following appraisal contains obtained the weighted values of criteria by using the arithmetic of Z-numbers. W1

0.00

2.27

1.82

W2

0.23

−0.18

2.00

W3

6.61

−3.89

0.00

Next, we calculate values of distance between each alternative ai = (ZCi1 , ..., ZCi4 ) and the ideal one a∗ = (Z1∗ , ..., Z4∗ ). The distance is found as follows:  D(ai , a∗ ) =

4 j=1

D2 (Zij , Z ∗ )

232

G. A. Huseynzada Table 6. The values of distance Alternative

D(ai , a∗ )

a1

0,63

a2

0,74

a3

0,57

According to the obtained values minimum alternative is the most appropriate candidate for IT department.

5 Conclusion Currently when it comes to dealing with interval and fuzzy MADM, several techniques have been created, but there is little study on multi-attribute decision making when dealing with Z-information. In this paper to solve mentioned human resources management problem we apply pairwise matrix on criteria including the Z-vectors and the optimum solution notion are separated by distance. Numerical definition on MADM ˙IT engineer selection problem indicates the quality and effectiveness of offered approach. It is possible to implement the suggested approach to the problem of choosing IT engineers in Z-number based calculation programming system.

References 1. Salehi, K.: An integrated approach of fuzzy AHP and fuzzy VIKOR for personnel selection problem. GJMBR 3(3), 89–95 (2016) 2. Afshari, A.R., Nikoli´c, M., Akbari, Z.: Personnel selection using group fuzzy AHP and SAW methods. JEMC 7(1), 3–10 (2017). https://doi.org/10.5937/jemc1701003A 3. Mammadova, M.H., Jabrayilova, Z.G., Nobari, S.M.: Application of TOPSIS method in support of decisions made in staff management issues. In: IV International Conference (PCI), no. 4, pp. 195–198 (2012) 4. Ersoy, N.: Decision making process for personnel selection under fuzzy environment. SSRJ 6(3), 67–75 (2017) 5. Hashemkhani, S.Z., Antucheviciene, J.I.: Team member selecting based on AHP and TOPSIS grey. Ekonomika Eng. Econ. 23(4), 425–434 (2012) 6. Aliyev, R.R.: Multi-attribute decision making based on Z-valuation. In: ICAFS (2016) 7. Jabbarova, K., Alizadeh, A.V.: Z-decision making in human resources department. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 498–507. Springer, Cham (2021). https://doi.org/10.1007/978-3030-64058-3_62 8. Afshari, A.R., Anisseh, M, Shahraki, M.R., Hooshyar, S.: PROMETHEE use in personnel selection. In: ICTM (2016) 9. Afshari, A.R., Yusuff, R.M, Hong, T.S., Ismail, Y.B.: A review of the applications of multi criteria decision making for personnel selection problem. Afr. J. Bus. Manage. 5(28) (2011) 10. Mammadova, M., Jabrayilova, Z., Mammadzada, F.: Fuzzy multicriterial methods for the selection of IT-professionals. IJISAE 3, 40–45 (2015)

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11. Chaya, J.S., Vanishree, B., Nanjundeswaraswamy, T.S.: Recruitment and selection process in the IT firms. GIS Sci. J. 8(5), 343–356 (2021) 12. Mammadova, M., Jabrayilova, Z., Mammadzada, F.: Fuzzy approach to estimate the demand and supply quantitative imbalance at the labor market of information technology specialists. IJISAE (2015). https://doi.org/10.18201/ijisae.24856.1039 13. Zadeh, L.A.: A note on a Z-number. Inf. Sci. 181, 2923–2932 (2011) 14. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inf. Sci. 290, 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 15. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers. Theory and Applications. World Scientific, Singapore (2015) 16. Aliyev, R.R.: Similarity based multi-attribute decision making under Z-information. In: Eighth International Conference on Soft Computing with Words and Perceptions in System Analysis, Decision and Control, pp. 33–39 (2015) 17. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 18. Aliev, R.A., Huseynov, O.H., Serdaroglu, R.: Ranking of Z-numbers and its application in decision making. Int. J. Inf. Technol. Decis. Mak. 15(6), 1503–1519 (2016). https://doi.org/ 10.1142/S0219622016500310 19. Agakishiyev, E.: Supplier selection problem under Z-information. In: ICAFS 2016 (2016) 20. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: Z-relation equation-based decision making. Expert Syst. Appl. (2021). https://doi.org/10.1016/j.eswa.2021.115387 21. Aliev, R.A., Guirimov, B.G., Huseynov, H., Aliyev, R.R.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iran. J. Fuzzy Syst. 18, 37–49 (2021) 22. Jabbarova, K.I.: Multiattribute evaluation of weapon systems under Z-information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 359–365. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_46 23. Aliyeva, K.: Eigensolution of 2 by 2 Z-matrix. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 758– 762. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_98 24. Aliev, R.A., Huseynov, O.H., Aliyeva, K.R.: Toward eigenvalues and eigenvectors of matrices of Z-numbers. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 309–317. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_39

Optimal Implicatıon Based Fuzzy Control System for a Steam Generator L. A. Gardashova(B)

and K. A. Mammadova

Department of Computer Engineering, Azerbaijan State Oil and Industry University, Baku, Azerbaijan [email protected]

Abstract. The main advantage of a fuzzy set approach to control engineering is that it can be used to replace very complex and computationally demanding systems of partial differential equations. In this paper, we propose a new method for choosing implications. Proposed method allows to compare six fuzzy implications. The problem of identifying a control system with nonlinearity and operating in uncertain conditions is considered, and the synthesis of the system is carried out according to the operation of fuzzy logic. The development of a fuzzy control algorithm for a highly uncertain control object – a steam generator, the architecture of the fuzzy control system and the definition of its elements are considered. The fuzzy identification of a dynamic object, the analysis of the influence of various fuzzy implications on the process identification and the determination of the optimal implication are carried out using the example of a steam generator of thermal-power-plant (TPP) power units. Keywords: Fuzzy set · Fuzzy relation · Implication · Fuzzy controller · Steam generator

1 Introduction In modern control systems, the use of fuzzy control algorithms, based on artificial intelligence technology, is widespread. The use of a fuzzy control algorithm in the automatic control system makes it possible to obtain higher quality indicators compared to the classical controller. A fuzzy control system reduces resource consumption and energy costs, improves product quality and provides higher resistance to destructive factors compared to a classical automatic control system. When forming mathematical models of systems, the operation of forming uncertainty factors serves as a means of increasing the compatibility (adequacy) of given models with reality, as a result of which the actual effectiveness of the decisions being made is substantiated. At the same time, when creating the system, much attention was paid to the area of mathematically poorly formed or incompletely formed knowledge [1–3]. Such models are called “soft”. They have empirical rules for building knowledge bases; qualitative, heuristic, intuitive, approximate values determined by fuzzy, indefinite intervals. The formation of such information, its processing and management, based on Zadeh’s fuzzy set theory, allows, when describing © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 234–246, 2023. https://doi.org/10.1007/978-3-031-25252-5_34

Optimal Implicatıon Based Fuzzy Control System for a Steam Generator

235

fuzzy concepts and procedures, to abandon the “excessive” accuracy brought in by traditional modeling approaches, while maintaining its seriousness. In [2], an approximate mathematical model of a thermal power plant was developed by using real time data on Computer Aided Design and Control software. Authors discuss different controller types being applied to the power plant model. It appears that fuzzy gain scheduled proportional and integral (FGPI) controllers demonstrate better performance than the rest of the controllers considered in the study. The description of information has strong influence on the outcome of the control process. In addition, parameterized operations in the fuzzy domain are legitimately aimed at effective analysis: not at single-purpose or intuitive aspects, but at using the apparatus of fuzzy set theory as reliable sources for obtaining quantitative information. In the [3–8], attention was drawn to the fact that the theory of fuzzy sets (for example, Fuzzy implications) more adequately reflects the essence of the control process. In scientific literature, there are multiple researches considering implications and their applications. In the last few decades, a number of different fuzzy implications have been proposed [9–17]. Fuzzy Implication Axioms, Dependence versus Independence of the Fuzzy Implication Axioms, Robustness of Fuzzy Logic Operators in Fuzzy Rulebased Systems, Fuzzy Adjunctions and Fuzzy Morphological Operations Based on Fuzzy Implications have been presented and currently are applied and discussed in scientific literature [18–26]. It is known that a steam generator, as a control object in energy production, possesses high uncertainty and non-linearity. So obtaining its simple deterministic model and synthesizing the corresponding control system do not meet the requirements for system quality indicators. Sometimes such systems even lead to unstable operation performance. When a control system [27–30] is based on the knowledge of an experienced specialist, control algorithms take uncertainties into account, which ensures high-quality control. The review of scientific literature devoted to the application of optimal fuzzy effects showed that, in the synthesis of fuzzy controllers, the issue of comparative study of optimal fuzzy effects in accordance with the accuracy criteria has not been resolved yet.

2 Statement of the Problem This paper considers the development of a fuzzy control algorithm for a steam-generator object, which embraces the architecture of the fuzzy control system and the definition of its elements. The technical implementation of a fuzzy control system for the channel “fuel consumption - outlet steam temperature” in the steam generator can be described as shown in Fig. 1. In the system described in Fig. 1, (1) is the managed object, which is a oncethrough steam generator. Here, the control action is the amount of fuel, and the controlled variable is a thermocouple (2), which measures the temperature of the steam at the outlet of the generator; (3) is a device that measures the force of thermoelectric motion and converts it into a unified signal; (4) is an analog-to-digital converter (ADC), which function is to convert an analog signal to the digital one; (5) is a comparator, which determines the difference between the required pre-set temperature and the current temperature of the steam generator; (6) is a block that differentiates the input error signal (e); (7) is a

236

L. A. Gardashova and K. A. Mammadova

fuzzifier; (F1) – fuzzy error signal (e) turns into a fuzzy set (E). The corresponding fuzzy ∼

sets E˜ and E˙ are determined by introducing the error and the rate of error change into the fuzzifiers (7).

Fig. 1. Scheme for the implementation of a fuzzy ACS of a steam generator

(8) is the logical extraction block, where the fuzzy error and error derivative sets (E˜ ∼

˙ respectively) are extracted based on the fuzzy link composition matrix with and E, maximin composition and the current control fuzzy set (U˜ ) is determined, i.e.,

∼

U˜ = E˜ ◦ (E˙ ◦R(e, e˙ , u))

(1)

µ(u) = max{min(µ(e, e˙ ), µ(e, e˙ , u)}

(2)

u

Here R(e, e˙ , u) is the membership matrix of a fuzzy relation, determined on the basis of an expert table of fuzzy linguistic rules about managing objects, i.e., the knowledge base, and through the optimal fuzzy implication operator. (9)

is a block of knowledge base and fuzzy control database. The definition of a fuzzy knowledge base is an important step in solving the problem of control synthesis and is based on expert assessment. The expert’s judgments about management are defined as linguistic rules in Table 1.

Optimal Implicatıon Based Fuzzy Control System for a Steam Generator

237

(10) is a defuzzification block, the fuzzy control outputs a fuzzy value from the set U˜ . The center of gravity method is used as a defuzzification method. (11) is a digital-to-analog converter, which converts the control action being in the form of a binary code into a unified analog electrical signal. (12) is a conversion device that converts an analog unified electrical signal into a unified pneumatic signal. Affects a single (0.2–1 kgQ/sm2 ) pneumosignal (13)-membrane mechanism of action (MMA). MMA, changing the amount of fuel, changes the temperature at the outlet of the steam generator in one direction or another. The knowledge base of the fuzzy control of the steam generator is defined in the form of linguistic rules as follows: If the control error is positive large (e= positive L) and the error change ) then the control will be negative rate is negative medium ( ̇ = small (u= negative S), If the control error has a negative medium (e=NM) and the error change rate is positively small ( ̇ = positive S), then the control will be positive small (u= PS), Also (3) If the control error has a positive medium (e= positive M), and the rate of error change has a negative medium ( ̇ =NM), then the control is zero (u=Z), Also, If the control error is positive medium (e= positive M) and the error change rate is positively small ( ̇ = positive S), then the control is negatively large (u=NL), Also, . .. . . .. . .. . ..

The fuzzy linguistic rules that we have defined are illustrated in Table 1. The following linguistic terms are adopted in this table: NL - negative large; NM-negative medium; NS - negative small; Z-zero; PositiveS - positive small; PositiveM - positive medium; PositiveL - positive large. The values of the control error, the rate of change of errors and modes of membership functions of term-sets output - control effect are shown in Table 1. Table of linguistic rules is stored in memory as a matrix of fuzzy relations in a knowledge base block. All terms represent usage of sigmoid membership functions. For example, µei (e) =

1 1 + [Ce (ei − ei )]2

, i = 1, 15

Membership functions of control error, change rate of error, and term sets of control effect are given in Tables 2, 3, 4, respectively

238

L. A. Gardashova and K. A. Mammadova Table 1. Table of Linguistic Rules (TLR).

Table 2. Control error Terms

NB

NM

NS

Z

PosS

PosM

PosB

e˜ i

0,24

0,39

0,68

1,00

0,86

0,49

0,26

Table 3. Change rate of error Terms

NB

NM

NS

Z

PosS

PosM

PosB

e˙ j

0,50

0,67

0,90

0,97

1,00

0,86

0,59

Table 4. Term sets of control effect Terms

NB

NM

NS

Z

PosS

PosM

PosB

u˜ j

0,07

0,15

0,40

1,00

0,50

0,16

0,07

3 Solution of the Problem The solution of the synthesis problem is to determine the structure and parameters of the membership function of the terms of these fuzzy sets - the error (Ei ), the error change ∼

˙ rate E˙ j and the control action (Ul ). Both the error E˜ i and the error rate of change E, as well as the control effect U˜ j , are calculated by the formulas of the corresponding membership functions of fuzzy set terms. From Tables 1, 2 and 3, a fuzzy set of 7 terms is selected for both the error and the error rate of change and control effect in the tentative judgments. Universal set for error E = [−9,9], universal set for error change rate E˙ = [−5,5], for control action U = [−18,0,18], they are described by their values in 15 discrete points; Ei , E˙ j , Ul are elements of fuzzy

Optimal Implicatıon Based Fuzzy Control System for a Steam Generator

239

sets of terms, respectively, such that at these points e = ei , e˙ = e˙ j , u = ul of the membership function µi (e) = 1, µj (˙e) = 1 and µl (u) = 1 Coefficients of membership functions (Ce , Ce˙ , Cu ) are calculated so that the corresponding membership functions of fuzzy term sets are µi (e) ≤ 0.5, µj (˙e) ≤ 0.5, µl (u) ≤ 0.5 [2, 5–7]. In each term, the corresponding -Ce , Ce˙ , Cu - for the fuzzy set take the corresponding values. Based on the table of linguistic rules established on the basis of the knowledge base (Table 1) and the above implications - the logics of Mamdani, ALI1, ALI2, ALI3, Lukashevich and KD, the matrix of fuzzy relations R(ei , e˙ j , ul ) is calculated and stored in memory as a membership matrix. Definition of a matrix of fuzzy relations based on the Mamdani logic based algorithm:   Rmamd ei , e˙ j = min(ei , e˙ j )    Imamd ei , e˙ j , ul = min(Rei ,˙ej (ei , e˙ j ) ul )  Rmamd (ei , e˙ j , ul ) =  µR (ei , e˙ j , ul ) =

˙ E×E×U

µR (ei , e˙ j ) ∧ µl (u)/(ei , e˙ j , ul )

µi (ei , e˙ j ), µR (ei , e˙ j ) ≤ µl (ul ) , i = 1, n; j = 1, n; l = 1, n µl (ul ), otherwise 7

Rmamd = U Rk (ei , e˙ j , ul ), k = 1, 7,

(4)

k=1

L. Zade’s fuzzy implication (maxmin composition rule)     Rzadeh ei , e˙ j = max(min ei , e˙ j , 1 − ei )  Izadeh (ei , e˙ j , ul ) = max(min (Rei ,˙ej (ei , e˙ j ) ul ), 1- Rei ,˙ej (ei , e˙ j ))      Rzadeh (ei , e˙ j , ul ) = µi ei , e˙ j ∧ µl (ul ) ∨ (1 − µi (ei , e˙ j ))/(ei , e˙ j , ul )) ˙ E×E×U

i = 1, n; j = 1, n; l = 1, n

(5)

In this work, using the truth value of the disjunction, the logical connector of the logics ALI1, ALI2, ALI3, KD, Lukasiewicz the methods for calculating the matrix of fuzzy relations are defined below. Definition of a matrix of fuzzy relations based on the implication ALI 1: ⎧   ⎨ 1 − ei , ei < e˙ j RALI 1 ei , e˙ j = 1, ei = e˙ j ⎩ e˙ j , ei > e˙ j   ⎧   ⎨ Rei ,˙ej ei , e˙ j ,  Rei ,˙ej < ul RALI 1 ei , e˙ j , ul = 1, µi ei , e˙ j  + µj (u) = 1 ⎩ µi ei , e˙ j + µj (u) > 1 µl (u),

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L. A. Gardashova and K. A. Mammadova

RALI1 (ei , e˙ j , ul ) =



(µ(ei , e˙ j ) ˙ E×E×U

→ µl (ul ))/(ei , e˙ j , ul ),

i = 1, n; j = 1, n; l = 1, n in here,    ⎧  ⎨ µi ei , e˙ j , µi ei , e˙ j  + µj (u) < 1  1   µi ei , e˙ j ∧ µl (ul ) → µRALI 1 ei , e˙ j , ul == 1, µi ei , e˙ j  + µj (u) = 1 ⎩ µl (u), µi ei , e˙ j + µj (u) > 1 7   Rk ei , e˙ j , ul , k = 1, 7 (6) RALI 1 = k=1

Determination of the fuzzy relation matrix based on ALI2 implication:     ei ≤ e˙ j  1, RALI 2 ei , e˙ j = min 1 − ei , e˙ j , ei > e˙ j   RALI 2 ei , e˙ j , ul    1, RALI 2 ei , e˙j ≤ ul    = min 1 − RALI 2 ei , e˙ j , ul , RALI 2 ei , e˙ j > ul 

  RALI 2 (ei , e˙ j , ul ) = (1 − µ ei , e˙ j , ul )/(ei , e˙ j , ul ) ˙ E×E×U

i = 1, n; j = 1, n; l = 1, n in here,  1   µi ei , e˙ j ∧ µl (ul ) → µRALI2 ei , e˙ j , ul    1, µi ei , e˙ j + µl (ul ) ≤ 1   = min(µi ei , e˙ j , µj (u)), µi ei , e˙ j + µl (ul ) > 1   RALI2 = ∩7k=1 Rk ei , e˙ j , ul k = 1, 7

(7)

Determination of fuzzy relation matrix based on ALI3 implication:  1, ei ≤ e˙ j RALI 3 (ei , e˙ j ) = e˙ j ˙j ei +(1−˙ej ) , ei > e  1, Rei ,˙ej (ei , e˙ j ) ≤ ul e˙ j RALI 3 (ei , e˙ j , ul ) = Re ,˙e (ei ,˙ej )+(1−ul ) , Rei ,˙ej (ei , e˙ j ) > ul i j

RALI3 (ei , e˙ j , ul ) = 1, n in here,



µ(ei , e˙ j ) ˙ E×E×U

→ µ(ul )/(ei , e˙ j , ul ),i = 1, n; j = 1, n; l =

Optimal Implicatıon Based Fuzzy Control System for a Steam Generator

  1   µi ei , e˙ j ∧ µl (ul ) → µRALI3 ei , e˙ j , ul ==



241

1, µi (ei , e˙ j ) + µl (u) ≤ 1 1−µ (e ,˙e )

i j , µi (ei , e˙ j ) + µl (u) > 1 1 − µ (e ,˙e i)+µ i i j l (ul )

RALI3 = ∩7k=1 Rk (ei , e˙ j , ul ), k = 1, 7

(8)

Determination of fuzzy relation matrix based on Lukashevich implication: RLukas (ei , e˙ j ) = min(1, 1 − ei + e˙ j ).   RLukas (ei , e˙ j , uL ) = min(1, 1 − Rei ,˙ej ei , e˙ j + uL ) RLukas (ei , e˙ j , uL ) = 1, n



µ(ei , e˙ j ) ˙ E×E×U

∧ µ(ul )/(ei , e˙ j , ul ), i = 1, n; j = 1, n; l =

1

µi (ei , e˙ j ) ∧ µl (ul ) → (1 − µi (ei , e˙ j )) ∧ µl (ul ) = max(µi (ei , e˙ j ) + µl (ul ) − 1; 0) RLukasevich = ∩7k=1 Rk (ei , e˙ j , ul ), k = 1, 7

(9)

Determination of fuzzy relation matrix based on KD implication: RKD (ei , e˙ j ) = max(1 − ei , e˙ j ). RKD (ei , e˙ j , uL ) = max(1 − Rei ,˙ej (ei , e˙ j ), uL )  RKD (ei , e˙ j , ul ) =

˙ E×E×U

µ(ei , e˙ j ) ∨ µl (ul )/(ei , ej , ul )

i = 1, n; j = 1, n; l = 1, n 1

µi (ei , e˙ j ) ∧ µl (ul ) → (1 − µi (ei , e˙ j )) ∧ µl (ul ) = min(1 − µi (ei , e˙ j ), µl (ul )) RKD = ∩7k=1 Rk (ei , e˙ j , ul ), k = 1, 7

(10)

Figures 2, 3, 4, 5 and 6 describe the results of computer simulation-modeling of the fuzzy regulation system according to different types of implication operators, i.e., the dependence of the transition process of ACS over time: Relationship matrix on the PD controller of Mamdani implication.

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10

8

6

4

2

0 0

20

40

60

80

100

120

Fig. 2. Transition process curve of fuzzy ACS using Mamdani implication. (Assignment grade g = 17) 20

18

16

14

12

10

8

6

4

2

0 0

20

40

60

80

100

120

Fig. 3. Transition process curve of fuzzy ACS using ALI1 implication. (Assignment grade g = 17) 20

18

16

14

12

10

8

6

4

2

0 0

20

40

60

80

100

120

Fig. 4. Transition process curve of fuzzy ACS using ALI2 implication (Assignment value g = 17) 12

10

8

6

4

2

0 0

20

40

60

80

100

120

Fig. 5. Transition process curve of fuzzy ACS by KD implication (Assignment value g = 17)

Optimal Implicatıon Based Fuzzy Control System for a Steam Generator

243

12

10

8

6

4

2

0 0

20

40

60

80

100

120

Fig. 6. Transition process curve of fuzzy ACS using Lukasevich implication (Task value g = 17)

According to Zade’s maxmin composition, the fuzzy set of control is determined by the formula (1). The defuzzification block determines a fuzzy control signal from the fuzzy control set. Defuzzification can be done in several ways. One of the widely used defuzzification methods in dynamic fuzzy control systems is the formula for finding the centroid center of gravity. N j=1 uj µj (uj ) (11) u(t) = N j=1 µj (uj ) To determine the impact of implications on the quality of the system when using each matrix Rk (ei , e˙ j , ul ), k = 1, 7 the quality criterion of the fuzzy control system is the mean square error (MSE). Jj =

1 N 2 e (t), N = 1, 40 j=1 N

(12)

Table 5 shows the types of fuzzy implications used in the calculation of matrices of fuzzy relations, and the values of the mean square error of control systems. From here, the type of optimal implication is determined based on the minimization of the mean square error. It can be seen from the table that the influence of implication operators on a fuzzy control system with different types of controllers is different. Thus, based on the table, we come to the conclusion that since the ALI1 implication is very effective in astatic and preventive-differentiating control laws, in some cases the ALI2 implication should be considered as the optimal implication in the steam generator control system. Thus, the fuzzy implication operator ALI2 has the smallest mean square error and the best transient process for a system with PD control. Table 5. Root mean square error (J) table Implications

Mamdani

ALI1

ALI2

ALI3

KD

Lukasiewicz

PD controller

14,798.77

2147.62

1625.21

4459.59

4384.85

4459.59

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4 Conclusion When modeling fuzzy objects, a significant influence of the type of optimal implication on the quality of ACS was revealed when calculating the relationship matrix, which is established and determined on the basis of fuzzy linguistic rules. The ACS transient process is stable and aperiodic. The integral quadratic error of ACS (steam generator temperature control) with imitation of a fuzzy PD controller is 1625.21. Temperature adjustment time T = nTd = 5 (n = 10; Td = 0.5), which meets practical requirements. For the above mentioned process fuzzy implication is determined: ALI-2. Our next problem is how to choose the Z implication to be able to describe reliability of information.

References 1. Aliev, R., Aliev, F., Babaev, M.: Fuzzy Process Control and Knowledge Engineerig in Petrochemical and Robotic Manufacturing. Verlag TUV Rheinland, Koln (1991) 2. ˙Ilhan, K., Ertu˘grul, Ç., Hasan, T.: A fuzzy logic controller application for thermal power plants. Energy Conv. Manag. 47(4), 442–458 (2006). https://doi.org/10.1016/j.enconman. 2005.05.010 3. Du, X., Li, P.: Fuzzy logic control optimal realization using GA for multi-area AGC systems. Int. J. Inf. Technol. 12(7), 63–72 (2006) 4. Aiswarya, P., et al.: Comparison of PID and fuzzy-PID control for nuclear steam boiler level control. Int. J. Innov. Technol. Res. 3(2), 1961–1965 (2015) 5. Ali, A.M., Ebrahim, M., Hassan, M.M.: Automatic voltage generation control for two area power system based on particle swarm optimization. Indones. J. Electr. Eng. Comput. Sci. 2(1), 132- 144 (2016). DOI:https://doi.org/10.11591/ijeecs.v2.i1.pp132-144 6. Isamiddin, S., et al.: Algorithms for synthesis of a fuzzy control system chemical reactor temperature. In: III International Workshop on Modeling, Information Processing and Computing.MIP: Computing-2021, pp. 64–70(2021). http://ceur-ws.org/Vol-2899/paper010. pdf 7. Khrystyna, F., Ievgeniia, K., Valery, S.: Optimal design of intelligent control systems of steam turbine using genetic algorithms. Int, Book Series.13, 105–112. http://www.foibg.com/ibs_ isc/ibs-13/ibs-13-p15.pdf 8. Singhala, P., Shah D.N., Patel. B.: Temperature control using fuzzy logic Int. J. Instrum. Control Syst. 4(1), 1–10(2014). https://doi.org/10.5121/ijics.2014.4101 9. Duy, N.T., et al.: Design of Sugeno fuzzy logic controller for resistance furnace. J. Multidiscip. Eng. Sci. Stud. 3(8), 2001–2006(2017). ISSN 2458–925X 10. Tarun Kumar, D., Yudhajit, D.: Design of a room temperature and humidity controller using fuzzy logic. Am. J. Eng. Res. 02(11), 86–97(2013). e-ISSN 2320–0847, p-ISSN 2320- 0936 11. Egoigwe, S.V., Nwobi, Ch., et al.: Application of fuzzy logic temperature controller for water bottle indust. Comput. Eng. Intell. Syst. 10(2), 16–22 (2019). https://doi.org/10.7176/CEIS 12. Kamari, M.L., Isvand, H., Nazari, M.A.: Applications of multi-criteria decision-making (MCDM) methods in renewable energy development: a review. Renew. Energy Res. Appl. 1(1), 47–54 (2020). https://doi.org/10.22044/RERA.2020.8541.1006 13. ˙Ihsan, K., Murat, Ç., Fulya, T.: A comprehensive review of fuzzy multi criteria decision making methodologies for energy policy making. Energy Strat. Rev. 24, 207–228 (2019). https://doi.org/10.1016/j.esr.2019.03.003

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14. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, New Jersey, London, Singapore, Hong Kong (2001) 15. Aliev, R., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inf. Sci. 181, 1045–1059 (2011) 16. Tserkovny, A.: A t-norm fuzzy logic for approximate reasoning. J. Soft. Eng. Appl. 10, 639–662 (2017). https://doi.org/10.4236/jsea.2017.107035 17. Tserkovny, A.: A fuzzy logic based resolution principal for approximate reasoning. J. Softw. Eng. Appl. 10, 793–823 (2017). https://doi.org/10.4236/jsea.2017.1010045 18. Sinuk, V.G, Panchenko, M.V.: Method of fuzzy inference for one class of MISO-structure systems with non-singleton inputs. IOP Conf. Series: Mater. Sci. Eng. 327 (2018). https:// doi.org/10.1088/1757-899X/327/4/042074 19. Yager, R.R.: On some new classes of implication operators and their role in approximate reasoning. Inf. Sci. 167(1–4), 193–216 (2004). https://doi.org/10.1016/j.ins.2003.04.001 20. Mammadova, K.A.: Construction of fuzzy power generation model of thermal power plants. Sci. Coll. «interconf» 1, 1065–1075 (2021). https://ojs.ukrlogos.in.ua/index.php/interconf/art icle/view/8840 21. Shi, Y., Gasse B., Kerre, E.: Fuzzy implications: classification and a new class. In: Baczy´nski, M., Beliakov, G., Bustince Sola, H., Pradera, A. (eds.) Advances in Fuzzy Implication Functions. Studies in Fuzziness and Soft Computing, vol. 300, pp. 31–51. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35677-3_2 22. Shi, Y., Ruan, D., Kerre, E.: On the characterizations of fuzzy implications satisfying I(x, y) = I(x, I(x, y)). Inf. Sci. 177(14), 2954–2970 (2007). https://doi.org/10.1007/978-3-642-356 77-3 23. Pei, D.: Unified full implication algorithms of fuzzy reasoning. Inf. Sci. 178, 520–530 (2008). https://doi.org/10.1016/j.ins.2007.09.003 24. Jafarli, M.M., Gardashova, L.A.: Using data mining technology for analysis of hydrogenperoxide decomposition reaction. In: International Conference on Actual Problems of Chemical Engineering Dedicated to the 100th Anniversary of Azerbaijan State Oil and Industry University, pp. 548–553 (2020) 25. Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Trans. Fuzzy Syst. 15(6), 1107–1121 (2007). https://doi.org/10.1109/TFUZZ.2007.896304 26. Mas, M., Monserrat, M., Torrens, J.: The law of importation for discrete implications. Inf. Sci. 179, 4208–4218 (2009). https://doi.org/10.1016/j.ins.2009.08.028 27. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing – ICAFS-2020 . ICAFS 2020. Advances in Intelligent Systems and Computing, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_2 28. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12

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29. Gardashova, L.A.: Synthesis of fuzzy terminal controller for chemical reactor of alcohol production. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, vol. 1095, pp. 106–112. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_13 30. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing – ICAFS-2020. ICAFS 2020. Advances in Intelligent Systems and Computing, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_7

Prediction of Runoff Using Artificial Neural Networks, MLR Regression, and ARIMA Model (A Case Study: Bared River, Lebanon) Youssef Kassem1,2,3,4(B) , Hüseyin Gökçeku¸s2,3,4 , Francis Surfia Dioh2 Marcus Paye Quoigoah2 , and Marilyn Hannah Godwin2

,

1 Faculty of Engineering, Mechanical Engineering Department, Near East University,

Nicosia 99138, North Cyprus, Cyprus [email protected] 2 Faculty of Civil and Environmental Engineering, Near East University, Nicosia 99138, North Cyprus, Cyprus [email protected], {20213607,20213021, 20215601}@std.neu.edu.tr 3 Energy, Environment, and Water Research Center, Near East University, Nicosia 99138, North Cyprus, Cyprus 4 Engineering Faculty, Kyrenia University, Kyrenia 99138, North Cyprus, Cyprus

Abstract. In this paper, Multi-layer perceptron neural network (MLPNN) and Radial basis function neural network (RBFNN) have been used to predict the monthly runoff in Bared River, Lebanon. Moreover, the accuracy of the proposed models is compared with the ARIMA model and Multiple Linear Regression (MLR). For this aim, maximum temperature, minimum temperature, solar radiation, wind speed, soil moisture and were collected and used as input parameters for the proposed models. The results showed that ARIMA and MLPNN models were suitable for predicting the monthly. Among the developed models, the ARIMA has the best performance for runoff prediction. Keywords: Runoff · Bared river · MLPNN · RBFNN · ARIMA · MLR

1 Introduction Climate change is an important factor in the strategic management of water resources in dry and semi-arid countries [1]. Several researchers have studied the effects of climate change on water resources [2, 3]. Thus, investigating the influence of climate change on the hydrologic cycle is vital for hydrology development. Several studies have concluded that climate change is the main indicator related to the changes in runoff in the basin or catchment area [4]. Accordingly, predicting the amount of water in a basin over a period is a very important topic for scientists and engineers for centuries [5]. Additionally, the analysis of runoff is very important for predicting floods and droughts [6]. Moreover, runoff modeling is a useful tool for designing and operating the various components of water resources © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 247–255, 2023. https://doi.org/10.1007/978-3-031-25252-5_35

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projects and water resource planning and management [7]. It also helps to reduce the influence of drought and water resources issues [8]. Recently, several empirical models of runoff series such as machine learning models and mathematical modeling are developed to construct a long-term runoff forecasting model [5–9]. Bared river, the third largest river in the Akkar district of North Lebanon, has a very important strategic position. It is fed by the springs in the mountains. Recently, the heavy rainfall with snow has led to an extreme flood, which caused flooded some streets up to the windows of the houses especially houses built near the river. Therefore, it is necessary to provide a predictive model that can estimate the runoff in the bared river to minimize the effect of floods in the area. In this regard, four empirical models, namely, MLPNN, RBFNN, ARIMA, and MLR are developed to predict the runoff. For this aim, the monthly global meteorological data including maximum temperature, minimum temperature, wind speed, solar radiation, rainfall, and soil moisture are utilized as input variables for the models.

2 Material and Methods 2.1 Data Due to the limitation of available the actual data of climate parameters, global meteorological data are utilized to understand the influence of geographical coordinates on the prediction of precipitation and predict monthly precipitation using various empirical techniques. In this study, global meteorological data were obtained from TerraClimate. TerraClimate dataset offers global monthly meteorological data with high-spatial resolution (1/24°, ~4-km) monthly climate as well as provides the data since the year 1958 to date [10]. The main reasons to utilize TerraClimate were the availability of consistent long-term monthly maximum temperature (Tmax), minimum temperature (Tmin), solar radiation (SR), wind speed (WS), soil moisture (SM), runoff (Q), and rainfall (R), which is allowed considering an eventual change in climate variables. The statistical parameters of the used variables are tabulated in Table 1. Table 1. Statistical parameters of monthly used data for the period of 1958–2021. Variable

Unit

Mean

Standard deviation

Tmax

◦C

24.62

Tmin

◦C

16.35

R

mm

62.57

71.38

114.07

SM

mm

89.87

66.95

WS

m/s

3.44

DR

W /m2

44.63

191.79

Q

mm

11.78

33.17

5.269 5.364

0.6567

Coefficient of variation 21.4 32.81

Minimum

Maximum

12.63

34.27

3.9

25.95

0

407

74.49

15.9

202.2

19.07

1.8

5.44

429.69

-264.98

265.29

281.6

0

341.7

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2.2 Machine Learning Models (MLMs) MLMs are utilized as a tool to describe a complex system [11]. Wide ranges of ML models are utilized to solve complex problems in a variety of fields [11]. In this study, MLPNN and RBFNN are developed to determine the CFPP of Biodiesel. MLPNN and RBFNN are the most popular artificial neural network approaches for modeling nonlinear and complex processes in the real world. Generally, MLPNN is a feedforward neural tool consisting of three layers (input layer, hidden layer and output layer) [12]. Besides backpropagation algorithm is used for training MLPNN. Furthermore, RBFNN is a variant of feed-forward neural network with a hidden interconnected layer. Distinct advantages of RBFNN include universal approximation abilities, no local minimum problem, and a faster learning algorithm over other ANNs based on previous scientific studies [13]. The description of the MLPNN and RBFNN models is given in [11, 13]. In this study, 70% of the data was used for training, while the remaining data were utilized to test the model. The results of the proposed models are compared with observed data. 2.3 ARIMA Model ARIMA model was developed by Box, Jenkins, and Reinsel [14]. It is very widely used in time series modeling. Moreover, it is defined by three terms (p, d, and q). Box–Jenkins algorithms are utilized to finalize the value of p, d, and q. The description of the ARIMA models is given in [15]. 2.4 MLR Model The MLR is a mathematical statistical model for establishing the relationship between independent and dependent variables (Eq. (1)). Q = f (Tmax.Tmin, SM , R, WS, SR)

(1)

MLR can be expressed as Q = A + B(Tmax) + C(Tmin) + D(R) + E(SM ) + F(WS) + G(DR)

(2)

where A = –5.194, B = –4.254, C = 5.152, D = 0.32, E = 0.066, F = 3.401, and G = –0.005

3 Results and Discussion 3.1 Estimating the Runoff Using MLPNN and RBFNN Aforementioned, two machine learning models were utilized to predict the runoff of biodiesel. Thus, Tmax, Tmin, SR, WS, SM, and R, are utilized as input parameters for the models. The best configuration of the network was found based on the lowest value of mean squared error. Moreover, the trial and error method is employed to find the best parameters for the model. Figures 1 and 2 show the architecture model for MLPNN and RBFNN. Additionally, Table 2 lists the summary and parameters for the proposed models. It is found that the root mean squared error (RMSE) is estimated to be equal to 13.73 and 19.04 for MLPNN and RBFNN, respectively.

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Fig. 1. The structure of MLPNN for predicting the runoff.

Table 2. Network information. Model

Layer

Parameters

Value/function

MLPNN

Hidden Layer(s)

Number of Hidden Layers

2

Number of Units in Hidden Layer 1a

4

RBFNN

Number of Units in Hidden Layer 2a

3

Activation Function

Sigmoid

Output Layer

Activation Function

Linear

Statistical indicator for the training phase

R-squared

0.82

MSE [mm]

188.39

RMSE [mm]

13.73

Number of Units

10

Activation Function

Softmax

Hidden Layer Output Layer

Activation Function

Linear

Statistical indicator for the training phase

R-squared

0.66

MSE [mm]

362.58

RMSE [mm]

19.04

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Fig. 2. The structure of RBFNN for predicting the runoff.

3.2 Estimating the Runoff Using ARIMA and MLR As discussed previously, ARIMA and MLR models were utilized to estimate the runoff of Bared River in Lebanon. Moreover, 70% of the data were used for training, and the remaining data for evaluating the model performance. The results showed that ARIMA (1, 0, 12) model has produced a good agreement with the observed data compared to the MLR model. Time series plots of the observed and predicted runoff values in the training phase are shown in Fig. 3.

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Fig. 3 Comparison of the estimated data with the observed data for runoff using ARIMA and MLR models

3.3 Performance Evaluation of Proposed Models The performance of artificial neural network models is compared with the ARIMA and MLR to find the best model for runoff prediction. The values of R-squared and root mean squared error (RMSE) are listed in Table 3. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the ARIMA model followed by MLPNN with a value of 0.816 for R-squared and 10.25 for RMSE. Figure 4 illustrates the time series plots of the observed and estimated monthly values of runoff in the testing phase. Table 3. Evaluation of model performance. Statistical indicator R-squared RMSE [mm]

MLPNN 0.816 10.25

RBFNN 0.688 12.70

ARIMA 0.859 8.56

MLR 0.513 15.91

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Fig. 4. Comparison of the estimated data with the observed data for all developed models.

4 Conclusions In this study, the ability of MLPNN, RBFNN, ARIMA, and MLR models for monthly runoff prediction was investigated. R-squared and RMSE were employed to evaluate the performance of the models. The results showed that ARIMA and MLPNN models were suitable for estimating the monthly runoff. Among the developed models, the ARIMA model presented significantly better prediction performance based on the value R2 and RMSE.

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In future work, various models with various combinations of parameters should be investigated to identify the parameter that influenced the runoff.

References 1. Ostad-Ali-Askari, K., Ghorbanizadeh Kharazi, H., Shayannejad, M., Zareian, M.J.: Effect of management strategies on reducing negative impacts of climate change on water resources of the Isfahan-Borkhar aquifer using MODFLOW. River Res. Appl. 35(6), 611–631 (2019). https://doi.org/10.1002/rra.3463 2. Karimi, V., Karami, E., Keshavarz, M.: Climate change and agriculture: Impacts and adaptive responses in Iran. J. Integr. Agric. 17(1), 1–15 (2018). https://doi.org/10.1016/S2095-311 9(17)61794-5 3. Ayt Ougougdal, H., Yacoubi Khebiza, M., Messouli, M., Lachir, A.: Assessment of future water demand and supply under IPCC climate change and socio-economic scenarios, using a combination of models in Ourika Watershed, High Atlas. Morocco. Water 12(6), 1751 (2020). https://doi.org/10.3390/w12061751 4. Li, Z., Li, Q., Wang, J., Feng, Y., Shao, Q.: Impacts of projected climate change on runoff in upper reach of Heihe River basin using climate elasticity method and GCMs. Sci. Total Environ. 716, 137072 (2020). https://doi.org/10.1016/j.scitotenv.2020.137072 5. Wang, W.C., Chau, K.W., Qiu, L., Chen, Y.B.: Improving forecasting accuracy of medium and long-term runoff using artificial neural network based on EEMD decomposition. Environ. Res. 139, 46–54 (2015). https://doi.org/10.1016/j.envres.2015.02.002 6. Ji, G., Lai, Z., Xia, H., Liu, H.: Wang, Z: Future runoff variation and flood disaster prediction of the yellow river basin based on CA-Markov and SWAT. Land 10(4), 421 (2021). https:// doi.org/10.3390/land10040421 7. Ghumman, A.R., Ghazaw, Y.M., Sohail, A.R., Watanabe, K.: Runoff forecasting by artificial neural network and conventional model. Alexandria Eng. J. 50(4), 345–350 (2011). https:// doi.org/10.1016/j.aej.2012.01.005 8. Tiwari, D.K., Tiwari, H.L., Nateriya, R.: Runoff modeling in Kolar river basin using hybrid approach of wavelet with artificial neural network. J. Water Climate Change 13(2), 963–974 (2022). https://doi.org/10.2166/wcc.2021.246 9. Zhihua, L.V., Zuo, J., Rodriguez, D.: Predicting of runoff using an optimized SWAT-ANN: a case study. J. Hydrol.: Reg. Stud. 29, 100688 (2020). https://doi.org/10.1016/j.ejrh.2020. 100688 10. Abatzoglou, J.T., Dobrowski, S.Z., Parks, S.A., Hegewisch, K.C.: TerraClimate, a highresolution global dataset of monthly climate and climatic water balance from 1958–2015. Sci. Data 5(1), 1–12 (2018). https://doi.org/10.1038/sdata.2017.191 11. Kassem, Y., Gökçeku¸s, H., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 1–28 (2020). https://doi.org/10.1007/s40808-020-00866-y 12. Xu, Y., Li, F., Asgari, A.: Prediction and optimization of heating and cooling loads in a residential building based on multi-layer perceptron neural network and different optimization algorithms. Energy 240, 122692 (2022). https://doi.org/10.1016/j.energy.2021.122692 13. Lin, H., Dai, Q., Zheng, L., Hong, H., Deng, W., Wu, F.: Radial basis function artificial neural network able to accurately predict disinfection by-product levels in tap water: Taking haloacetic acids as a case study. Chemosphere 248, 125999 (2020). https://doi.org/10.1016/ j.chemosphere.2020.125999

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14. Kao, Y.S., Nawata, K., Huang, C.Y.: Predicting primary energy consumption using hybrid ARIMA and GA-SVR based on EEMD decomposition. Mathematics 8(10), 1722 (2020). https://doi.org/10.3390/math8101722 15. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Wind speed prediction of four regions in northern Cyprus prediction using ARIMA and Artificial Neural Networks models: a comparison study. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F. (eds.) 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS2018. Advances in Intelligent Systems and Computing, vol. 896, pp. 230–238. Springer, Cham. https://doi.org/10.1007/978-3-030-04164-9_32 (2018)

Devices with Fuzzy Logic Control of Artificial Lung Ventilation Aynur J. Jabiyeva(B) Biomedical Engineering Research Group at Department of Instrument Engineering, Azerbaijan State Oil and Industry University, Azadlig 20, Nasimi, Baku, Azerbaijan [email protected]

Abstract. This article presents the development of a ventilator and its control algorithm. The main feature of the developed ventilator is compressed by a pneumatic drive. The control algorithm is based on the adaptive fuzzy inference system (ANFIS), which integrates the principles of fuzzy logic. The paper also presents a simulation model to test the designed control approach. The results of the experiment provide verification of the developed control system. The novelty of the article is, on the one hand, the implementation of the ANFIS controller, pressure control, with a description of the training process. On the other hand, in the article presented a draft ventilator with a detailed description of the hardware and control system. Keywords: Pneumatic drive · Artificial lung ventilation · Coronavirus · Fuzzy logic

1 Methods and Models The article uses fuzzy logic as they deal with its uncertainty and inaccuracy. Of the many real problems, it naturally allows control algorithms to be based on human activities, and not on mathematical models [1]. In the presented article, fuzzy logic simulates human thinking and the ability to make a decision based on not very accurate information, which allows the use of a controlled system, such as a high-frequency lung apparatus, in applications compatible with traditional control algorithms based on fuzzy algorithm models. One such area is medical decision making, which involves various factors of varying relative importance in the context of experience [1–6]. Many hospitalized patients on specific grounds, rapid and abrupt deterioration, often accompanied by shortness of breath and lack of individual apparatus. During the pandemic, the information about the patients in the period of equipment failure was taken from the specialists of the National Rehabilitation Institute of Azerbaijan, candidates of sciences and doctors with more than 20 years of experience. This study deals with the development of fuzzy logic for automatically controlling levels oxygen Pressurized Ventilation (PSV) performed in patients with severe lung disease (COPD) [2]. Currently, there is not generally an accepted approach to pulling © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 256–264, 2023. https://doi.org/10.1007/978-3-031-25252-5_36

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the patient away from mechanical ventilation, a clear opinion in the medical community where it is possible somehow algorithmically shape cutting process from a mechanical ventilator. Fuzzy logic seems appropriate for this job because it naturally represents the subjective human concepts used in medical decisions [3]. It is associated with all processed inputs, defines duplicated functionality between input and finally decides the response received. The aim of this study was development of fuzzy logic algorithms to control pressure-assisted ventilation in the intensive care unit patients using Heart rate, tidal volume measurement, respiratory rate, and the involvement of arterial oxygen pressure [4]. Algorithms based on fuzzy logic show the potential to improve the work of medical professionals. This article describes a fuzzy logic algorithm that can help explore the types of tasks that humans are not suited for by mimicking the complexity of human thought processes situations and performing repetitions indeed. In practice, there may not be an exact model for medicine, the situation can be very different when modeling is challenging, fuzzy logic is regarded as the best option as a tool by which the human mind can work with approximate information and extract and produce meaningful information [5]. We retrospectively exemplify its application in 10 patients with severe chronic obstructive pulmonary disease, contrasting the results of the algorithm’s decisions with the actual data outcomes. Unexpected diseases and disasters are becoming major problems that our world is facing. In this article, in addition to using other methods, we also applied the adaptive neuro-fuzzy inference system (ANFIS) [7]. When a patient is presented at the imaging counter, the system will capture their vital signs and include the patient’s physiological state and general appearance as well as their complaints. This data will be managed and analyzed on the data server and the patient’s emergency situation will be immediately informed. Considering the proposed method, it will help to reduce the burden of the emergency doctor, especially in the event of the patient’s lung arrest and serious disaster. Fuzzy inferential clustering was used to find fuzzy rules for the ANFIS model. The results showed that it was evaluated by measuring specificity and sensitivity for binary classification of training data. Therefore, it was chosen as the technique to develop the initial forecasting model.

2 Statement of the Problem and Its Solution The Patient Early Warning System (MEWS) is a proven guideline or bedside assessment tool to that extent successfully used to achieve this goal by locating high-risk patients in an effort to take prompt preventive intervention. In order to arrive at a decision, MEWS analyzes physiological or vital signals such as body temperature, blood pressure (BP), heart rate, respiration rate, oxygen saturation, and blood sugar. Patients having a MEWS score of at least 5 points are transferred right away to the emergency department. If we apply the ANFIS principle, Adaptive Neural Fuzzy Inference System parameters construct a fuzzy inference system (FIS) obtained from training samples, the considered FIS has two inputs x and y with two related membership functions (MFs) and one output (z), two non- A general set of rules with fuzzy if–then rules is represented as the following algorithm (Fig. 1.), Rule 1: if x is A1 and y is B1, then …

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A. J. Jabiyeva Connecting the patient to the ventilation system

Patient choice

Determining the patient's condition

Yes

Yes

Disconnecting the patient from the ventilation system

No Mild condition

Turning on the ventilator No. 1

No

There is a need for a ventilator

Yes

No

Slightly severe condition

Turning on the ventilator No. 2

Yes

No Serious condition

Turning on the ventilator No. 3

Yes

Turning on the ventilator No. 4

Very serious condition

No

Turning on the ventilator No. 5

Patient status and connection time to the ventilator

Fig. 1. Algorithm based on fuzzy logic for artificial lung ventilation

The multi-ventilator method does not optimize carbon dioxide removal for a variety of reasons, and oxygen levels will be difficult to control and optimize. Patients with COVID-19 seem to respond to PEEP fairly well. Of all, PEEP is only a method to raise mean airway pressure, the primary factor impacting lung function recovery. In severe hypoxemia, reverse Ratio ventilation can be employed to raise the pressure even more in the middle airways. It has been proven that fuzzy logic is able to transfer knowledge from humans and experts employing linguistic expressions, into computer models. Systems for fuzzy inference (FINS) use a set of “if–then-else”, “if–then” regulations created on the basis of the knowledge gained by experts (biomedical engineers in relation to this work), to help in medical diagnosis in conditions or they recommend treatment according to the current situation. Core Principle: Patient independence from the ventilator. Adaptive network-based fuzzy inference systems method [10] a hybrid intelligent system is one of the best solutions in data modeling, capable of reasoning and learning in an uncertain and uncertain environment. It is a combination of two or more mechanical ventilator technologies. This combination was usually done to overcome single smart technologies [7–9]. As a rule, in the hospital, the ventilator is adjusted to the needs of a particular patient. We would not want one patient’s tachypnea to hyperventilate patients on the same

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ventilator with others. Therefore, basically each patient should breathe independently when using a multi-patient ventilator and will not affect the ventilation of other patients connected to the ventilator. This can be achieved as described below. Pressure cycle ventilation is preferred over volume cycle ventilation. Pressure cycle ventilation and volume cycle ventilation have the following advantages [11–14]: • Volumetric ventilation: the benefit is the supply of a volume that is certain of oxygen ( the drawback is the inability to regulate peak pressure). • Pressure cycling ventilation: the advantages are assured peak pressure is limited (the drawback is the absence of an oxygen volume control system). Once you start using the numerous people using a ventilator, thus controversy will to a large extent disappear. There are a few major drawbacks to using volume loop mode: 1. Using Multi-Patient Volume Cycle mode does not provide oxygen volume control for any patient, nor does it provide maximum airway pressure control. 2. The volume cycle mode of patients using the same ventilator should have the same size, the same FiO2, and the same PEEP requirements. Using pressure cycle mode solves the following problems: 1. In pressure cycling: in this mode, we maintain control over the movement pressure and maximum airway pressure. 2. Using the pressure cycling mode avoids harmful interaction between patients. 3. Patients using the same ventilator do not have to be the same size. Continuous mandatory ventilation (CMV) is required, and patients can usually turn on the ventilator to breathe. It’s possible that modern ventilators don’t require constant ventilation. However, the following action will have the same result: 1. Raise the threshold of the lung machine as much as possible so that patients can breathe 2. Respirolytic sedation can be utilized to lessen the patient’s breaths per minute and stop the ventilator from turning on. Ventilation efficiency will be less than fine-drawn. A multi-fan technique will not optimize carbon dioxide removal for a variety of reasons, and oxygen levels will be challenging to regulate and optimize. Patients with COVID-19 seem to respond to PEEP fairly well. Of all, PEEP is only a method to raise mean airway pressure, the primary factor impacting lung function recovery [5, 6]. In severe hypoxemia, reverse Ratio ventilation can be employed to raise the pressure even more in the middle airways. Five ventilators provide individual settings for 10 patients.

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The main disadvantage of the scheme described above is that patients need to be selected due to the relative level of lung damage severity (PEEP and FiO2 requirements) [14]. This problem can be solved in the following way: imagine we installed five fans: • Ventilator 1: settings for minor injuries (FiO2 50%, PEEP 10 cm, peak pressure 20 cm) • Moderate injury settings for Ventilator 2 (FiO2 60%, PEEP 14 cm, peak pressure 26 cm) • Setting for high injury on Ventilator 3 (FiO2 80%, PEEP 18 cm, peak pressure 30 cm). • Ventilator 4 settings for hypoxia (FiO2 100%, PEEP 22 cm, peak pressure 35 cm). • Rescue settings (FiO2 100%, PEEP 22 cm, peak pressure 35 cm, ventilation) for Ventilator 5 is inversely proportional to inspiratory time >> expiratory time).

Fig. 2. Statistical measurement for the input and output variables

Each ventilator can connect 1 to four patients. If patients are deteriorating, they can be changed to more ventilators (e.g., ventilators No. 2–3). Alternatively, as patients improve, they can be switched to fewer ventilators. This system allows multiple ventilators to provide individual settings for multiple patients. This article’s goal is to create a knowledge-based method [15–17] for the treatment of dyspnoea. To achieve this goal, a fan was developed. Fans are called smart fans because they use fuzzy logic to control the status of pneumatic equipment. Currently, there is no generally accepted method for weaning patients off the ventilator, but it is understandable that the medical world believes that this process can somehow be developed algorithmically. For this purpose, fuzzy logic looks apt because it easily describes subjective human concepts used in. The current study’s objective was to create a fuzzy logic system that uses measurements of heart rate, oxygen volume, respiration regulating heart rate and arterial oxygen saturation to support pressure ventilation in intensive care unit patients. The fuzzy logic method is covered in this paper, and ten patients with severe chronic obstructive pulmonary disease are retrospectively evaluated using how it works. We do

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this by comparing many decision-making in medicine processes the system’s predictions what is actually happens. Fuzzy logic’s suggested uses matched the current state on average 70% of the time, and 90% of the time, within 2 cm H2O. When we compared our algorithm’s predictions to cases where degree of pressure supports changes were in fact made by the attending doctor, physicians tended to decrease support levels slightly more aggressively than the algorithm. In the light of continuous observations of the patient’s vital signs, we concluded that our fuzzy algorithm is able to regulate breathing rate with pressure support. Fuzzy logic is used to automatically control mechanical ventilation with pressure support. ANFIS is an example of a hybrid intelligent system that solves these problems [7]. It depends on the data learning rules and membership functions. This Inference Systems model for ANFIS infers from a first-order system to generate an if-on rule to construct a model that maps input to output with high efficiency. tle('Pa ent 1'); text(25,80 3% text(25,77,'\rightarrow Ven lator No.1 opera on'); text(25,74,'\rightarrow Ven lator No.2 opera on'); text(25,71,'\rightarrow Ven lator No.3 opera on'); text(25,68,'\rightarrow Ven lator No.4 opera on'); text(25,65,'\rightarrow Ven lator No.5 opera on'); Len_Pat_1=length(Pa ent_1); a=0; for i=1:Len_Pat_1+1; OX1(i)=a; a=a+1; Pa ent_2=[41 45 48 52 53 51 48 47 44 41 36 31 28 25]; figure (2); plot(Pa ent_2); xlabel('Days'); % Ось ОХ ylabel('Co % Ось ОY tle('Pa ent 2'); text(10,50 1% text(10,49,'\rightarrow Ven lator No.1 opera on'); text(10,48,'\rightarrow Ven lator No.2 opera on'); text(10,47,'\rightarrow Ven lator No.3 opera on'); text(10,46,'\rightarrow Ven lator No.4 opera on'); text(10,45,'\rightarrow Ven lator No.5 opera on'); Len_Pat_2=length(Pa ent_2); a=0; for i=1:Len_Pat_2+1; OX2(i)=a; a=a+1; end; axes2=gca; set(axes2,'XTick', OX2); set(axes2,'YTick',[20 30 40 50 60 70 80 96]); set(axes2,'YTickLabel', {'','Mild','','Slightly severe','Serious','','Very serious','Cri cal'}

Fig. 3. Software computational process of artificial lung ventilation

Previously inputs and outputs were passed to the ANFIS model to extract the rules. The “fuzzification” level is set and adapts the parameters for the selected membership. After that comes the power firing level, which is the IF conditions for setting the rules. Firepower output is normalized in the normalization layer. Before the last layer, there is another adaptation layer that works as a “defuzzification” layer of the rules, where the parameters of the ventilator model are adjusted to get the best match between input and output data. The circuits were tested on a turbine ventilator connecting two test circuits to two patient circuits. Two patients are predicted to weigh 70–75 kg with breaths per minute (RR) 20 m/min, ratio between inhaled and exhaled air (I:E) 1:1 and inhaled oxygen concentration (FiO2) of 100%). Initial inspiratory pressure was 10 cm, and positive

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expiratory pressure (PEEP) was recorded at 15 cm H2O. H2O. The first 15-h study was conducted between two simulated patients under similar conditions -static airway compliance (Cstat) Airway resistance and 50 ml/cm H2O 5 cmH2O/l/s. Measured W in pressure control mode was 953 ml, but to everyone the sick patient was given 470 ml. Then we did two more tests. Our tests support the Technically, it is possible to ventilate two patients at once, but there are challenges and risks involved associated with this arrangement continues. Given current information and data on this topic, this should only be done in emergencies due to mechanical failure. We suggest a schedule (Fig. 2) for initiating type 2 ventilation. Coordination of the patient for compliance and possibly airway resistance is key. Your clinician must be prepared to recognize signs of possible under or over ventilation and be prepared to initiate manual ventilation in case of problems (Fig. 4).

Fig. 4. Membership functions of regulation error, ventilation error with volume cycle and pressure cycle. Information for each patient

The model showed the best results in all 10 statistical measurements for training and unseen data. ANFIS works like a small window in the model to show which parameters affect the prediction result. Membership options have been adapted to provide a better match between input and output during ANFIS training. He changed the form of membership in accordance with the new adapted parameter. The most effective variables are the airway and respiration (variable 1), as its membership pattern changed significantly after exercise compared to the other variables. Some Pressure control (PC) mode was used to assess the experimental circumstances (inspiratory time: expiratory time ratio: 1:2, positive expiratory pressure) (PEEP) (Fig. 3) 12 cmH2O, breathing time to climb 0.1 s). First, conformity for the two test lungs eventually got bigger to 22 cmH2O at peak inspiratory pressure at 25 breaths per minute and then at 15 breaths per minute (10–70 ml cmH2O-1). Then the right Clung was gradually increased and the left was set to 50 ml/.cmH2O-1. In the third case, three concentrations of were injected into right lung during testing pinching the flexible clamp on the tube but was not delivered to the left test lung. The lungs were identical 50 ml

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in each test lung cmH2O-1 and 30 was chosen cmH2O 15 breaths per minute. This investigation was replicated using 70 ml cmH2O-1 on the right and 20 ml cmH2O-1 Clung on the left. Finally, we simulated coughing by manually squeezing the test lungs in a setting with and without a check valve. Each test condition was measured for 1.5 min. VT per calculations for the test lung were the mean of every breath. VT is portrayed in mlkg-1, assuming a patient who has an anticipated body weight of 70–75 kg. With the result obtained of the experiments gave the following results: The presented approach gave satisfactory mechanical results based on the ANFIS ventilation controller. The ventilation was capable to approximately follow the benchmark pressure. Thus, it might be argued that the technique is appropriate for application. Pressure-controlled ventilation, inspiratory/expiratory requirements, and oxygen volume ratio or delivery have been investigated.

3 Conclusions The solution of the given problem is simulated. In the article, we presented a ventilator based on pneumatic systems. Pressure cycling ventilation has been successfully used with positive outcomes. • It is practically a single ventilator can be used to ventilate multiple patients. Most likely, this is possible using basic parameters that protect the lungs. However, this tactic comes at a price: poor ventilation and a lack of control over precise oxygen levels (with high pCO2). • The main purpose prevents one patient from having an adverse effect on other patients. Without allowing any patient to activate the ventilator, this can be accomplished utilizing pressure cycling ventilation. • On a ventilator, patients should be completely unconscious and unresponsive (or, if, paralyzed on a ventilator 5). • The efficiency of each patient’s ventilation can be monitored with end oxygen CO2. • By utilizing a few ventilators with various parameters, it is possible to support a large group of patients with quite individual parameters. The main results are as follows: we have given a detailed description of the new concept of the ventilator, the development of a control algorithm based on an adaptive neuro-fuzzy inference system, graphical representation and experimental analysis of the simulation model. The experiment’s findings demonstrated that the main problem was solved, and the main features were to maintain the PEEP value of the initial pressure. This is due to a leak in the print instrument interface. These phase issues occurred when low pressure levels were present during the reference. The article also presents the results of mechanical ventilation in the assisted ventilation mode, this is exclusively intended to support patients who do not have lung pathology. Biochemical testing of the ventilator is now possible. In the future, these ideas will first be focused on animals. Animal testing will be the focus of future effort. During ventilation the animal’s vital signs will be watched closely. As a result, the results will be examined, and the appropriate adjustments will be made. for human use.

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References 1. Ishola, N.B., et al.: Adaptive neuro-fuzzy inference system-genetic algorithm vs. response surface methodology: A case of optimization of ferric sulfate-catalyzed esterification of palm kernel oil. Process. Saf. Environ. Prot. 111, 211–220 (2017) 2. Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-Fuzzy and Soft Computing. Prentice Hall, Upper Saddle River (1997) 3. Al-Hmouz, A., Shen, J., Al-Hmouz, R., Yan, J.: Modeling and simulation of an adaptive neuro-fuzzy inference system (ANFIS) for mobile learning. IEEE Trans. Learn. Technol. 5, 226–237 (2011) 4. Hoehl, S., et al.: Evidence of SARS-CoV-2 Infection in Returning Travelers from Wuhan, China. N. Engl. J. Med. 382, 1278–1280 (2020) 5. World Health Organization: Coronavirus Disease (COVID-19) Pandemic. https://www.who. int/emergencies/diseases/novel-coronavirus-2019. Accessed 29 Apr 2019 6. Wang, D., Zhou, M., Nie, X., Qiu,W., Yang, M., Wang, X., Xu, T., Ye, Z., Feng, X., Xiao, Y.: Epidemiological characteristics and transmission model of Corona Virus Disease 2019 in China. J. Infect. (2020) 7. Lipinski, T., Ahmad, D., Serey, N., Jouhara, H.: Review of ventilation strategies to reduce the risk of disease transmissionin highoccupancy buildings. Int. J. Thermofluids 7, 100045 (2020) 8. Carter, C., Osborn, M.: COVID-19 disease: invasive ventilation. Clin. Integr. Care 1, 100004 (2020) 9. Gattinoni, L., et al.: Lung recruitment in patients with the acute respiratory distress syndrome. N. Engl. J. Med. 354, 1775–1786 (2006) 10. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-03064058-3_2, Das, A., Menon, P.P., Hardman, J.G., Bates, D.G.: Optimization of mechanical ventilator settings for pulmonary disease states. IEEE Trans. Biomed. Eng. (2013) 11. Esteban, A., et al.: Characteristics and Outcomes in Adult Patients Receiving Mechanical VentilationA 28-Day International Study. JAMA (2002) 12. Rezaei, E., Karami, A., Yousefi, T., Mahmoudinezhad, S.: Modeling the free convection heat transfer in a partitioned cavity using ANFIS. Int. Commun. Heat Mass Transf. 39, 470–475 (2012) 13. Hawker, F.H., Torzillo, P.J., Southee, A.E.: PEEP and “reverse mismatch”. A case where less PEEP is best. Chest 99, 1034–1036 (1991) 14. Adilova, N.E.: Consistency of Fuzzy If-Then rules for control system. Adv. Intell. Syst. Comput. 1095, 137–142 (2020). https://doi.org/10.1007/978-3-030-35249-3_17 15. Adilova, N.E.: Quality criteria of fuzzy If-Then rules and their calculations. Adv. Intell. Syst. Comput. 1306, 55–62 (2021). https://doi.org/10.1007/978-3-030-64058-3_7 16. Gardashova, L.A.: Z-set based inference using ALI-2 implication for control system design. Lect. Notes Netw. Syst. 362, 75–84 (2021). https://doi.org/10.1007/978-3-030-92127-9_14 17. Imanov, E., Ozkilic, O., Imanova, G.: Flight information system by using fuzzy expert inference. Procedia Comput. Sci. 120, 304–310 (2017). https://doi.org/10.1016/j.procs.2017. 11.243

Structural Analysis of Piston Machines by Using Computer Software Valeh Bakhshali(B)

, Nail Mardanov , Ismayil Ismayil , and Aygun Bekirova

Department of Mechanics, Azerbaijan Technical University, H. Javid Avenue, 25, AZ1073 Baku, Azerbaijan {v.bakhshali,ismayil_i}@aztu.edu.az

Abstract. The durable and reliable work of compressor-pump stations used in the oil and gas industry has great importance for practice. In reality these areas are characterized by uncertainty information. All structural elements of Piston Machines such as connecting rods, pistons, and piston rings are heavy-duty loaded mechanical systems. The connecting rod of the crank-piston mechanisms of such systems undergo high stresses and wear, and their kinematical couplings are subject to fatigue and failure due to friction, seizure, oscillations, and impact. Friction loss reduction and service life extension remain the main problems in the design and exploitation of reciprocating machinery. The central problems are the optimal design of the crank-piston group and the piston-ring assembly, and the choice of better materials for rubber coupling, leading to a balance between pulsation control and performance. Increasing the efficiency and durability of the piston compressors and pumps directly depends on the correct calculations and design of these elements. By using ANSYS software the structural model of a connecting rod was developed. Using ANSYS software, simulation and stress analysis are performed on the basis of the 405GP15/70 and ARIEL heavy-duty balanced opposed piston compressors used in the Caspian sea - Black sea Region. The article investigated the main causes of failures through the collection and analysis of data from different parts of the machines used for transporting the oil and gas resources. The stress and deformations are analyzed for the connecting rod made of steel material or special aluminum alloy by applying pressure on it in the structural analysis in this article. Structural analysis was performed in ANSYS software. An analysis of static stress and damages due to the application of pressure is presented and analyzed in this work. By observing the analysis results, we can decide whether our designed connecting rod is safe or not under applied load conditions. Investigation of complex problems with respect to friction and wear (clearances), stresses, and strain phenomena in the piston machines gives the opportunity to solve the problems of increasing the durability of these machines. Keywords: Piston compressor · Connecting rod · Thermodynamics · Structural analysis · ANSYS · Uncertainty · Fuzzy angles

1 Introduction The technical security and environmental situation on the oil and gas pipeline are depending on durability and reliability of machines and equipment used in oil industry. Piston © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 265–273, 2023. https://doi.org/10.1007/978-3-031-25252-5_37

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pumps and compressors are widely used for the exploration and transportation of oil and gas. Piston and centrifugal machines are heavy-duty systems that are still failureprone due to high stresses and wear proses. Specialized methods will be developed for the influence of impacts, vibrations, temperature, and film lubrication and unified in a system model. The research efforts will lead to more reliable and efficient design alternatives for reciprocating machines which are used for the transport of oil and gas and will thus contribute directly to the competitiveness of a key industry in the Caspian Sea Black Sea Region, for example in Baku-Tbilisi-Ceyhan (BTC) Main Oil Pipeline, there are 8 pump-compressor stations (2 stations in Azerbaijan, 2 stations in Georgia and 4 stations in Turkey territory). Besides BTC today the region is functioning the Trans Adriatic Pipeline (TAP) which transported Caspian natural gas to Europe. Connecting with the Trans Anatolian Pipeline (TANAP) at the Greek-Turkish border, TAP will cross Northern Greece, Albania, and the Adriatic Sea before coming ashore in Southern Italy to connect to the Italian natural gas network. The energy security of the Black Sea - Caspian Sea Region depends on the technical conditions -reliability and durability of the machines and equipment used in oil and gas pipelines in the Region. The overall goal of the research is the development of an integrated model of the piston machine system that is then used to evaluate and improve the current design and increase the environmental conditions. Providing the technical security of oil and gas pipelines is one of the very important problems of exploitation and transport in the oil and gas industry. All structural elements of Piston Machines (PM) such as connecting rods, pistons, and piston rings are heavy-duty loaded mechanical systems. The main objectives are to investigate and analyze the thermal stress and mechanical stress distribution of pistons in real conditions during the working process of the piston machine. The work describes the stress distribution of the piston by using the finite element method to predict the higher stress and critical region on the component. By using ANSYS software the structural model of a piston will be developed. Compressor-pump stations are used on the oil and gas pipeline for the transport of this mineral resource. Current methods of reciprocating and centrifugal machinery design, see e.g. [1, 2], are based on partial empirical relations and do not take into account many of the factors that are affecting the mechanical and thermodynamic processes in these machines. Till to day, neither applied formulas are available for durability and reliability of the parts, for mechanical losses in the bearings, for energy losses in the kinematical couples of machines used in the oil industry, nor has there been basic research of the impact phenomena in these kinematic couples. On the other hand, very detailed models leading to computer-intensive simulations have recently been developed for piston ring dynamics in the context of blow-by estimation [2], for lubrication conditions of the ring/liner contact, for dynamically loaded bearings, and for stress and failure analysis of assembly parts. However, until now, the insight gained with these models has not found its way into more detailed models for reciprocating machines such as piston and centrifugal compressors. To this end, a modular system modeling approach as described below combined with model reduction is necessary in order to keep the computational efforts at reasonable magnitudes [3].

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2 The Mechanical and Thermodynamically Analysis of the Piston Machines The working process taking place in the cylinder in all PM is the result of three main processes: the thermodynamic process in the cylinder, the heat exchange process between gas and walls of the cylinder, and the hydrodynamic process of gas flux through density in the distribution parts of the cylinder. Analyses of the complex problems depend on friction and wear processes in PM labyrinth sealings making it possible for the all-around solution of increasing its reliability and durability. Such a process as it is known can be determined by four equations of mathematical physics, describing the main laws of the forms of matter existence. They are the system of equations describing gas flux in the channel consisting of the equation of continuity, the equation of motion, the equation of energy (first law of thermodynamics), and the equation of state of gas flux [1–3]. The goal of this work is to determine both total deformation and normal stress distributions of different materials like aluminum alloy, and cast iron piston crowns to improve the mechanical efficiency of piston compressors. Comparisons with results from piston by means of static analysis using ANSYS software. Figure 1 is presented the scheme of the crank-piston mechanism of the piston compressor with the double-acting cylinder with an indicator diagram. Where is showed the gas pressure with respect to the volume of the cylinder, i.e. p = f (V ). Processes of compressing and discharge in the cylinder accepted as polytrophic are subjected to the equation: pV m = const

(1)

where p is gas pressure in the cylinder, V is a volume of the cylinder, m is the polytrophic factor. In accordance with the analyses mentioned above and on the basis of expression (1), the gas pressure compressing on the piston p and p , correspondingly from the upper and lower surfaces of the piston we obtained the following expressions, taking into account the gaps in kinematic couples [2]: p˜ = ⎡

fp pb V0m1

⎤m1 2 ˜ + R2L sin2 ϕ˜ Vhr + (Sp − R(1 − cosϕ) ⎢ ⎥ ⎣ ⎦ ˜ ϕ˜ − ReL1 sinαsin ˜ ϕ˜ + e1 cosα˜ + e2 cos)f ˜ p − ReL2 sinsin

p˜  = ⎡

m2 fp ph Vhr

Vhr +

⎤m2

(2)

 2 ⎢ ⎥ ⎣ R(1 − cosϕ) ⎦ ˜ − R2L sin2 ϕ˜ − ReL1 sinα˜ sinϕ˜ f p ˜ sinϕ˜ + e1 cosα˜ + e2 cos ˜ − ReL2 sin

where pb and ph are the pressure of gas in the compressor inlet and outlet branch pipes; ϕ is a fuzzy rotational angle of the crankshaft, m1 and m2 are factors of polytrophic processes of compressing and expanding gas in the cylinder; V 0 is the gas volume at

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Fig. 1. Crank-piston mechanism of the reciprocating compressor

the beginning of compressing process, S p is the piston working displacement, f p is an area of working surface of the piston, R - is the radius of the crankshaft, L is connecting rod length; Vhr is the harmful volume space of the cylinder, e1 and e2 are clearances in kinematic couples of connecting rod, α and Θ are fuzzy angles which characterized the contact points in these clearances. It should be noted that as a result of friction and wear processes in kinematic couples of PM are formed the clearances on it, which are harmful phenomena. For this reason, kinematical couples of machines functioned the impact phenomena with respect to these clearances. For the determination of the volume of the cylinder, we take into account the clearances e1 and e2 in kinematic couples of connecting rod of PM [4, 5]. In accordance with the analyses mentioned above and on the basis of expression (2),  the gas pressure compressing on the piston p and p , correspondingly from the upper and lower surfaces of the piston is obtained.  For determining of main gas pressures p and p in the cylinder influencing the piston group we divide the period of one working cycle into six identity phases in the limits of each one where the regularity of pressure from both sides of the piston remains unchangeable [6–8].

3 Dynamical Parameters for the Piston Machine The piston and connecting rod play the main role in piston compressors used in the oil industry. Analyses of the failure of the piston group (crank piston mechanism) due to various thermal and mechanical stresses are very important for practice. The working

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condition of the piston group is so worst in comparison to other parts of the machine. The main objective of this work is to investigate and analyze the stress distribution of the piston, and the structural analysis of a piston using two different materials that are used in this work. We created pressure on the piston head at 45 MPa and 10 MPa on these two materials. Finally, we find out which one is a suitable material for the piston in these two materials. The design of the piston is carried out using SolidWorks software, static analysis is performed using finite element analysis (FEA). In multi-stage compressors with crossheads are used double-acting disk pistons. The high-speed compressor pistons shall be extremely light. They are made of aluminum alloys or cast iron, lightweight design with cutouts on the side surface that reduce the weight of the piston and reduce the friction works [9–11]. The equivalent – Mises stress is determined by expression:

(σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ3 − σ1 )2 , (3) σMises = 2 where σ1 , σ2 and σ3 are main normal stresses in the piston. The normal stress and the unit longitudinal deformation in piston are determined as σ = Eε, ε =

du , dy

(4)

where E is the modulus of elasticity of material, ε is the unit longitudinal deformation of piston and u is the absolute total deformation of piston. The mechanical and material properties of crank-piston mechanism of the piston compressor have been provided in Table 1. The mathematical calculation is presented using expressions (3), (4) in ANSYS the maximum stresses and deformations criterion by Mises, based on Mises-Hencky theory using finite element analysis. The stresses on the piston shall not exceed the allowable stresses [12–14].

4 Modeling and Meshing of the Connecting Rod The static analysis for the connecting rod was done by FEA using ANSYS software on the basis of the expressions (3) and (4). For ANSYS simulation the geometry of the solid work is separated into elements. These elements are interlinked to one another at a point called a node. In present examination work, we have used FEA for the Structural analysis of solid works Software is used to prepare the connecting rod. After completing solid works modeling, the model is saved in IGES file then it is imported to ANSYS software for the FEA. In Fig. 2 is shown a meshed model of connecting rod of the double-acting piston. The end hinge of the connecting rod is to be fixed. Using expressions (2) and Table 1 we investigate the structural parameters of PM.  The gas pressures p and p in the cylinder influencing the piston group from expression (2) are changing in time. Here we consider the extremal loading of the connecting rod. The load ph = 4.5 MPa is applied on the top and the load pb = 1.01 MPa is applied on the bottom of the piston surfaces as for the first stage of the piston compressor 405GP15/70. The piston is made of different materials such as Carbon steel, Cast iron, Aluminum

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V. Bakhshali et al. Table 1. Parameter values for piston compressor machine

Parameters

Values

The piston stroke, m

Sst = 0.22 m

The radius of crank shaft, m

R = 0.11 m

The thickness of piston ring

a = 0.0115 m

Height of piston ring

b = 0.009 m

Length of connecting rod

L = 0.52 m

Internal diameter of the sealing rings

d1 = 0.05 m

External diameter of the sealing rings

d2 = 0.072 m

Height of the sealing rings

b1 = 0,012 m

Radius of the finger of crank shaft

rA = 0,075 m

Number of the piston rings

z0 = 2

Mass of connecting rod made of cast iron

mcr = 26.4 kg

Mass of piston group made of cast iron

mp = 114.5 kg

Moment of inertia of the connecting rod

Jo = 4.28 kg.m2

Coefficient of friction between piston rings and cylinder wall

μp = 0.1

Coefficient of friction between piston rod and sealing rings

μp = 0.08

The pressure of gas in the inlet branch pipe

pb = 1.01·105 Pa

The pressure of gas in the outlet branch pipe

ph = 4.5 · 105 Pa

The polythrope indicators of the gas in cylinder

m1 = 1.4 (compression), m2 = 1.35 (expansion)

Angular velocity of the crank shaft

n = 500 rpm

a)

b)

Fig. 2. Meshed model of the connecting rod: a – general view, b – across section of piston

alloys, etc. Figure 3 is shown the static analysis of the connecting rod. In an attempt in this article, the connecting rod is modeled by using SolidWorks software, and static analysis is done by using ANSYS Workbench software. There is evaluated the normal

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stresses and total deformations. The Workbench focuses on attaching existing geometry, setting up the finite element model, solving, and reviewing results.

a)

b)

Fig. 3. Static analysis of the connecting rod: a – normal stress diagram, b – total deformation diagram

Figure 3 is shown the static analysis of the connecting rod. In an attempt in this article, the piston is modeled by using SolidWorks software, and static analysis is done by using ANSYS Workbench software. There is evaluated the normal stresses and total deformations. The Workbench focuses on attaching existing geometry, setting up the finite element model, solving, and reviewing results. The novelty of the article is characterized by new theoretical methods for the determination of forces of gas pressure in cylinders of reciprocating machines with taking into account the wear processes and the clearances in kinematic couples of crank-piston mechanisms. The reliability of the received scientific results is provided with the correctness of the statement of tasks and decisions on the basis of laws of physics, mechanics and thermodynamics. The results of the investigation is generalized for any piston machines used in the oil and gas industry.

5 Conclusions On the thermodynamic basis and conditions of the real working process of the piston compressors with a double-acting cylinder have considered and substantiated the gas pressure acting on the piston group and uncertainty information based analytical methods for determining these forces are presented. Structural analysis also was performed in ANSYS software. An analysis of static stress and damages due to the application of

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pressure is presented and analyzed in this work. The structural analysis is done on the connecting rod model using Cast iron and Aluminum alloy. Which material is durable for the manufacturing of the connecting rod is decided by comparing both the material analysis. The results of the investigation can be useful for the design and exploitation of piston machines used in the oil and gas industry.

References 1. Rangwala, A.S.: Reciprocating Machinery Dynamics: Design and Analysis. Marcel Dekker, New York (2001). https://doi.org/10.1115/1.1399378 2. Davitashvili, N., Bakhshaliev, V.: Dynamics of Crank-Piston Mechanisms. Springer, Heidelberg (2016). https://doi.org/10.1007/978-981-10-0323-3 3. Bakhshali, V.I., Mardanov, N.T., Bekirova, A.A., Ismayil, I.A.: Development of methods for processing acoustic emission signals of sensors for the compressor-pump station’s control. In: In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) 11th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence - ICSCCW-2021. Lecture Notes in Networks and Systems, Springer, Cham, vol. 362, pp. 704–710. (2022). https://doi.org/10. 1007/978-3-030-92127-9_93 4. Wittenburg, J. Kinematics.: Theory and Applications. Springer, Heidelberg (2016). https:// doi.org/10.1007/978-3-662-48487-6 5. Bakhshali, V.I.: Nanomechanics and its applications: mechanical properties of materials. In: Proceedings of the International E-Conference on Advances in Engineering, Technology and Management - ICETM 2020. Institute of Research Engineers and Doctors, pp. 77–81. USA (2020). https://doi.org/10.15224/978-1-63248-188-7-15 6. Yan, X., Dai, X., Zhang, K., Li, J., He, K.: Effect of teeth bending and mushrooming damages on leakage performance of a Labyrinth seal. J. Mech. Sci. Technol. 32(10), 4697–4709 (2018). https://doi.org/10.1007/s12206-018-0917-y 7. Hu, D., Jia, L., Yang, L.: Dimensional analysis on resistance characteristics of Labyrinth seals. J. Therm. Sci. 23(6), 516–522 (2014). https://doi.org/10.1007/s11630-014-0736-0 8. Burstein, L, Ingman, D.P.: Pore ensemble statistics in application to lubrication under reciprocate motion. Tribol. Trans. 43(2), 205–212 (2000). https://doi.org/10.1080/104020000089 82330 9. Boyaci, A., Hetzer, H., Seemann, W., Proppe, C., Wauer, J.: Analytical bifurcation analysis of a rotor supported by floating ring bearings. J. Nonlinear Dyn. 57(4), 597–507 (2009). https:// doi.org/10.1007/s11071-008-9403-x 10. Ilie, F.: Modelling of the contact processes in a friction pair with selective-transfer. J. Mater. Res. Technol. 12, 2453–2461. https://doi.org/10.1016/j.jmrt.2021.04.048 11. Sofiyev, A.H., Schnack, E., Demir, F.: Elasto-plastic stability of circular cylindrical shells subjected to axial load, varying as a power function of time. Struct. Eng. Mech. 24(5), 621–639 (2006). https://doi.org/10.12989/sem.2006.24.5.621 12. Wannatong, K., Chanchaona, S., Sanitjai, S.: Simulation algorithm for piston ring dynamics. J. Simul. Model. Pract. Theory 16(1), 127–146 (2008). https://doi.org/10.1016/j.simpat.2007. 11.004 13. Shaheen, W., Kanapathipillai, S., Mathew, P., Prusty, B.: Optimization of compound die piercing punches and double cutting process parameters using finite element analysis. Proc IMechE, Part B: J. Eng. Manuf. 234(1–2), 3–13 (2019). https://doi.org/10.1177/095440541 9855507

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14. Götze, A., Jaitner, D.: Combined experimental and simulative approach for friction loss optimization of DLC coated piston rings. Autom. Engine Technol. (2022). https://doi.org/10. 1007/s41104-022-00115-7

Using of Conventional Neural Network to Diagnose Scabies by Dermoscopy Husam Zendah1(B)

and Kamil Dimililer2

1 Computer Engineering, Near East University, Nicosia, North Cyprus, Via Mersin 10, Turkey

[email protected]

2 Electrical and Electronic Engineering, Applied Artificial Intelligence Research Centre

(AAIRC), Near East University, Nicosia, North Cyprus [email protected]

Abstract. In medicine, particularly dermatology, artificial intelligence has made major advances. The usage of different networks for scabies detection, including such deep learning, has proven to be highly advantageous in terms of overall performance. The goal of this work, however, is to conduct an analytical inquiry for the early diagnosis of scabies using a deep learning system trained using a VGG-16. The objectives of this study were the investigation of deep learning, the collection of quantitative data, the use of the VGG-16 model for both testing and training, as well as the interpretation of results. The method involved reviewing a dataset acquired again for study and using a higher processing machine that boosts the effectiveness of results. VGG-16 model has been trained and tested on the same two different categories. Aside from developments in hardware technology and processing, new categorization approaches based on deep learning have raised the relevance of dermatological applications. Many difficulties may be solved through these programs, such as limited access owing to distance, physical impairment, a lack of dermatologists, jobs, scheduling, and so on. They also assist doctors in making objective and timely diagnostic judgments. As a result, therapies may be administered on time, which is especially critical for life-threatening skin illnesses. Costs can also be decreased. Furthermore, the software for free or less expensive than an in-medical consultation. The VGG-16 model performed exceptionally well in the research, with excellent accuracy of 97.67%. Keywords: CNN · Transfer learning · Scabies · Dermoscopy

1 Introduction The skin is the biggest organ in the human body and serves various functions. Because the skin is exposed to the outside world, illnesses and infections are more common. A lesion area is an infectious patch on the skin. Scabies is a skin infection caused by a human itching mite [1]. The scabies mite burrows into the skin’s top layer, where it lives & lays its eggs. Scabies is characterized by acute itching as well as a pimple-like skin disease. The scabies mite is often disseminated by direct, prolonged skin-to-skin contact with a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 274–281, 2023. https://doi.org/10.1007/978-3-031-25252-5_38

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scabies person. Scabies is present all across the world and affects people of various ethnicities and socioeconomic backgrounds. Scabies can spread quickly in crowded areas where intimate body and skin contact was common. Scabies outbreaks are common in institutions including nursing homes, long-term care facilities, and prisons. Scabies infestations are very widespread in child-care centers. Despite technological improvements and advances in the domains of medicine, the number of individuals affected by illnesses [2] continues to rise. Worse, most of these diseases remain undiscovered until they are in their latter stages, giving them fewer odds of survival [3, 4]. Deep Learning is an Artificial Intelligence area in which a computer algorithm analyses raw data and learns the discriminating features needed to uncover hidden patterns in it [5–8]. During the preceding decade, there were considerable advances in the ability of DL-based programs to evaluate various types of data, notably photos [9–13]. The most common DL model can be trained by supervised methods, in which datasets comprise inputs (for example, dermoscopy images of skin disorders) and direct contractual labels (for example, diagnosis or skin disease categories such as ‘Normal’ or ‘Abnormal’) [14, 15]. As a result of these factors, constructing image analysis devices becomes a significant area of study [16]. In the hands of unskilled dermatologists, dermoscopy has been shown to improve the diagnosis accuracy of skin disorders. This research examines common skin scabies conditions with distinctive symptoms that may be exploited as image recognition objects. The essential points of this study are stated below. 1. 2. 3. 4.

Find out an appropriate dataset that can be used to train the model. Organize and optimize the data in getting a more accurate prediction result. How the CNN model can be applied in this research? Applying neural network optimization to minimize the function with maximized efficiency.

In Sect. 2, we will be discussing how the model was constructed. In Sect. 3, we demonstrate the result of this research. Finally, Sect. 4 concludes this paper.

2 Materials and Method 2.1 Datasets Dermoscopy picture database collected from TRIPOLI MEDICAL CENTER’s Dermatology Service in Tripoli, Libya. The Dermoscopy pictures were acquired under identical conditions at the Dermatology Service of Hospital using the Dermoscopy, RGB color scheme. This picture database comprises 138 Dermoscopy photos of scabies lesions, comprising 74 abnormal images and 64 Normal images (Fig. 1). 2.2 Data Preparation During the data preparation process, processing time on data pre-treatment techniques is often employed in the image processing phase. This is because pre-processing consumes

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Fig. 1. Scabies/abnormal/normal dermoscopy images

around 50–80% of the time in most deep learning projects, and it includes both pixel value scaling and the usage use of digital image augmentation methods during both training and testing assessment of the model. Dataset Training set should be supplemented most likely including rescaling at random, vertical flips, and luminance, contrast, and color perturbations, in addition to random cropping. Because the photographs in the training dataset were of varying sizes, they would have to be resized before they could be used as model input. 2.3 Data Augmentation Data augmentation is a type of data pre-processing. Frequently, the amount of data available is insufficient to execute the categorization assignment adequately. In these circumstances, we supplement the data. For instance, if we are dealing using a dataset categorizing scabies into two categories, we might not have a sufficient number of photos (since high-quality photos are difficult to get by). augmentation is frequently employed to improve the volume and diversity of training data. Only the training set should be augmented, never the validation set. As you are aware, pooling enhances invariance. If a scabies image is in the image’s upper left corner, you may use pooling to determine if the scabies is a little left/right/up/down in the upper left corner. However, given training data that includes data augmentation such as rotation, cropping, translation, lighting, scaling, noise addition, and so on, the model learns all of these changes. This considerably improves the model’s accuracy. As a result, even if scabies appears in any part the model should be able to reproduce the image and identify it with great accuracy. 2.4 CNN A Convolutional Neural Network is a Deep Learning system that can take an image as input, assign importance (learnable weights and biases) to distinct aspects/objects in the image, and distinguish one from the other. It is a network architecture that learns directly from data, eliminating the need for manual feature extraction. Such as image classification. 2.4.1 Convolutional Layer The Convolution Operation’s goal is to extract high-level information such as edges from the input image; the first ConvLayer is in charge of capturing low-level features such as

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edges, color, gradient direction, and so on. With further layers, the architecture adjusts to the High-Level characteristics as well, resulting in a network with a comprehensive comprehension of the pictures in the dataset. The procedure produces two sorts of results: one in which the dimensionality of the convolved feature was reduced in comparison to the input, and another in which the dimensionality would either be raised or remains constant. 2.4.2 Pooling Layer A pooling layer performs a conventional downsampling operation, reducing the inplane dimensionality of the maps to introduce translation invariance to smaller shifts and distortions and lower the number of future learnable parameters. It is worth noting that there are no learnable parameters in any of the pooling layers, but filter size, stride, and padding are pooling hyperparameters. 2.5 Activation Function The activation function determines whether or not to stimulate a neuron by computing the weighted sum and then adding bias to it. The activation function’s objective is to induce non-linearity into a neuron’s output. 2.5.1 ReLU The ReLU is by far the majority popular and widely employed world activation function. Since then, it has been put to use in Almost all deep learning and deep neural network approaches (Fig. 2).

Fig. 2. ReLU

2.6 Fully-Connected Layer The fully linked layer establishes the association between the location of visual features and a class. Indeed, the input table corresponds to a feature map for a specific feature: the high value shows the position (more or less exact depending on the pooling) of this feature in the picture. If the placement of a feature at a specific point in the image is typical of a particular class, the associated value in the table is given considerable weight.

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2.7 Optimizer Adam When translating inputs to outputs, an optimization method determines the values of the parameters (weights) which minimize the error. These optimization techniques, also known as optimizers, have a significant impact on the correctness of the deep learning model. They also have an impact on the model’s speed training. 2.7.1 Adam Adam represents the adaptive moment estimation which is another way of computing current gradients from earlier gradients. Adam also uses momentum by combining fractions of previous gradients with the current one. This optimizer has gained popularity and is now widely used in neural network training. It’s easy to become overwhelmed by the sophistication of some of these new optimizers. Just keep in mind that they all have the same goal: to reduce our loss function. Even the most complicated methods are fundamentally basic. 2.8 Transfer Learning Transfer learning is a frequent and successful approach for training a network on a small dataset, in which a network is trained on a massive dataset, such as ImageNet, and then reused & applied to the particular task of interest. A fixed feature extraction method is a procedure that removes FC layers from a pre-trained network while keeping the remaining network as a fixed feature extractor, which consists of a succession of convolution and pooling layers referred to as the convolutional base (Fig. 3).

Fig. 3. Transfer learning model

2.8.1 VGG 16 VGG16 is simply a convolution neural network (CNN) design that took first place in the 2014 ILSVR (Imagenet) contest. It is recognized as one of the greatest vision model architectures currently available. The major characteristic of VGG16 is that, rather than a large number of hyper-parameters, they focused on generating the convolution operation of a 3 × 3 filter using a stride 1 and always used the same padding & max pool layer

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of a 2 × 2 filter with such a stride 2. This convolution & max pool layer setup is kept throughout the design. Finally, as an output, it has two FC (fully connected layers) and a softmax. The number 16 in VGG16 refers to its 16 weighted Layers (Fig. 4).

Fig. 4. VGG16 model

3 Experiments 3.1 Experimental Results and Analysis I created CNN model to test the dataset, and the trials revealed that when we utilize Transfer Learning in this scenario, the model would achieve 97.67% accuracy after 20 epochs. More information on the model may be found in the Figure below (Fig. 5).

Fig. 5. Accuracy and loos per epoch of the model

The assessment parameters of the analysis that was trained using the dataset for the two photos are shown in the Fig. 6 below, along with the percentage of accuracy and predictions of the images for each image.

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Fig. 6. Evaluation results of the model

4 Conclusion Convolutional Neural Networks have revolutionized image categorization challenges. As previously noted, dilated CNN has been effectively employed in image detection issues; nevertheless, to the best of our knowledge, this marks the first-time scabies photos have been classified using the CNN approach combined with transfer learning. In this research, we offer a method for developing a classifier that detects whether scabies is normal or aberrant in a Dermoscopy picture. In the ImageNet Large Scale Visual Recognition Challenge, the VGGNet-16, a pre-trained convolutional neural network (CNN) model, is employed as a feature vector extractor for microscopic pictures. Extensive experiments and parameter adjustment revealed that my suggested model performed well when working with a gathered dataset, with 97.67% accuracy using these extracted feature vectors.

References 1. Heukelbach, J., Feldmeier, H.: Scabies. Lancet 367(9524), 1767–1774 (2006). https://doi. org/10.1016/S0140-6736(06)68772-2 2. Dimililer, K., Ever, Y.K., Ugur, B.: ILTDS: Intelligent lung tumor detection system on CT images. In: Corchado Rodriguez, J., Mitra, S., Thampi, S., El-Alfy, E.S. (eds.) Intelligent Systems Technologies and Applications 2016. ISTA 2016. Advances in Intelligent Systems and Computing, vol. 530, pp. 225–235 (2016). https://doi.org/10.1007/978-3-319-47952-1_17. 3. Dimililer, K., Hesri, A., Ever, Y.K.: Lung lesion segmentation using Gaussian filter and discrete wavelet transform. ITM Web Conf. EDP Sci. 11, 01018 (2017). https://doi.org/10. 1051/itmconf/20171101018 4. Waldis, A., Mazzola, L., Kaufmann, M.A.: Concept extraction with convolutional neural networks. In: Proceedings of 7th International Conference on Data Science Technology and Application, pp. 118–129 (2018) 5. Polunin, A., Yandashevskaya, E.: Using of convolutional neural networks for Steganalysis of Digital Images. Proc. Ins. Syst. Program. RAS, 32(4), 55–164 (2020). https://doi.org/10. 15514/ISPRAS-2020-32(4)-11. 6. Dimililer, K.: DCT-based medical image compression using machine learning. Signal Image Video Process. 16(1), 55–62 (2022). https://doi.org/10.1007/s11760-021-01951-0

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Determination of the Dynamic and Interactive Event in Exascale Computing Systems via Request Clustering Nigar Ismayilova(B) Azerbaijan State Oil and Industry University, Baku AZ1010, Azerbaijan [email protected]

Abstract. Load balancer is one of the main problems in Exascale Computing system management. The dynamic nature of executed requests and used resources makes the assignment process complicated between requests and machines. In this work fuzzy c-means clustering method for grouping the resources into different clusters with soft borders was proposed. Application of the soft approach allows to cluster requests without hard separation of the request space and consequently to determine the occurrence of the dynamic and interactive event. Keywords: Exascale computing system · Dynamic and interactive event · Requests clustering · Fuzzy C-means

1 Introduction Optimization of load balancer – finding the best assignment between processes and resources represents an important topic to study because of increasing the usage of HPC technologies in various fields of science and industry. The challenges with optimization methods for task scheduling in different type of distributed computing systems are growing with progress of computational resources and scientific inventions. The optimal distribution of tasks between resources in cluster computing systems with the standing quantity of requests and computational machines based on general network optimization methods such as bipartite matching, minimax criteria, finite element methods have been successfully applied [1–3]. On the other hand, for dynamic environments with unstable nature of resources and requests it is necessary to apply new approaches based on artificial intelligence. The purpose of load balancer in cloud computing systems is optimization of comprehensive computing capacity, which differs from the load balancer’s maximization of computing mission in another distributed systems such as cluster computing, grid computing, peer to peer computing and exascale computing [4]. By popularization of modern wireless communications, the necessity of load balancer in fog computing systems grows. The goal of load balancer in such systems is to minimize execution time and energy consumption. Increasing the number of resources used in computing systems and heterogeneity of the solved requests increases the complexity of the load balancer process. As usual, the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 282–288, 2023. https://doi.org/10.1007/978-3-031-25252-5_39

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main problem in systems with dynamic structures is the recognition and classification of the unlabeled data. AI forecasting method opens wide areas for high-performance load balancer models based on least-connection scheduling algorithms [5, 6]. Progress and intensive usage of heterogeneous computing environments such as grid computing, P2P computing, and cloud computing, as well as challenges in Exascale computing systems demonstrate the necessity and effectiveness of proposed dynamic load balancers for distribution of load [7, 8]. Several investigations have used artificial intelligence techniques to assign requests to suitable resources, where one or both has dynamic nature [9, 10]. In the dynamic and heterogeneous systems the main problem for finding the appropriate assignment between requests and machines is related to occurrence of dynamic and interactive (D&I) event. In this situation different kinds of problems which make necessary to change the load balancer management technique may appear. The first problem appearing in dynamic distributed systems related to the D&I events is to define the moment of D&I occurrence for making decisions about the changing of the load balancer mechanism. For this purpose, analysing of the requests and determination of the D&I occurrence case is the solution of the half problem. Application of fuzzy logic-based solutions gives suitable opportunities for making decisions in uncertain environments as dynamic and heterogenous computing system [11–13].

2 Dynamic and Interactive Event Mechanism of load balancer activity can be modeled by the following formula [12]:   Load distribution : Processrequirements → [Resourceattributes ] ∴  (1) ∀Process ∈ HPCProcesses → Scheduled Resourceactivity = 100% Accordingly, this formula describes conditions for optimal load balancer. It is an assignment process of requests to computing machines where each process in the system must be scheduled and the activity of all resources should be 100%. Dynamicity of processes and computing machines and occurrence of dynamic and interactive events makes problems during optimal processing of the load balancer in Exascale computing systems. Two problems remain with the dynamic and interactive (D&I) event’s occurrence: a) determination of the dynamic and interactive events in the computing systems; b) handling of the assignment process between requests and machines. In this work has been proposed approach for the solution of the first case by fuzzy c-means clustering of the requests in the computing system. The limitation of Exascale computing system is mainly related to the dynamic nature of both resources and requests. The dynamicity of requests can be defined as the result of three cases: a) executed request created new processes; b) process needs connection with other executed processes; c) process requires connection with the global space [13].

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3 Grouping of the Requests Using Their Requirements Clustering processes allow us to determine the dynamic and interactive events (D&I) by extracting the unusual situation. It means that, if we observe the process which does not belong to the determined classes of the processes or belongs to them with small membership degrees, then we will assume that D&I has occurred. In this situation, we have two ways: Determination of the new class of processes. Resolve the clustering problem by considering the observed D&I and including the observed situation in one of the existed clusters. Before solving the clustering problem, we need to clarify the vector of request attributes and distance metric for calculating similarities between them. Let’s assume that we have a request vector in distributed Exascale system defined by the following parameters:   (2) R = Reqnature , Reqtype , Reqtime , Reqlocation , Reqrequirements . This vector gives information about the request, its nature, type of the process, time required for the execution of the task, source of the process, here Reqrequirements represents technical requirements of the request defined by the following matrix:   RIO/time RM /time RF/time Reqrequirements = (3) RIO/value RM /value RF/value Request requirements matrix defines time required by the given process from the computation environment as input/output resource, memory, and file connection, as well as values of these requirements. When in the distributed computing system, we observe requests that can be executed using the computing and processing capabilities of the resources of the system load balancer will work successfully. However, if there appears the request whose requirements are beyond the capabilities of the system’s resources or are very different from the requests’ requirements executed before its appearance, we define it as the D&I and propose new solution methodologies. For the realization of this approach in this work application of the fuzzy c-means clustering technique for clustering of the request based on their attributes vector has been proposed and assumed that if the next request does not belong to one of the found clusters or belongs with the small membership degree then the dynamic and interactive event has occurred. The main problem here is to define the correct distance metric for the calculation of the distances between the requests, as you see from the expressions (2)–(3) request requirements vector contains both categorical and numerical attributes. Considering this fact, we proposed to use distance metric based on a hybrid approach combining cosine distance metric for categorical (attributes’ categories will be converted to discrete numbers) and Euclidian distance (L2 – norm) for numerical attributes. Generally, it is not possible to classify executed processes into different groups using their attributes, but the usage of the fuzzy c-means clustering method allows to group requests into different groups softly without hard borders [13]. This method also

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provides the possibility for determination of the D&I occurrence via clustering even during incomplete information about the request [14, 15]. Based on the fuzzy c-means clustering algorithm for soft grouping of the requests during execution of the dynamic and heterogenous computing system our goal is to minimize the following function: Jm =

C N

2 µm ij Reqi − Cj  ,

(4)

i=1 j=1

where m is any real number greater than 1, µij – is the degree of membership Reqi to cluster j, Cj – is the center of cluster, and  ∗  is similarity calculated using different metrics as mentioned above, C – number of clusters, N – number of requests. Clustering process realized through the optimization process iteratively by updating membership degrees µij and cluster centers Cj : µij =

C k=1



1 Reqi −Cj  Reqi −Ck 

N

2 m−1

Cj =

m i=1 µij · Reqi

N m i=1 µij

(5)

These formulas can be explained by the following algorithm: 1. In the first step are defining centers by randomly chosen requests equal to the number of clusters planned for grouping of the requests; 2. Next step defines membership degrees of each request to the cluster centers using the first part of the formula (5), for finding the membership degree of the i-th request to the j-th cluster we find distance between the i-th request and the j-th cluster center by separating the request and the cluster center into two parts: categorical (for this part we use cosine similarity for the distance) and numerical (where we apply Euclidian distance metric) parts, divide it to the distance between i-th request and all cluster centers, then we find its 2/(m-1)-th power and summarize them, m is selected regarding to the degree of fuzziness that significantly affect the result of clustering; 3. Then we recalculate cluster centers by using the second part of the formula (5) by sum of multiplications of the membership degrees to all request and dividing this sum to the sum of all membership functions for the given cluster. Steps 2 and 3 iteratively repeated until finding the minimum of the function described in formula (4). By this way we can define different groups of the familiar processes in distributed computing system before D&I occurrence. The main opportunity of application fuzzy c-means clustering for grouping executed processes is soft borders between request groups. Accordingly, appearance of new unknown request or process can be defined by calculation of the membership degree of the process to the defined clusters, i.e. if the new process does not belong to defined clusters or belongs with very low membership degree leads to D&I occurrence. Thus, one of the significant challenges for optimization of the load balancer process in Exascale Computing System, determination of the D&I event can be solved using proposed approach.

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4 Argument Determination of the D&I events in heterogeneous computing systems is very important for choosing the mechanisms for the management of such systems. D&I appearance leads to changing of the computing system, which requires defining new ways for load balancer, resource discovery, and process migration. Artificial intelligence is one of the main tools for handling uncertainty, determination of unknown cases, and controlling them. Fuzzy logic is the technique that allows increasing the intelligence level of the approach [19–22, 23]. Using this opportunity grouping of the requests for determination of the unknown events, namely D&I events gives chances to manage the computing system with the heterogeneous nature. Traditional algorithms proposed for load balancer such as round robin are not able to define D&I and handle the situation after D&I occurrence [16]. In this case after D&I occurrence, as the server is not familiar with the appeared situation, it will be failed, and we will observe the cascading process in the whole computing system. In this regard, the proposed algorithm allows us to control the computing system after D&I occurrence by determination of the request nature which leads to the D&I occurrence. After the clustering of the requests based on their characteristics, request bringing to the D&I occurrence is determined using the formula (5). If the membership degree for the current request is very low for all clustering groups, it means that we are dealing with the state that was not seen before. In this situation there are two ways for solutions for load balancer, resource discovery and process migration: 1. we can include the request to the cluster for which membership degree is higher than others; 2. we can create the new group of requests by re-clustering. As the group of the unseen request has been defined, load balancer can use one of the previous solutions applied to other requests of the cluster. The advantage of the formula (5) is that, by this formula we can softly group requests based on their characteristics for determination of the particular states.

5 Conclusion Determining the D&I occurrence in Exascale Computing Systems can be considered as a significant step forward in load balancer framework design for managing the dynamic and heterogenous computing systems. By application of the fuzzy c-means clustering algorithm for grouping executed requests and consequently determination of the unknown requests which defines the D&I occurrence case is useful for the next step of the Exascale Computing Systems management, handling D&I event and define the best assignment between requests and available resources.

References 1. Chu, W.C., Yang, D.L., Yu, J.C., Chung, Y.C.: UMPAL: an unstructured mesh partitioner and load balancer on World Wide Web. J. Inf. Sci. Eng. 17(4), 595–614 (2001) 2. Shen, C.C., Tsai, W.H.: A graph matching approach to optimal task assignment in distributed computing systems using a minimax criterion. IEEE Transact. Comput. 100(3), 197–203 (1985)

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Evaluation of Techniques Used in Phenol Removal from Wastewater Using Fuzzy PROMETHEE Method Basil Bartholomew Duwa1,3 , Ay¸seGünay Kibarer3(B) , Berna Uzun1,2,4 Serife ¸ Kaba3 , and Dilber Uzun Ozsahin3,5

,

1 Operational Research Center in Healthcare, Near East University, 99138 Nicosia, Cyprus

{basil.barthduwa,berna.uzun}@neu.edu.tr

2 Statistics Department, Carlos III University of Madrid, Getafe, Madrid, Spain

[email protected]

3 Department of Biomedical Engineering, Faculty of Engineering, Near East University,

99138 Nicosia, Cyprus {aysegunay.kibarer,serife.kaba}@neu.edu.tr 4 Department of Mathematics, Faculty of Applied Sciences, Near East University, 99138 Nicosia, Cyprus 5 Medical Diagnostic Imaging Department, College of Health Sciences, University of Sharjah, Sharjah, United Arab Emirates [email protected]

Abstract. Phenolic chemicals have high toxicity level even at low concentrations, making them a priority contaminant. Conventional and innovative treatment strategies are examined in this review. As reported by the World Health Organization (WHO), around 144 million Olympic-sized swimming pools of wastewater are generated annually around the world. Approximately 48% of that effluent is dumped into the environment untreated. Therefore, to properly treat and remove contaminants such as phenol from wastewater deposits, it is now important to develop innovative treatment methods. This study focuses on evaluating five (5) alternate techniques used in phenol removal from wastewater using decision-making techniques, specifically the Preference Ranking for the Organization Method for Enrichment Evaluation PROMETHEE, a Fuzzy technique in data analysis. These removal techniques employed were distillation, adsorption, chemical oxidation, membrane separation, and biodegradation. Parameters such as duration, safety, ease of operation, side effects, efficiency, affordability, reliability, and energy consumption of each alternative were evaluated using the PROMETHEE, Multi-criteria decision-making paradigm. The representation of the comprehensive individual ranking of all the current alternatives revealed that the Membrane separation method is the optimal choice because it has the highestranking flow representation (0,0621); while the distillation separation method is the second with an optimum net ranking flow of 0,0263. However, the chemical oxidation method is revealed to be the least ranked technique based on the criteria selected. Keywords: Biodegradation · PROMETHEE fuzzy logic · Phenolic chemicals · MCDM · Membrane separation © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 289–296, 2023. https://doi.org/10.1007/978-3-031-25252-5_40

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1 Introduction The flow of untreated wastewater from industries, agricultural, and residential operations into water bodies are the primary cause of the presence of phenolic compounds in water bodies. These substances are revealed to be poisonous, and they are capable of inflicting severe consequences that linger for an extended period on both people and animals. Even in low quantities, they are carcinogenic and cause harm to the red blood cells as well as the liver. When these compounds interact with bacteria, inorganic compounds, or other organic compounds in water, substituted compounds or other moieties can be produced. These substituted compounds or other moieties may be just as dangerous as the original phenolic compounds [1]. The quality of water is imperative for human health, which as well is useful in the quality of aquatic life in the water bodies. Thus, as the human population is becoming increasingly difficult to guarantee that there will always be sufficient quantities of clean water available for everyone [2]. Recently, there has been an increase in the level of concern among decision-makers and scientists on the impacts of human and animal exposure to chemical compounds in the environment, specifically the aquatic environment. In this context, phenolics are some of the chemicals that present the greatest cause for concern because of their propensity to remain in the environment for extended periods, accumulate, and to have harmful effects on both people and animals. Phenolic chemicals can be found in high quantities in nature and are thought to be responsible for the colors of flowers and fruits. Others are synthesized, and their products find use in many different areas of people’s everyday lives [3, 4]. As a consequence of this, a variety of techniques for the treatment of wastewater have been developed and put into practice for the removal of phenolic compounds from industrial, domestic, and municipal wastewaters before their discharge into water bodies. The goal of these techniques is to mitigate the harmful effects that these chemicals have on human and aquatic life as much as possible. Extraction, polymerization, the electroFenton process, photocatalytic degradation, and other similar processes are examples of some of these procedures [5]. Phenolic compounds exhibit a high level of toxicity even when present in low concentrations, which places them as pollutants. This evaluation looks at both traditional treatment methods and cutting-edge approaches to the treatment of wastewater by using advanced mathematical techniques to evaluate the major methods applied in the extraction of phenols in water. 1.1 Techniques Applied in Phenol Removal in Wastewater The major techniques used in separating and extracting phenols in wastewater are explicitly explained individually in this section. Distillation\Evaporation: The removal of phenols from wastewater can be accomplished using several different processes, including evaporation and distillation. It is done by taking advantage of the phenols’ relatively high evaporation rates. Methods that use distillation typically have substantial energy costs and are normally only viable for extremely high concentrations of phenol [6, 7]. Purification can be accomplished using

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steam distillation, depending on how volatile the phenol is. Although the liquid-liquid extraction method is very effective at removing chemicals from wastewater, the process is relatively time-consuming, expensive, and may be associated with injuries due to the huge number of organic solvents (some of which are toxic) that are used in the procedure [8]. Adsorption\Extraction: Adsorption, which makes use of solid consumables like activated carbon, is a typical method for removing phenols. The economics are contingent not only on the cost of the adsorbent but also on the cost of disposing of or recycling it [9]. Therefore, new solutions are being explored including chemical functionalization of the activated charcoal, impregnation by nanoparticles, and the use of chitin/chitosan as limited bio sorbents, which are viable alternatives to extract phenolic chemicals from the environment. Adsorption is considered one of the preferred methods used in removing phenolics from water since it is simple to design and implement. The process creates no hazardous byproducts. [10]. Membrane Separation: The membrane separation method is a special kind of barrier that, when applied to a gas or liquid, can facilitate the separation of different species through a variety of different separation processes, such as diffusion, sieving, or sorption. The semipermeable aspect of the membranes is what ultimately leads to the selective separation that takes place [11]. Chemical Oxidation: The oxidation of phenols and other organics is a tedious process. Traditional oxidizing chemicals such as ozone, chlorine, permanganate, etc., and catalysts and circumstances such as irradiation can all be utilized [12, 13]. Biodegradation: An established and effective way of removing phenols from water is the use of biological treatment. Biodegradation of phenols can be accomplished by the employment of aerobic or anaerobic microbes [14]. The application of enzymes to remove phenolic substances from wastewater has been described in several scientific studies. “Shesterenko and colleagues” work is one of these reports. It was revealed to have removed phenols from water using Agaricus bisporus tyrosinase and inorganic coagulants immobilized on polymer-carriers [15]. Phenolic compounds are regarded to be a priority pollutant since even in small concentrations, they pose a significant risk to human health and the environment. This study compares and contrasts the efficacy of established modern techniques with those that are considered to be on the leading edge of medical innovation. Comparisons are performed between the effectiveness of various therapies that use phenol and many routinely employed derivatives.

2 Materials and Methodology 2.1 PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) One of the most difficult aspects of dealing with problems that arise in the real world is gathering accurate data in order to do system analyses. Therefore, advanced simulation techniques such as the Fuzzy-Logic based models are applied in the evaluation of major decision problems. The fuzzy PROMETHEE is a decision-making technique that evaluates and compares decision problems where the conflicting multiple criteria occurs. In

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contrast to other multi-criteria decision-making methods, PROMETHEE has the advantage of enables decision makers determine preference values of each alternative with different types of preference functions assigned to each criterion. The concept of fuzzy logic refers to one variety of many-valued logic. The truth value of variables in this kind of logic can be any real number that is between 0 and 1, inclusive. It is used for the goal of managing the concept of partial truth, in which the truth value may fluctuate between being fully true and being entirely false. This is accomplished through the utilization of this idea management tool. On the other hand, the truth values of variables in Boolean logic can never be anything other than the integer values 0 or 1, as these are the only two outcomes that are even remotely feasible. [16]. The PROMETHEE approach has been successfully applied to a significant number of major applications in a variety of studies, such as in industries, healthcare, water resources, banking and finance, tourism, and business management, among others. The PROMETHEE technique requires two important and different kinds of data: information concerning the criteria weights that are taken into consideration and the preference function of the researcher or the decision-maker when comparing the variables in terms of individual criterion [17]. The notion of fuzzy sets was developed to address the problem of dealing with the unpredictability of human judgment. The formulation and solution of problems that are too complicated or vague to be susceptible to analysis by standard methodologies are developed through the application of fuzzy set theory [18]. The selected importance weights of the criteria are determined by the experts as shown in Table 1. Table 1. Linguistic fuzzy scale. Linguistic scale

Triangular fuzzy scale

Importance ratings of criteria

Very High (VH)

(0.75, 1,1)

Efficiency, safety, reliability

Important (H)

(0.50, 0.75, 1)

Ease of operation, side effects

Medium (M)

(0.25, 0.50,0.75)

Affordability, duration

Low (L)

(0, 0.25, 0.50)

Energy required

Very Low (VL)

(0,0,0.25)

Table 2 shows the data of phenol removal technique. The PROMETHEE MCDM technique was mainly applied in the decision making of the alternatives used in the extraction of phenol in wastewater after the defuzzification process. The Yager index is used as the defuzzification process since it considers all the point in the set to clarify the fuzzy numbers. The Gaussian preference function is assigned to each criterion which considers the difference of the alternatives using the standard deviation of the related data of the criterion.

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Table 2. Datasets for the phenol removal from wastewater techniques Alternative| Criteria

Duration Affordability Safety Easy for Energy Efficiency Reliability Side operation consumption effects

Aim

min

min

max

max

max

max

max

min

Distillation [19]

H

L

VH

YES

L

VH

VH

L

Adsorption [20]

M

M

H

YES

M

H

H

M

Membrane separation [21]

L

L

VH

YES

H

VH

VH

M

Chemical oxidation [22]

H

H

L

NO

L

VH

H

M

Biodegradation M [23]

L

H

YES

L

H

VH

L

3 Results and Discussion In the PROMETHEE Net ranking flow on Table 3, the membrane separation method showed higher result with 0,0621 net ranking flow as the preferred alternative. The distillation separation technique also performed distinctly well with the net ranking of 0,0263; while the Biodegradation method exhibited as the third preferred technique (0,0031). However, other techniques flawed, such as the chemical oxidation method, which was revealed to be the 5th ranked in phenol removal, with −0,0843; while the Adsorption method is preferred than the chemical oxidation method with −0,0072 net ranking flow result. In addition, the positive ranking flow shows the strength of the alternatives, while the negative ranking flow shows the weakness of the alternatives, which subsequently assist in obtaining the complete ranking. Similarly, the pictorial representation of the study analysis, showed both the positive and negative ranking results as seen in Fig. 1. Based on the figure representing the PROMETHEE evaluation results, the membrane separation technique shows the highest positive results above the 0-treshold and the least negative result below the 0-treshold. In contrast, the chemical oxidation method shows the highest negative result below the 0-treshold and the least positive result above the 0-treshold. The most common method that shows high phenol Table 3. Ranking results. Phi

Phi +

Phi-

0,0655

0,0034

Rank

Alternatives

1

Membrane separation

2

Distillation

0,0263

0,0412

0,0149

3

Biodegradation

0,0031

0,0255

0,0224

4

Adsorption

−0,0072

0,0189

0,0261

5

Chemical oxidation

−0,0843

0,0041

0,0884

0,0621

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removal in wastewater in several studies, is the adsorption and the biological methods, Contrary to this study, the researchers did not adopt a modern analytical model, such as the Fuzzy-PROMETHEE MCDM. Therefore, this study is exceptional when compared to other studies, by introducing classical data analytical models (Fuzzy-PROMETHEE).

Fig. 1. PROMETHEE rainbow

4 Conclusion Phenolics are exceedingly dangerous and toxic to all forms of life, including humans, and animals both terrestrial and aquatic. In the presence of chlorine, phenolic compounds can also transform into carcinogenic chlorophenols. Both the U.S Environmental Protection Agency (EPA) and the National Pollutant Release Inventory (NPRI) of the United States of America and Canada, respectively, consider them to be high-priority water pollutants. In many different jurisdictions, there are stringent discharge limitations for phenols that are typically less than 0.5 mg/L. There is a distinct and unmistakable differentiation between which the alternatives are favored and taken into consideration in the process of removing phenol from wastewater at various locations, as determined by the comparative evaluation of the numerous phenol removal techniques used in this research. This study will serve as a blueprint and a guide to many individuals, institutions, research institutes, governmental agencies, and non-governmental organizations that consider protecting the vast water bodies from human disposal.

References 1. Khan, S.A.R., Ponce, P., Yu, Z., Golpîra, H., Mathew, M.: Environmental technology and wastewater treatment: Strategies to achieve environmental sustainability. Chemosphere 286, 131532 (2022). 0.1016/j.chemosphere.2021.131532

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2. Singh, A., et al.: Biological remediation technologies for dyes and heavy metals in wastewater treatment: new insight. Bioresour. Technol. 343, 126154 (2022). https://doi.org/10.1016/j.bio rtech.2021.126154 3. Aktas, N., Kibarer, G., Tanyolac, A.: Effects of reaction conditions on laccase-catalyzed alphanaphthol polymerization. 75(9), 840–846 (2000). https://doi.org/10.1002/1097-4660(200009 )75:9840::AID-JCTB292.CO;2-9 4. Anku, W.W., Mamo, M.A., Govender, P.P.: Phenolic compounds in water: sources, reactivity, toxicity and treatment methods. Nat. Resour. 419–443 (2017). https://doi.org/10.5772/66927 5. Sun, J., et al.: Oxidative degradation of phenols and substituted phenols in the water and atmosphere: a review. Adv. Compos. Mater. 1–14 (2022). https://doi.org/10.1007/s42114022-00435-0 6. Naguib, D.M., Badawy, N.M.: Phenol removal from wastewater using waste products. J. Environ. Chem. Eng. 8(1), 103592 (2020). https://doi.org/10.1016/j.jece.2019.103592 7. de Elguea-Culebras, G.O., Bravo, E.M., Sánchez-Vioque, R.: Potential sources and methodologies for the recovery of phenolic compounds from distillation residues of Mediterranean aromatic plants. An approach to the valuation of by-products of the essential oil market–A review. Ind. Crops and Produ, 175, 114261 (2022). https://doi.org/10.1016/j.indcrop.2021. 114261 8. Eryılmaz, C., Genc, A.: Review of treatment technologies for the removal of phenol from wastewaters. J. Water Chem. 43(2), 145–154 (2021). https://doi.org/10.3103/S1063455X210 20065 9. Farajzadeh, M.A., et al.: Experimental and density functional theory studies during a new solid-phase extraction of phenolic compounds from wastewater samples before GC–MS determination. Microchem. J. MICROCHEM 177, 107291 (2022). https://doi.org/10.1016/j.mic roc.2022.107291 10. Othmani, A., Magdouli, S., Kumar, P.S., Kapoor, A., Chellam, P.V., Gökku¸s, Ö.: Agricultural waste materials for adsorptive removal of phenols, chromium (VI) and cadmium (II) from wastewater: a review. Environ. Res. 204, 111916 (2022). https://doi.org/10.1016/j.envres. 2021.111916 11. Adeel, M., Xu, Y., Ren, L.F., Shao, J., He, Y.: Improvement of phenol separation and biodegradation from saline wastewater in extractive membrane bioreactor (EMBR). Bioresour. Technol. Reports 17, 100897 (2022). https://doi.org/10.1016/j.biteb.2021.100897 12. Tian, S., et al.: Insight into the oxidation of phenolic pollutants by enhanced permanganate with biochar: The role of high-valent manganese intermediate species. J. Hazard, Maters. 430, 128460 (2022). https://doi.org/10.1016/j.jhazmat.2022.128460 13. Kadhum, S.T., Alkindi, G.Y., Albayati, T.M.: Remediation of phenolic wastewater implementing nano zerovalent iron as a granular third electrode in an electrochemical reactor. Int. J. Environ. Sci. Technol. 19(3), 1383–1392 (2021). https://doi.org/10.1007/s13762-021-032 05-5 14. Kuc, M.E., Azerrad, S., Menashe, O., Kurzbaum, E.: Efficient biodegradation of phenol at high concentrations by Acinetobacter biofilm at extremely short hydraulic retention times. J. Water Process Eng. 47, 102781 (2022). https://doi.org/10.1016/j.jwpe.2022.102781 15. Iliuta, I., Iliuta, M.C.: Intensified phenol and p-cresol biodegradation for wastewater treatment in countercurrent packed-bed column bioreactors. Chemosphere 286, 131716 (2022). https:// doi.org/10.1016/j.chemosphere.2021.131716 16. Ozsahin, I., Sharif, T., Ozsahin, D.U., Uzun, B.: Evaluation of solid-state detectors in medical imaging with fuzzy PROMETHEE. J. Instrum. 14(01), C01019 (2019). https://doi.org/10. 1088/1748-0221/14/01/C01019 17. Yildirim, F.S., Sayan, M., Sanlidag, T., Uzun, B., Ozsahin, D.U., Ozsahin, I.: Comparative evaluation of the treatment of COVID-19 with multicriteria decision-making techniques. J. Healthc. Eng. (2021). https://doi.org/10.1155/2021/8864522

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18. Sayan, M., Sultanoglu, N., Uzun, B., Yildirim, F.S., Sanlidag, T., Ozsahin, D.U.: Determination of post-exposure prophylaxis regimen in the prevention of potential pediatric HIV-1 infection by the multi-criteria decision-making theory. IEEE, International Journal Advances Science Engineering Technology, pp. 1–5 (2019). https://doi.org/10.1109/ICASET.2019.871 4442 19. Ozsahin, D.U., et al.: Evaluating cancer treatment alternatives using fuzzy PROMETHEE method. Int. J. Adv. Comput. Sci. Appl. 8(10) (2017). https://doi.org/10.14569/IJACSA.2017. 081024 20. Ozsahin, D.U., Isa, N.A., Uzun, B., Ozsahin, I.: Effective analysis of image reconstruction algorithms in nuclear medicine using fuzzy PROMETHEE. IEEE, International Journal Advances Science Engineering Technology, pp. 1–5 (2018). https://doi.org/10.1109/ICASET. 2018.8376892 21. Mohammadi, S., Kargari, A., Sanaeepur, H., Abbassian, K., Najafi, A., Mofarrah, E.: Phenol removal from industrial wastewaters: a short review. Desalin. Water Treat. 53(8), 2215–2234 (2015). https://doi.org/10.1080/19443994.2014.883327 22. Raza, W., Lee, J., Raza, N., Luo, Y., Kim, K.H., Yang, J.: Removal of phenolic compounds from industrial wastewater based on membrane-based technologies. J. Ind. Eng. Chem 71, 1–18 (2019). https://doi.org/10.1016/j.jiec.2018.11.024 23. Lefèvre, S., Boutin, O., Ferrasse, J.H., Malleret, L., Faucherand, R., Viand, A.: Thermodynamic and kinetic study of phenol degradation by a non-catalytic wet air oxidation process. Chemosphere 84(9), 1208–1215 (2011). https://doi.org/10.1016/j.chemosphere.2011.05.049

Research of the Manufacturing Quality of Plastic Details with Complex Forms of Connection Naila A. Gasanova(B) , Agali A. Quliyev , Aynur V. Sharifova , Tamilla U. Khankishiyeva , and Rafiga S. Shahmarova Azerbaijan State Oil and Industry University, Azadlig 34, Nasimi, Baku, Azerbaijan [email protected]

Abstract. This article examines the nature passing of the shrinking deformation of plastic thread elements depending on their size and manufacturing regimes. At the same time, within a wide range of regime parameters, achievable limits of quality indicators of details working in structures of equipment for exploration, drilling and operation in the oil and gas industry are investigated. Mathematical dependencies between quality indicators (shrinkage and strength) of details against pressing temperature are established. The scientific-practical methods for insurance of plastic details quality in oil field equipment based on the mathematical models of their production have been developed. These mathematical models reflect the regularity of influence of production regime and structure of the details on the quality indicators (durability in stretching, hardness, roughness of surface, density and shrinkage for the optimization of their production regimes). In this article the quality of thread details of the oil-field equipment depending on modes of production of their various constructions and composition of press materials were reviewed. By adjusting the operating parameters during production of details are defined quality indicators: tensile strength, hardness of details and others. Keywords: Smooth and threaded plastic parts · Shrinking deformations · Pressing pressures · Pressing temperature · Regime parameters · Size error · Quality indicators

1 Introduction The use of plastic details in various constructions makes it possible to reduce the cost and labor intensity of manufacturing machines and devices, to reduce the weight of constructions while improving their quality and reliability. Researches were carried out with the aim of increasing labor productivity and replacing non-ferrous and ferrous metals with plastic masses. Details for this purpose are selected with a certain characteristic, so that in the future the developed technological process could be used in the oil and gas industry. As is known, in order to ensure a high-quality connection of smooth and threaded details making from various plastics, it is primarily necessary to establish boundaries of the sizes error. The nature passing of shrinking deformation and error in the entire plastic thread elements differs greatly from the smooth details [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 297–304, 2023. https://doi.org/10.1007/978-3-031-25252-5_41

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Threaded parts do not meet the requirements of the 3rd accuracy class, since the screwing is ensured due to the guaranteed clearance, the value scattering of the actual average diameter is practically commensurate with the tolerance for the average thread diameter according to the 3rd accuracy class, and for large diameters it exceeds it.

2 Optimal Control of Technological Regimes To obtain the required accuracy of plastic thread, first of all, the optimal control of technological regimes is required and, as a result of the establishment oscillation limits of shrinkage as the main indicator of manufacturing quality. The analysis of works devoted to the issues of the accuracy making the threading on plastic details revealed that the specified process is much more complicated in its specificity and differs from the accuracy of manufacturing smooth parts from plastics [2]. In our opinion, a complex solution is required to study the issue of the accuracy of thread production on plastic parts, i.e., here it is errors caused by oscillation in shrinkage of native thread elements (d , d1 , d2 , s, α/2) and errors caused by processing regimes must be taken into account. The influence of each regime parameter on the oscillation in the shrinkage of thread elements is studied separately and at the same time the complex influence of the mode parameters on the errors in the manufacture of these elements as a whole is determined for further development of the thread size tolerance. In connection with the above, we are considering the study of the shrinkage process and oscillation in the shrinkage of elements of plastic threaded details with sizes M20 × 2 (valve body). These sizes are often used in the oil and gas industry.

3 Establishing the Mathematical Dependence Between the Quality Indicators (Shrinkage and Strength) of Details on the Pressing Temperature The study of the joint action of all technological parameters on the accuracy of manufacturing individual elements of plastic threaded parts is complex problem, and its solution for both smooth and threaded plastic parts possible only with the use of mathematical modeling. Using the mathematical method, mathematical models of the process of manufacturing plastic parts are determined, while shrinkage, surface roughness and hardness of manufactured parts made of thermosetting plastics are taken as quality indicators. For the mathematical characterization of the dependence of quality indicators on the technological parameters proposed by us, are two models: -the first order polynomial

-the second order polynomial

Research of the Manufacturing Quality of Plastic Details

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where a0 , ai , b0 , bi , bij , bii are the coefficients of the regression equation; k is the number of input variables; xi – values of independent input variables – technological parameters; y– the value of the input parameter of quality indicator. Based on the mathematical description of paired dependencies on technological parameters, the mathematical model describing the process passing shrinkage of plastic threaded details can be written in general form (1) Here Qk − shrinkage k-th element of thread; xi − processing modes (X1 − specific pressure, MPa; X2 − pressing temperature, °C; X3 − holding time, mm/min). For the experiment, the second-order orthogonal plan was used and the number of experimental points was chosen according to the method proposed by Box-Wilson (Tables 1, 2). The plans of experimental shown in Tables 1 and 2 have a number of positive properties. Firstly, this plan can be obtained as a result of completing the first-order plan, which creates convenience for the experimenter when obtaining an inadequate mathematical model of the first order, which makes it possible to go to the second order, adding experiments only at star points and in the center of the plan. Secondly, the arrangement of starry points on the axes does not violate the orthogonally of the first-order columns and interaction effects. This enables the corresponding independent coefficients of the regression equation to be obtained. To determine the coefficients a0 , ai , aij , aii in the regression Eq. (1), we used an algorithm that simplifies the notation system with the introduction of a dummy variable X0 = 1, as a result of which we obtained: X0 = Z0 ; X1 = Z1 ; X2 = Z2 ; X3 = Z3 ; X12 = Z4 ; X22 = Z5 ; X32 = Z6 ; X1 X2 = Z7 ; X1 X3 = Z8 ; X2 X3 = Z9 . In the new designation system, the second-order polynomial is written as a linear homogeneous equation Qi =

q 

ai zi

(2)

i=0

Coefficients of the regression Eq. (2) are found by the least squares method, i.e. from the minimum condition  2 q n n    2  Qk − Q = ai zi =0 (3) Qk − k=1

k=1

i=0

min

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N. A. Gasanova et al. Table 1. Size M20 × 2 Material K-214–2

Factors

X1 = P, MPa

X2 = t, 0 °C

X3 = τ, min/mm

Shrinkage of thread elements, %

Main level

36

160

0,7

Qi

Upper level

38

175

0,8

Lower level

34

145

0,6

Interval of variation

2

15

0,1

Experiences

X1

X2

X3

Qd

Qd1

Qd2

Qd3

1

+1

+1

+1

0,960

0,890

1,200

1,910

2

+1

+1

−1

0,310

0,420

0,410

1,420

3

+1

−1

+1

0,996

0,920

0,210

1,860

4

+1

−1

−1

0,340

0,580

0,860

1,510

5

−1

+1

+1

0,980

0,980

0,620

1,880

6

−1

+1

−1

0,320

0,480

0,960

1,310

7

−1

−1

+1

1,00

1,040

0,840

1,910

8

−1

−1

−1

0,510

0,680

0,920

2,100

9

+α

0

0

0,890

0,890

0,570

1,610

10

−α

0

0

0,510

0,560

0,880

2,210

11

0

+α

0

0,980

0,920

0,790

1,860

12

0

−α

0

0,880

0,580

0,640

1,860

13

0

0

+α

0,320

0,310

0,830

1,650

14

0

0

−α

0,990

0,860

0,940

1,920

15

0

0

0

0,910

0,660

0,870

1,860

16

0

0

0

0,880

0,780

0,830

1,790

17

0

0

0

0,870

0,840

0,840

1,820

18

0

0

0

0,890

0,910

0,890

1,810

19

0

0

0

0,885

0,920

0,880

1,830

By permutation and simplifying the Eq. (3), we get a system of linear equations with respect to coefficients 9    Qk z1 = a1 9k=1 z1 z1 + a2 9k=1 z2 z1 + ...+a9 9k=1 z9 z1 k=1   9 9 9 9 k=1 Qk z2 = a1 k=1 z1 z2 + a2 k=1 z2 z2 + ...+a9 k=1 z9 z2 ......................................................... ......................................................... 9 9 9 9 k=1 Qk z2 = a1 k=1 z1 z9 + a2 k=1 z2 z9 + ...+a9 k=1 z9 z9

(4)

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Table 2. Size M33 × 3 Material K-18–53 Factors

X1 = P, MPa

X2 = t, 0 °C

X3 = τ, min/mm

Shrinkage of thread elements, %

Main level

36

160

0,7

Qi

Upper level

38

175

0,8

Lower level

34

145

0,6

Interval of variation

2

15

0,1

Experiences

X1

X2

X3

Qd

Qd1

Qd2

Qd3

1

+1

+1

+1

0,410

0,420

0,460

0,700

2

+1

+1

−1

0,510

0,509

0,490

0,680

3

+1

−1

+1

0,460

0,470

0,510

0,650

4

+1

−1

−1

0,620

0,610

0,560

0,810

5

−1

+1

+1

0,540

0,580

0,490

0,920

6

−1

+1

−1

0,680

0,640

0,564

0,960

7

−1

−1

+1

0,560

0,720

0,630

0,740

8

−1

−1

−1

0,710

0,760

0,740

0,980

9

+α

0

0

0,440

0,540

0,550

0,670

10

−α

0

0

0,670

0,720

0,610

0,840

11

0

+α

0

0,650

0,760

0,600

0,760

12

0

−α

0

0,580

0,810

0,760

0,750

13

0

0

+α

0,420

0,450

0,640

0,660

14

0

0

−α

0,630

0,580

0,607

0,810

15

0

0

0

0,640

0,620

0,580

0,850

16

0

0

0

0,570

0,610

0,625

0,840

17

0

0

0

0,560

0,640

0,620

0,830

18

0

0

0

0,580

0,590

0,630

0,860

19

0

0

0

0,590

0,608

0,620

0,870

Determining the coefficients of Eq. (4), it is necessary to apply actions with the matrix, for which Eq. (4) is writing in matrix form B=A+C

302

where

N. A. Gasanova et al.

    9 9 9 9            2     z1 z2 z1 ... z9 z1  Qk z1       a0     k=1    k=1 k=1 k=1     a  1 9 9 9 9               2      z2 z1 z2 ... z9 z2 Qk z2 a2        A =  k=1  ; B =  k=1  ; C = ...  k=1 k=1        . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . .       ...     9    9 9 9      a    9     z9 z1 z2 z9 ... z92  Qk z9        k=1

k=1

k=1

(5)

k=1

The solution to Eq. (5) is to find the elements matrix of column C. As is known from matrix theory, the solution is provided to the following form C=A

−1

+B

−1

where A − is the inverse matrix for solving the system of equations, the program package situated in the work [3] was used. Substituting the calculated values of the coefficients in Eq. (1), we obtain a mathematical model describing the process passing of shrinkage of the plastic threaded details. It consists of 4 equations for each size (M20 × 2, M33 × 3): for shrinkage of outer diameter − Qd , inner diameter − Qd1 , average diameter − Qd2 and pitch − Qs . For size M20 × 2 Qd = 0, 885 − 0, 13X1 − 0, 42X2 − 0, 092X3 + 0, 002X1 X2∗ + +0, 021X1 X3 + 0, 008X2 X3∗ − 0, 061X12 + 0, 024X22 − 0, 042X32 , Qd1 = 0, 870 − 0, 021X1 − 0, 037X2 − 0, 082X3 − 0, 003X1 X2∗ − −0, 005X1 X3∗ − 0, 002X2 X3∗ − 0, 094X12 − 0, 061X22 − 0, 040X32 , Qd2 = 0, 860 − 0, 160X1 − 0, 032X2 − 0, 076X3 − 0, 002X1 X2 + +0, 010X1 X3 − 0, 032X12 − 0, 007X22 + 0, 016X32 , Qs = 1, 840 − 0, 261X1 − 0, 066X2 − 0, 210X3 + 0, 022X1 X2 + +0, 009X1 X3∗ − 0, 002X2 X3∗ + 0, 141X12 + 0, 172X22 + 0, 231X32

(6)

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For size M33×3 Qd = 0, 580 − 0, 0812X1 − 0, 0168X2 − 0, 040X3 + 0, 004X1 X2∗ + +0, 02X1 X3 − 0, 018X2 X3 − 0, 018X12 + 0, 016X22 − 0, 021X32 , Qd1 = 0, 621 − 0, 080X1 − 0, 010X2 − 0, 042X3 + 0, 006X1 X2∗ + +0, 011X1 X3 + 0, 002X2 X3∗ − 0, 018X12 + 0, 012X22 − 0, 015X32 ,

Qd2 = 0, 630 − 0, 074X1 − 0, 014X2 − 0, 042X3 + 0, 006X1 X2∗ +

(7)

+0, 011X1 X3 + 0, 0014X2 X3∗ − 0, 026X12 + 0, 130X22 − 0, 021X32 , Qs = 0, 860 − 0, 182X1 − 0, 038X2 − 0, 076X3 − 0, 0018X1 X2∗ +

+0, 0020X1 X3∗ + 0, 0018X2 X3∗ + 0, 048X12 − 0, 142X22 + 0, 021X32 . The obtained mathematical models describing the process passing of shrinkage of the threaded detail (M20 × 2, M33 × 3) were checked for adequacy. To test the hypothesis about the adequacy the results of experiment with the found relation Eqs. (6) and (7), it is sufficient to estimate the deviation predicted by the regression equation of the output value Qk from the results of experiment Qk at points X k of the factor space. When checking for the adequacy of Eqs. (6) and (7), it was found that they adequately reproduce the investigated process. From the analysis of Eqs. (6) and (7), describing the dependence of the shrinkage elements of the plastic threaded details on technological factors, it can be seen that taking into account the linear effects (in the levels of variation, Table 2) and regime parameters in all cases, the shrinkage decreases and out of the indicated factors the greatest influence is exerted by the pressing pressure, which is confirmed by the results of works [4–8]. The influence of paired interactions X1 X2 , X1 X3 and X2 X3 is almost insignificant, and their coefficients a12 , a13 and a23 , when tested for significance, turned out to be insignificant in the chosen levels of variation of the variables. Of these, only X1 X2 is significant for the shrinkage of the pitch, and X2 X3 is significant for the shrinkage of the outer diameter of the thread (size M33 × 3). It should be noted here that the noticeable effect of the pressing pressure on shrinkage is due to the fact that with an increase in pressure along the entire section of the material, additional latent heat is formed, which increases the pressing temperature, and due to which the shrinkage in step increases in comparison with diameters, since the thickness of the thread profile is much less than the thickness of the part body. On the other hand, at large limits variation of the holding time the temperature is evenly distributed over the outer diameter. As a result, the process passing of chemical shrinkage during molding is almost stopping. In the longitudinal direction, the shrinkage decreases because the direction of pressing coincides with the direction the passing of the shrinkage of the pitch, as a result of which the pressure is completely absorbed by the press-material [6–8]. The influence of square members on shrinkage of thread diameters is negative, i.e. with an increase in these factors to the second degree (at the selected levels), the shrinkage always decreases, and under the shrinkage of the pitch − vice versa, which is associated with the anisotropy of shrinkage, i.e. the shrinkage of the pitch in the longitudinal direction is usually greater than in the transverse direction.

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4 Discussion and Conclusions The obtained mathematical models (6) and (7), describing the dependence of the shrinkage of plastic thread elements with different pitch and diameter on the operating variables, make it possible, solving optimization problems, to establish optimal modes that ensure the minimum shrinkage of all elements, thread elements. Therefore, for plastic threaded connections, a special system of tolerances is provided, which includes, in addition to the existing accuracy classes of threads, new accuracy classes 4 and 5th, as well as threads with an especially large pitch. Mathematical models of the process of manufacturing parts from various engineering plastics are proposed, reflecting the relationship between the components of the vector of quality indicators (shrinkage, strength, accuracy) of plastic parts with regime parameters of processes, composition of materials, designs of parts, in order to optimize quality indicators.

References 1. Kerimov, D.A.: Scientific bases and practical methods of optimization of parameters of quality of plastic details of the oil-field equipment. Dissert. of Doct.techn.sciences., Baku (1985) 2. Braginsky, V.A., Mirzoyev, R.G.: System from fit tolerances of details from plastic. (Review of literary data). Plastics in mechanical engineering and instrument making, MDNP, M. (1965) 3. Kerimov, D.A., Kurbanova, S.K.: Bases of designing of plastic details and press-moulds. Baku: Publishing house “Elm”, 504 (1997) 4. Kerimov, D.A., Gasanova, N.A.: Determination of quality of plastic details under interval uncertainty. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 848–851. Springer, Cham (2019). https://doi.org/10.1007/ 978-3-030-04164-9_111 5. Gasanova, N.A.: Definition of mechanical indicators of plastic details of the oil field equipment. Int. J. Innov. Res. Comp. Sci. Tech. 8(4), 313–314. https://doi.org/10.21276/ijircst.2020.8.4.11 6. Aslanov, J.N., Sultanova, A.B., Huseynli, Z.S., Mustafayev, F.F.: Determination of radial strains in sealing elements with rubber matrix based on fuzzy sets. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 765–773. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_101 7. Babanli M.B.: Fuzzy Logic-based Material Selection And Synthesis, World Scientific Publishing Company( 2019). ISBN: 9813276584, 9789813276581 8. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12

Tableaux Deduction System for Fuzzy Logic with Estimates of Fuzziness Values Gerald S. Plesniewicz

and Alexey N. Aparnev(B)

National Research Princeton University MEI, Krasnokazfrmennaya, 14, 111250 Moscow, Russian Federation [email protected]

Abstract. Let LZ be Zadeh’s fuzzy propositional logic determined by the norm min{x, y} with implication ϕ → ψ considered as the shorthand ~ ϕ ∨ ψ. A simple estimate for a formula ϕ has he forms ϕ ≥ a, ϕ > a, ϕ ≤ a and ϕ < a where ϕ is a formula of the logic LZ. An composite estimate is a propositional combination of simple estimates. We call the logic of estimates LE the set of all estimates (simple and composite) with their natural semantics determined by fuzzy interpretations for LZ. For the logic LE, some sound and complete inference system, based on the use of analytic tableaux, is presented. Keywords: Fuzzy logic · Estimates · Fuzziness values · Inference rules · Hintikka set

1 Introduction. Main Definitions Let LZ denote Zadeh’s fuzzy propositional logic with a set P of propositional variables. Its syntax is the same as that of classical propositional logic. The semantics of the logic LZ are determined by fuzzy interpretations of formulas. Such interpretations are extensions of interpretations of propositional variables from P. A fuzzy interpretation of propositional variables is simply a function “_”: P → [0,1] (where [0,1] is the unit interval). Fuzzy interpretations of arbitrary formulas of the logic L are defined inductively from the values of “p” (p ∈ P) with using the norm min{x, y}. Note that formula ϕ → ψ is treated as a shorthand for the formula ~ ϕ ∨ ψ. We will consider estimates for fuzzy logic formulas from LZ as expressions with the following syntax: • (p ≥ a), (p > a), (p ≤ a), (p < a) are atomic estimates, where p ∈ P and a ∈ [0,1]; • (ϕ ≥ a), (ϕ > a), (ϕ ≤ a), (ϕ < a) are simple estimates, where ϕ is a formula from LZ; • an arbitrary estimate is propositional combination of simple estimates. An estimate is composite if it contains propositional connectives. Semantics of estimates is determined naturally by interpretations that are extensions of interpretations “_” of formulas from LZ. So, for any estimate λ and a ∈ [0,1] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 305–312, 2023. https://doi.org/10.1007/978-3-031-25252-5_42

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We will consider estimates as sentences of some logic called the logic of estimates LE. We emphasize that LE is a crisp logic, but interpretations of its propositional variables are fuzzy. The logic LE (as every crisp logic) induces a logical consequence relation between estimates. For a set of estimates E and an estimate λ, the logical consequence E |= λ holds by definition if there is no interpretation under which all the estimates from E are true and the estimate λ is false. The concept of logical inconsistency (or non-satisfiability) directly connected to the concept of logical consequence. Generally, a set E of sentences of some logic L is satisfiable if there is an interpretation under which all sentences from E; otherwise, E is called unsatisfiable (or inconsistent). Clearly, if L contains the negation ‘ ~’ then E |= λ ⇔ ‘E ∪ {~λ,}is inconsistent’ for all formula λ from LE. Thus, the problem of logical consequences can be reduced to the problem of recognizing inconsistency. Early, S. Kundu considered estimates of Zadeh’s logic statements, for which he constructed a sound and complete inference system based on the resolution principle [4, 6]. In this paper we present some sound and complete inference system based on using analytic tableaux [2, 3]. Let  denote the presented inference system. We can also use the terminology of the theory of knowledge bases. For example, a knowledge base is a finite set estimates (as sentences of the logic LE). Facts are atomic estimates or disjunction of atomic estimates. A fact base is a finite set of facts.

2 Equivalences in the Logic of Estimates LE Estimates λ and μ are equivalent if, under any interpretation, they have the same truth values: λ ≡ μ ⇔df “λ” = “μ” for any interpretation “_”. The following lemma gives a list of equivalences used in proving the soundness and completeness of the system of inference rules . In the lemma, ϕ is a formula of the logic L, and a ∈ [0,1]. Lemma 1. The following equivalences hold in the logic of estimates LE: ~ (ϕ ≥ a) ≡ (ϕ < a), ~ (ϕ > a) ≡ (ϕ ≤ a), ~ (ϕ ≤ a) ≡ (ϕ > a), ~ (ϕ < a) ≡ (ϕ ≥ a), (~ ϕ ≥ a) ≡ (ϕ ≤ 1– a), (~ ϕ > a) ≡ (ϕ < 1– a), (~ ϕ ≤ a) ≡ (ϕ ≥ 1– a), (~ ϕ < a) ≡ (ϕ > 1– a), 1: ((ϕ ∧ ψ) ≥ a) ≡ ((ϕ ≥ a) ∧ (ψ ≥ a)), ((ϕ ∧ ψ) > a) ≡ ((ϕ > a) ∧ (ψ > a)), ((ϕ ∧ ψ) ≤ a) ≡ ((ϕ ≤ a) ∨ (ψ ≤ a)), ((ϕ ∧ ψ) < a) ≡ ((ϕ < a) ∨ (ψ < a)), 2: ((ϕ ∨ ψ) ≥ a) ≡ ((ϕ ≥ a) ∨ (ψ ≥ a)), ((ϕ ∨ ψ) > a) ≡ ((ϕ > a) ∨ (ψ > a)), ((ϕ ∨ ψ) ≤ a) ≡ ((ϕ ≥ a) ∧ (ψ ≥ a)), ((ϕ ∨ ψ) < a) ≡ ((ϕ > a) ∧ (ψ > a)), ((ϕ → ψ) ≥ a) ≡ ((ϕ ≤ 1– a) ∨ (ψ ≥ a)), ((ϕ → ψ) > a) ≡ ((ϕ < 1– a) ∨ (ψ > a)), ((ϕ → ψ) ≤ a) ≡ ((ϕ ≥ a) ∧ (ψ ≥ a)), ((ϕ → ψ) < a) ≡ ((ϕ > a) ∧ (ψ > a)). The first four equivalences are obvious. Proof of 1: “((ϕ ∧ ψ) ≥ a)” = 1 ⇔ “(ϕ ∧ ψ)” ≥ a ⇔ (“ϕ” ∧ “ψ”) ≥ a ⇔ min{“ϕ”, “ψ”} ≥ a. ⇔

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“ϕ” ≥ a and “ψ” ≥ a ⇔ “(ϕ ≥ a)” = 1 and “(ψ ≥ a)” = 1 ⇔ (“ϕ ≥ a” ∧ “ψ ≥ a”) = 1. ⇔ “((ϕ ≥ a) ∧ (ψ ≥ a))” = 1. Hence “((ϕ ∧ ψ) ≥ a)” = 1 ⇔ (ϕ ≥ a) ∧ (ψ ≥ a))” = 1 for any interpretation “_”. Therefore, equivalence 1 is true. Proof of 2: “((ϕ ∧ ψ) ≤ a)” = 1 ⇔ “(ϕ ∧ ψ)” ≤ a ⇔ (“ϕ” ∧ “ψ”) ≤ a ⇔ min{“ϕ”, “ψ”} ≤ a. ⇔ “ϕ” ≤ a or “ψ” ≤ a ⇔ “ϕ ≤ a” = 1 or ψ ≤ a” = 1 ⇔ (“ϕ ≤ a” ∨ “ψ ≤ a”) = 1 ⇔ “((ϕ ≤ a) ∨ (ψ ≤ a))” = 1. Hence “((ϕ ∧ ψ) ≤ a)” = 1 ⇔ (ϕ ≤ a) ∧ (ψ ≤ a)” = 1 for any interpretation “_”. Therefore, equivalence 2 is true. The remaining equivalences are proved similarly.

3 System  The system  has the inference rules placed in the two tables – Table 1 and Table 2. The rules from the first table are used when building inference trees for knowledge bases written in the logic of estimates LE. The second table contains the rules for detecting contradictions arising in the inference trees that we build for knowledge bases using the system . A pair [λ, μ] of simple estimates is said to be conflicting if there is some inference rule from Table 2 such that applying the rule to the pair [λ, μ] we get as output the contradiction sign X. For example, consider the pair of estimates s = [((p ∧ q) ≥ 0.7), ((p ∧ q) ≤ 0.5)] and the rule 4* (from Table 2). From the antecedents of the rule 4* we get the pair s if we put ϕ: = (p ∧ q), a: = 0.7 and b: = 0.5. Since a = 0.7 > 0.5 = b, the conditions for the applicability of the rule 4* are satisfied, and we can execute this rule. Then we obtain the value X. Therefore, s is a conflicting pair. The first 6 rules from Table 1 are the usual inference rules used in the analytictableaux systems for propositional logic (see, for example, the books [3, 5]). Clearly, classic propositional logic is a fragment of LE since p is equivalent to (p ≥ 1). The rules 1 – 6 are used by algorithms for building inference trees for knowledge bases written in propositional logic. In essence, the same algorithms can be used when constructing inference trees for knowledge bases written in LE logic. In this case, the rules from Table 1 are applied in a similar way as the rules for propositional logic. The rules of Table 1 are divided into conjunctive and disjunctive. A rule is disjunctive if its consequent contains the connective ‘or’; if the consequent contains the connective ‘and’ or contain no connectives, then the rule is conjunctive. Consider an example of building an inference tree T0 for the knowledge base Kb0 = {(((p1 ∨ ~ p3 ) > 0.3) → (p2 ≤ 0.4)), (((p1 ∧ p2 ) ≤ 0.9) → (~p1 ≤ 0.5))}. The vertices of inference trees have right and left labels. For example, the second vertex of the tree T0 (Fig. 2) has the left label “0:” and the right label “[5, 6]”. The label “0:” tells that the corresponding estimate for a vertex belongs to the knowledge base Kb0 , and the label “[5, 6]” tells that rule 6 from Table 1 was applied at step 5 to this estimate. The result of applying this rule was the pair of estimates [5: ~ ((p1 ∧ p2 ) > 0.9),, 5: (~p1 ≤ 0.5)] which as the “fork” was attached to two branches whose ends are

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marked with explanation mark ‘!’ on Fig. 1. (A branch in a tree is a path starting from the root of the tree.) Recall that the sound rules of inference in any crisp logic are those that keep the formulas true. It is easy to see that, thanks to Lemma 1, all the inference rules from Table 1 are sound. Table 1. Inference rules. (Here are λ and μ ∈ LE, ϕ and ψ ∈ LZ) Rule number

Antecedent

Consequent

1

~ ~λ

λ

2

(λ ∧ μ)

λ and μ

3

~ (λ ∧ μ)

~ λ or ~ μ

4

(λ ∨ μ)

λ or μ

5

~ (λ ∨ μ)

~ λ and ~ μ

6

(λ → μ)

~ λ or μ

7

~ (λ → μ)

λ and ~ μ

8

~ (ϕ ≥ a)

(ϕ < a)

9

~ (ϕ > a)

(ϕ ≤ a)

10

~ (ϕ ≤ a)

(ϕ > a)

11

~ (ϕ < a)

( ϕ ≥ a)

12

(~ ϕ ≥ a)

(ϕ ≤ 1– a)

13

(~ ϕ > a)

(ϕ < 1– a)

14

(~ ϕ ≤ a)

(ϕ ≥ 1– a)

15

(~ ϕ < a)

(ϕ > 1– a)

16

((ϕ ∧ ψ) ≥ a)

(ϕ ≥ a) and (ψ ≥ a)

17

((ϕ ∧ ψ) > a)

(ϕ > a) and (ψ > a)

18

((ϕ ∧ ψ) ≤ a)

(ϕ ≤ a) or (ψ ≤ a)

19

((ϕ ∧ ψ) < a)

(ϕ < a) or (ψ < a)

20

((ϕ ∨ ψ) ≥ a)

(ϕ ≥ a) or (ψ ≥ a)

21

((ϕ ∨ ψ) > a)

(ϕ > a) or (ψ > a)

22

((ϕ ∨ ψ) ≤ a)

(ϕ ≤ a) or (ψ ≤ a)

23

((ϕ ∨ ψ) < a)

(ϕ < a) and (ψ < a)

24

((ϕ → ψ) ≥ a)

(ϕ ≤ 1– a) or (ψ ≥ a)

25

((ϕ → ψ) > a)

(ϕ < 1– a) or (ψ > a)

26

((ϕ → ψ) ≤ a)

(ϕ ≥ 1– a) and (ψ ≤ a)

27

((ϕ → ψ) < a)

(ϕ > 1– a) and (ψ < a)

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4 Completeness of the System  for Logic of Estimates LE A system  of inference rules for a given logic L is complete when, for any knowledge base Kb and any statement λ written the L, the logical consequence Kb |= λ holds if λ is. Derived from Kb by means of the rules of the system . Further, we use the standard terminology accepted in the theory of analytic tableaux [2]. Let B be a branch of an inference tree T and λ is an estimate in T. Then we say that: (i) λ is deployed if some inference rule (from Table 1) has been applied to λ; (ii) B is closed if it ends with the symbol ‘X’; (iii) B is open if it is not closed; (iii) T is closed if all its branches are closed; (iv) B is complete if every its composite estimate is deployed; (v) T is completed if every its branch is complete or closed. Table 2. Rules for closing branches of inference trees. (Here is λ --- μ denotes that the estimates λ and μ belong to the same branch.) Rule number

Antecedents

Consequent

1*

ϕ > a, ϕ < a

X

2*

ϕ ≥ a, ϕ < a

X

3*

ϕ > a, ϕ ≤ a

X

4*

(ϕ ≥ a), (ϕ ≤ b), a > b, (ϕ ≥ a) --- (ϕ ≤ b)

X

5*

(ϕ ≥ a), (ϕ < b), a ≥ b, (ϕ > a) --- (ϕ ≤ b)

X

6*

(ϕ > a), (ϕ ≤ b), a ≥ b, (ϕ ≥ a) --- (ϕ < b)

X

7*

(ϕ > a), (ϕ < b), a ≥ b, (ϕ > a) --- (ϕ < b)

X

Theorem 2. Let Kb be a knowledge base in LE and λ be an estimate written with propositional variables from Kb. It takes place: (I) If Kb |= λ then every completed inference tree for Kb ∪ {~ λ} must be closed; (II) If some completed inference tree for Kb ∪ {~λ} is closed then Kb |= λ. We prove Theorem 2 using the so-called Hintikka sets. A set H of estimates is said to be Hintikka set (in the system ) if (a) H contains no conflicting pairs of atomic estimates; (b) H is downward saturated relatively the rules that correspond to inference rules of the system . Let’s rewrite the rules from the table into corresponding conditions, as can be seen from the following examples: • Rule 1 is rewritten into the condition ‘If ~ ~ X ∈ H then X ∈ H’;

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0: (((p1 p2) ≤ 0.9) → (~p1 ≤ 0.5)) [5, 6] ______________|__________________ | | p3) > 0.3)) [2, 9] ! 1: (p2 ≤ 0.4) [8, 9*] 1: ~ ((p1 2: ((p1 p3) ≤ 0.3) [3, 22] _______|_________ 3: (p1 ≤ 0.3) [14, 16*] | | 3: ( p3 ≤ 0.3) [4, 14] 5: ~ ((p1 p2) ≤ 0.9) [6, 3] 5: (~p1 ≤ 0.5) [9, 14] ! 4: (p3 ≥ 0.7) 6: ((p1 p2) > 0.9) [7, 2] 9: (p1 ≥ 0.5) | 7: (p1 > 0.9) B3 ____|__________________ 7: (p2 > 0.9) [8, 9*] | | 8: x 5: ~ ((p1 p2) > 0.9) [10, 9] 5: (~p1 ≤ 0.5) [11, 14] 10: ((p1 p2) ≤ 0.1) [13,18] 11: (p1 ≥ 0.5) [12, 5*] ____|________________ 12: x | | 13: (p1 ≤ 0.1) [14, 16*] 13: (p2 ≤ 0.1) B1 B2 Fig. 1. Inference tree T0 for the knowledge base Kb0

• • • •

Rule 2 is rewritten into the condition ‘If (X ∧ Y) ∈ H then X ∈ H and Y ∈ H’; Rule 7 is rewritten into the condition ‘If ~ (X → Y) ∈ H then X ∈ H and ~ Y ∈ H’; Rule 10 is rewritten into the condition ‘If ~ (X ≤ a) ∈ H then (X > a) ∈ H’; Rule 18 is rewritten into the condition ‘If ((X ∧ Y) ≤ a) ∈ H then (X ≤ a) or (Y ≤ a).

Lemma 2. Every Hintikka set (in the logic of estimates LE) is satisfiable. Proof. Let P = P(H) be the set of all propositional variables from a Hintikka set H. For each p ∈ P, we write down all atoms from H with p: (p ≥ a1 ), (p ≥ a2 ),…, (p ≥ an ) and (p ≤ b1 ), (p ≤ b2 ),…, (p ≤ bm ), where it is possible that some non-strict inequalities are replaced by strict inequalities. Let pmax = max{a1 , a2 ,…, an } and pmin = min{b1 , b2 ,…, bn }. Note that pmin ≤ pmax . Indeed, suppose that pmin > pmax . Take the indices r and s such that pmin = ar and pmax = bs . Then. we have the pair [(p ≥ ar ), (p ≤ bs )] which is conflicting since ar > bs . This contradicts with the requirement (a) that Hintikka set must not contain conflicting pairs of atoms. “(p ≥ ai )” = 1 ⇔ “p” ≥ ai ⇔ p# ≥ ai , “(p ≤ bi )” = 1 ⇔ “p” ≤ bi ⇔ p# ≥ bi . Thus, “α” = 1 for all atomic estimates from H. We prove by induction on the structure of estimates that the estimates from H are true under this interpretation: “λ” = 1 for all λ ∈ H. Induction base: The statement the “α” = 1 for all atomic estimates from H. Induction transfer. In particular, for the rules 1, 2, 7, 10, 18 we have: Rule 1 (Table 1): ~ ~λ |– λ. By inductive hypothesis, “λ” = 1. We have “~ ~λ” = ~ ~ “λ” = ~ ~ 1 = 1. Hence, “ ~ ~ λ” = 1.

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Rule 2: (λ ∧ μ) |– λ and μ. By inductive hypothesis, “λ” = 1 and “μ” = 1. We have “(λ ∧ μ)” = (“λ” ∧ “μ”) = (1 ∧ 1) = 1. Hence, “(λ ∧ μ)” = 1. Rule 7: ~ (λ → μ) |– λ and μ. By inductive hypothesis, “λ” = 1 and “~μ” = 1. We have “ ~ (λ → μ)” = ~ (“λ” → “μ”) = ~ (1 → 1) = 1. Hence, “ ~ (λ → μ)” = 1. Rule 10: ~ (ϕ ≤ a) |– (ϕ > a). By inductive hypothesis, “(ϕ > a)” = 1. We have “ ~ (ϕ ≤ a)” = 1 ~ ⇔ (“ϕ” ≤ a) = 1 ⇔ “ϕ” > a) = 1 ⇔ “(ϕ > a)” = 1. Hence, “ ~ (ϕ ≤ a)” = 1. Rule 18: ((ϕ ∧ ψ) ≤ a) |– (ϕ ≤ a) or (ψ ≤ a). By inductive hypothesis, “(ϕ ≤ a)” = 1 or “(ψ ≤ a)” = 1. We have “((ϕ ∧ ψ) ≤ a)” = 1 ⇔ “(ϕ ∧ ψ)” ≤ a) ⇔ “ϕ” ≤ a or “ψ” ≤ a ⇔ “(ϕ ≤ a)” = 1 or “(ψ ≤ a)” = 1. Hence, “((ϕ ∧ ψ) ≤ a)” = 1. Proof of Theorem 2 (I). Let the relation Kb |= λ holds, and T be any completed inference tree which was built for the set Kb ∪ {~λ}. Suppose that T is not closed. Let B be an open branch of T. Then B is a Hintikka set. Therefore, B is satisfied set (due Lemma 2). The set Kb ∪ {~λ} is also satisfied since Kb ∪ {~λ} ⊆ B. There is an interpretation “_” which make true all estimates from Kb ∪ {~λ}. In particular, “ ~ λ” = 1, “λ” = 0, and “μ” = 1 for all μ ∈ Kb. Since Kb |= λ, we have “λ” = 1. (Contradiction: “λ” = 0 and “λ” = 1). Proof of (II) Theorem 2 (II). In the book [3] there is the proof of the Theorem 2.67 (page 39) that a complete tableau T built for a formula ϕ (in propositional logic) is unsatisfied if T is closed. This proof can be adapted to the case of the logic of estimates LE.

5 Deduction in the Logic of Estimates LE We will show by example how logical deduction is performed in the logic of estimates LE. Consider again the inference tree T0 (Fig. 2) built for the knowledge base Kb0 . It easy to check that the tree T0 is completed. We see that T0 has 5 branches, of which the third and fourth are closed, and the rest (denoted B1 , B2 , B3 ) are open. Let B be an open branch of an inference tree T. Denote by B the conjunction all atoms lying on the branch B. For example, for T0 we have. B1 = ((p3 ≥ 0.7) ∧ (p1 ≤ 0.1)), B2 = ((p3 ≥ 0.7) ∧ (p2 ≤ 0.1)), B3 = ((p2 ≤ 0.4) ∧ (p1 ≥ 0.5). We can close the open branches of T if adding to T suitable atoms. For example, let us take atom (p2 > 0.4). Then in the tree T0 with (p2 > 0.4), there are conflicting pairs [(p2 > 0.4), 13: (p2 ≤ 0.1)] and [(p2 > 0.4), 1: (p2 ≤ 0.4)] which close the branches B2 and B3 . For finding such conflicting pairs we will use a special bipartite graph (T) whose the left vertices are estimates B (composite, as a rule) and the right vertices are atomic estimates with the variables x i and yi as their boundaries (see Fig. 2). The edges of (T) are pairs of estimates [λ, α] where: (i) α is an atom of the forms (p ≥ x), (p > x), (p ≤ y), (p > y); (ii) α is atom (p ≥ x) and λ contains (p < a) with some a; α is atom (p > x) and λ contains (p ≤ a) with some a; α is atom (p ≤ y) and λ contains (p > a) with some a; α is atom (p ≤ y) and λ contains (p > a) with some a. For

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B1

B2

B3

(p1 > x1 ) / x1 = 0.1 ○ (p1 ≥ x1) (p1 < y1) (p1 ≤ y1) (p2 > x2) / x2 = 0.4 ○ (p2 ≥ x2) (p2 < y2) (p2 ≤ y2) (p3 > x3) (p3 ≥ x3) (p3 < y3) / y3 = 0.7 (p3 ≤ y3) Fig. 2. Graph (T0 )

example, the graph (T) have the edge connecting B2 with (p3 < y3 ) since B2 contains (p3 ≥ 0.7). We see from Fig. 2 that the set C = {(p1 > x 1 ), (p2 > x 2 )} is a minimal (for inclusion) covering of all left vertices of the graph (T). (The estimates from C are marked by circle ◯.) In Fig. 2 after slashes the values of variables x j and yj are written for the vertices with positive degrees. In general case, let V 1 , V 2 ,…, V m be all left vertices connected to the right vertex V = (p < y). Then each conjunction V k contains the atomic estimate (p ≥ aj ), and we set y = min{a1 , a2 ,…, am }. This value is the answer to the query (p ≥ y): Kb. We have that Kb |= (p ≥ min{a1 , a2 ,…, am }).

References 1. Aliseda, A.: Abductive Reasoning. Springer (2006). https://doi.org/10.1007/1-4020-3907-7 2. Agostino, M., Gabbay, D., Hahnle, Possega J.: Handbook of Tableaux Methods. Springer (2001). https://doi.org/10.1023/A:1017520120752 3. Ben-Ari, M.: Mathematical Logic for Computer Science. 3rd edition. Springer (2017). https:// doi.org/10.1007/978-1-4471-4129-7 4. Chen, J., Kundu, S.: A sound and complete fuzzy logic system using Zadeh’s implication operator. In: Ra´s, Z.W., Michalewicz, M. (eds.) ISMIS 1996. LNCS, vol. 1079, pp. 233–242. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61286-6_148 5. Fitting, M.: First-Order Logic and Automated Theorem Proving. Springer (1996). https://doi. org/10.1007/978-1-4612-2360-3 6. Kundu, S.: An improved method for fuzzy-inferencing using Zadeh’s implication operator. In: Proceedings of IJCAL Workshop on Fuzzy logic in AI, pp. 117–125. Springer (1995)

Research of Bitumen-Based Asphalt Compositions Using Neural Network D. S. Mamed Hasan-zade(B)

, A. I. Babayev , and G. S. Hasanov

Azerbaijan State Oil and Industry University, Ave. Azadlig., 20, AZ1010 Baku, Azerbaijan [email protected]

Abstract. The work is dedicated to the research of the production process of bitumen-based asphalt compositions. The main function of the bituminous binder in pavement mixture is to bind the aggregate particles together by providing adhesion between the components in the composite. Despite that fact that the weight ratio of bituminous binders is low (5–7%) in the mixture, their impact on the operating characteristics of pavement is quite high. The increase in transportation and speed intensity at global and regional scales is making the demand for the performance indicators of pavement more stringent. Thus, it creates the necessity of modifying bitumens used in road construction to bring them to the required parameters. In the article, a new modified asphalt pavement bitumen composition with higher quality binding properties, favorable temperature and tensile properties based on brittle bitumen raw materials melting at high-temperature (110 °C) and technological additives, and preparation of asphalt pavement based on it, optimization of the components used in the process according to the physical and mechanical properties of the commodity product, possible aspects of artificial intelligence relationships in the exploitation process have been investigated. The article deals with the research of bitumen-based asphalt compositions using ANFIS model. Keywords: Asphalt composition · Bitumen · Asphalt pavementneural network · Mass extensibility · Softening temperature · Penetration depth

1 Introduction The creation of solid and durable foundation of asphalt pavement, the quality of which is determined by physical and mechanical properties of the used bituminous binder is one of the topical issues. Since asphalt pavement bitumen used to obtain high-quality asphalt pavement usually does not meet the set requirements, various additives are added to the composition of bitumen compositions. These additives include various industrial wastes, as well as production wastes of polymer materials. In this regard, recently much attention has been paid to the research on changing operating characteristics of bitumen by using wastes in the content of polymer-bitumen compositions. In recent years, bitumen compositions modified with various polymer wastes have been widely used to create practical asphalt pavement. Among them, in particular, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 313–320, 2023. https://doi.org/10.1007/978-3-031-25252-5_43

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polyisoprene (SKI-3), divinyl styrene elastomers, ethylene-propylene copolymers, highpressure polyethylene, polypropylene production waste, etc. can be shown [1–5]. Bitumen modified with polymers is bituminous is a new type of constructing material with the ability to create bituminous binder, insulating coating layer being subjected to possible transformations due to mechanical mixing of polymer-rubber-containing wastes with bitumen in the form of a solid and liquid solution in various proportions and temperature, pressure of the environment, mixing intensity, time, chemical activity tendencies of the components, thereby improving its properties according to the initial indicators. It is known that bitumen is essentially a complex mixture of hydrocarbon chains with different molecular weights. The proportional change of these components in bitumen significantly affects both its rheological and physical properties. Differences in the bitumen structure, polymer macromolecules subjected to transformations during the process, elastomer-based rubber granules originally vulcanized with sulfur, but most of the double bonds are not used, allow obtaining various materials with needed properties due to the possible transformations between heavy hydrocarbons of various structures (asphaltenes, maltenes, aromatics, resins and saturated) that make up the composition of used oil and bitumen. Bitumen modified with polymers is most often used in the production of pavement and asphalt pavement components. This is related to their effect at high temperature [6, 7]. As it is known asphalt produced from heavy oil residues is natural asphalt. Artificial asphalt is a mixture of minerals such as gravel, sand, sandstone, limestone and viscous binding elements, etc. [8, 9]. Asphalt concrete is a complex mixture of bitumen and mineral materials and is used in road construction, pothole repair, etc. One of the main factors determining the positive operating characteristics of asphalt is the existence of crushed gravel constituting the basis of asphalt mass, soft, flexible, durable adhesive layer that is resistant to oxidation, numerous shocks and vibrations caused by the contact of a tire with coating, and natural biological bacteria. Stringent requirements arising from repeated and enhancing traffic loads further increase the demand for this indicator. Especially recently, the reduction of economic and environmental losses along with sustainability of pavement is becoming a necessity. It is known that the requirements of EURO-6, in addition to fuel, are aimed at improving the operating characteristics of even more vehicles. This, along with other factors, is closely related to the composition, structure, and quality of road construction materials. In order to determine these dependencies, the characteristics of pavement raw materials components, production technology, operating conditions should be considered as a system. The gravel being of the same or different size, the elasticity of the glue that binds them together, have a significant effect on whether the shocks caused by the contact between a tire and road are monotonous or variable, hard or soft, smooth (these indicators are recorded by special sensors and transferred to the electronic control center of the transport). All this is recorded in the artificial intelligence system, and maneuvering characteristics of the vehicles are adjusted according to the operational capabilities of the road. The research work is dedicated to the modification of bituminous binders using various additives and the preparation of new asphalt components for the further use of pavement in order to reduce economic and ecological losses along with the durability of pavement.

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2 Materials Used in Practice According to SS 10585–99, black oil of M-40 characterized by kinematic viscosity at 80 °C of 43 mm2 /s, density at 20 °C of 922.1 kg/m3 , pour point of minus 12 °C was used in the research work. Its decomposition point was 184 °C, the ash content of the mass was 0.0228%, and the mass fraction of sulfur was 0.23% (Table 1). Table 1. Physical and mechanical properties of black oil M-40 used in accordance with SS 10585– 99 № Name

Indicators

1

kinematic viscosity at 80 °C, mm2 /s 43

2

density at 20 °C, kg/m3

3

Installation point, °C

−12

4

Combustion point, °C

184

5

Ash content, %

0.0228

6

Mass fraction of sulfur, %

0.23

7

Mass fraction of water, %

Not

922.1

Bitumen which is characterized by softening temperature of 110 °C, needle penetration depth of 16 x 0.1 mm at 25 °C and stretchability of 3 cm at 25 °C was used as raw material in ring and ball test. High-pressure polyethylene (LDPE) production wastes with a molecular weight of 700–11,000 was used as a modifier in bitumen content, based on published data [10, 11], and crumb rubber with 0.06 mm diameter, a waste product from the production of rubber products, was used.

3 Methodology of Sample Preparation In order to obtain a homogeneous polymer-bitumen composition, bitumen is mixed with black oil of M-40 (SS 10585–99) at temperature of 120 °C. LDPE and rubber crumbs are added to the resulting mixture at the indicated temperature and stirring vigorously. By continuing to stir the bitumen mixture, temperature is raised to 170 °Cand kept at that temperature for 30–40 min. Mineral content of bitumen composition is prepared as follows. Pure river sand was used to conduct experiments. Stone dust is the material obtained as a result of processing river stone in thermal centrifuges. Gravel is a construction material produced by grinding stones and passing them through sieves. Chemical composition of used cement is as follows: 67% calcium oxide, 22% silicon oxide, 5% aluminum oxide, 3% iron oxide and 3% other substances. Depending on the amount of mineral components and bitumen, asphalt compositions are divided into several types: a) sandy (for pavements and pedestrian); b) fine-grained (for roads with heavy traffic), rubber-bitumen for covering stadiums and bicycle roads, etc.

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Asphalt includes petroleum-derived asphalt and asphalt oil. These compounds include asphaltenes, resins, cyclic compounds and saturated hydrocarbons [5]. Bituminous polymer mixtures with optimal operating properties were added to bitumen of BND 60/90 and tested. The tests were carried out according to the standards such as softening temperature (SS 11506–73), penetration (SS 11506–73), tensile strength (SS 11505–75).

4 Results and Discussion Researches were conducted to study the impact of the asphalt content on some qualities of the prepared pavement [12, 13]. Based on the conducted research (Table2) it was determined thatthe change in the amount of each of the components constituting asphalt composition has a noticeable impact on physical and mechanical properties of asphalt. So, keeping the other components practically constant in the samples, the physical and mechanical properties of asphalt compositions at the mass limits of bitumen -30.8, gravel stone -10.3%, softening temperature is 90 °C, needle penetration depth is 75mm, tensile strength is maximum being 13mm. However, these indicators are not achieved at the mass limits of river sand −36.5%, clay −23.4%. Cement is a binder between organic and inorganic substrates due to its composition of oxides. In addition to its direct function, gravel stone creates a mill effect in the course of the technological process, which makes it possible for the components to be evenly distributed in the system. That is, the system itself is quite dynamic. This opens up wide opportunities for the application of artificial intelligence in asphalt production technology. Table 2. Physical and mechanical properties of asphalt compositions N

Name

KiSh, °Csoftening temperature respectively

Needle penetration depth at 25 °C × 0,1 mm

Tensile strength of sm, at 25 °C SS 11505–75

1

Composition: % mass Bitumen – 17.5 Clay – 23.4 River sand – 36.5 Stone dust – 8.8 Cement – 8.8 Gravel stone – 5.0

110

58

8

2

Composition: % mass Bitumen – 14.0 Clay – 23.4 River sand – 36.5 Stone dust – 8.8 Cement – 8.8 Gravel stone – 5.0

115

60

10

3

Composition: % mass Bitumen – 30.8 Clay– 10.5 River sand – 7.7 Stone dust – 20.5 Cement – 10.3 Gravel stone – 10.3

90

75

13

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Comparing the data presented in Table 3, it can be seen that melting temperature of bitumen, which has a high melting temperature (100 °C) and is taken as raw material, decreases by about 2 times in all three cases of addition of additives. That is, the bitumen, which is not suitable for road construction due to its fragility, is modified and turned into a raw material suitable for road construction due to its physical and mechanical properties. While increasing the amount of waste from polyethylene production in the content of the composite from 1.5% to 7.7% does not significantly affect the penetration coefficient, high tensile strength of 13.5 mm is observed at 2.2% of polymer addition. This is explained by the fact that in the amount of 7.7% of polymer, its even distribution does not take place in the content of the composite. Like polyethylene, rubber crumb also shows a high result of 13.5 mm at low tensile strength of 2.2%. Black oil plays an important role in the even distribution of additives in the bitumen mixture. The third sample shows that the reduction of black oil from 22.1% to 11.6% causes the tensile index to decrease from 13.5 mm to 3.0 mm, which is explained by insufficient distribution of the components in the medium. Table 3. Physical and mechanical properties of polymer-bitumen compositions. N

Name

1

2

KiSh, °Csoftening temperature respectively SS 11506- 73

Needle penetration depth at 25 °C x 0.1 mm, SS 11501–73

Tensile strength of sm, at 25 °C SS11505–75

3

4

5

High melting bitumen (raw material)

110

16

3

1

Bitumen composition: % mass Bitumen- 77.5 Rubber crumb – 1.6 LDPE (waste) – 1.5 Black oil 19.4

54

134

9

2

Bitumen composition: % mass Bitumen- 73.5 Rubber crumb - 2.2 LDPE (waste) – 2.2 Black oil- 22.1

47

139

13.5

3

Bitumen composition: % mass Bitumen- 77.6 Rubber crumb - 3.1 LDPE (waste) – 7.7 Black oil - 11.6

43

143

3.0

We use ANFIS model [14–16] (Fig. 1.) to compute Y1, Y2 and Y3. Fragments of the obtained results are given in Fig. 2, 3, 4. These parameters help to increase the durability of pavement achieved by reducing fatigue and thermal cracking, as well as reducing susceptibility to high temperatures (for example, wear rutting, pushing, rockiness) and increased retention of aggregates in applications, for example, chip breakers. These indicators constitute a set of mutually

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confirming and mutually exclusive factors for complex systems, capable of aggregating fuzzy representations [17–19], the mechanism of which is closely related to both the quantitative ratio of components and the technology of their production.

Fig. 1. The structure of neural network

Fig. 2. Mass extensibility (Y1 )

Fig. 3. Softening temperature (Y2 )

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Fig. 4. Penetration depth (Y3 )

5 Conclusion Thus, the following conclusions can be reached within the framework of the conducted research. It was determined that the change in the amount of each of the components constituting the composition of asphalt has a noticeable effect on the physical and mechanical properties of asphalt. Softening temperature, needle penetration depth, tensile index characterizing elasticity have improved to the level that will ensure the production of high-quality consumer products within the mentioned limits. Research show that changing the ratio of the components has an active impact on the results. In the article, neural network was constructed according to the impact of the components on certain properties of the composition was investigated. Depending on the initial data, Mass extensibility (Y1), Softening temperature (Y2), Penetration depth (Y3) were determined through the neural network. These results are satisfactory and show that the used method is correctly applied.

References 1. Leonenko, V.V., Safarov, G.A.: Some aspects, modification of bitumen with polymeric materials. J. Chemistry and Technol. Fuel Oils 5, 43–48 (2001) 2. Nekhroshev, V.P., Rossel, L.P.: Modification of road bitumen properties with plasticizers based on tactical polypropylene. Oil and gas of Western Siberia: a collection of articles of the All-Russian Scientific and Technical Conference. Tyumen: Tyum.SU publishing house (2005) 3. Rozental, D.A., Tobolina, L.S., Fedosova, V.A.: Modification of bitumens with polymer additives. Oil Refining. Thematic Rev. 6, 1–48 (1998) 4. Schulte, W.: Temperatura bsenkungim Asphaltstrabenbau. Asphalt (BRD) (2003). http://yric. az/GTK_Book_1.pdf 5. Muhamatdin, I.I., Galimullin, I.N.: Adhesive additives for paving bitumen. Oil Refining and Petrochemistry 2, 33–37(2017) 6. Heritage Research Group, Firestrone Polymers. LLC (US) US Patent. Method for producing asphalt composition. Patent 2194729, USA (2004) 7. Graves, D., Burner, P., Herjenroter, W., Ris, T., et al.: Modified asphalt binders and asphalt pavement compositions. Patent 6569351, USA (2005)

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8. Federov, V.V., Syroezhko, A.M., Begak, O.Y., Proskuyakov, V.A., Borovikov, G.I.: Journal of Applied Chemistry 75, 1027 (2002) 9. Pozdnyaeva L.V.: Petroleum resin as a modifier of oil road bitumen. M, GP RosDorNil (2003) 10. Khristoforova, A.A., Filippov, S.E., Gogolev I.N.: Development of hard surfaces of career roads with the use of activated crumb rubber.Electronic scientific journal. Engineering Bulletin of the Don 4, 347–350 (2011) 11. Khristoforova, A.A., Sokolova, M.D., Potlov, S.N.: The influence of the mode of mechanical activation of crumb rubber on the most important operational properties of sealing rubbers. Materials Tehcnology, Instruments 13(1), 73–76 (2008) 12. Mamed Gasan-zade, D.S., Babaev, A.I., Hasanov, G.S.: News of Azerbaijan higher technical schools materials. In: II International Conference Reconstruction and Restoration in Postconflict Situations. Baku-2022, 24(2), pp. 179–184 (2022). http://rrpcs2022-conf.asoiu.edu.az 13. Mamed Gasan-zade, D.S., Babaev, A.I., Hasanov, G.S.: Polymer-bitumen composition. Azerbaijanian patent, I 2022 0025 (2022) 14. Aliev, R.A., Fazlollahi, B., Aliev, R.R., Guirimov, B.G.: Linguistic time series forecasting using fuzzy recurrent neural network. J. Knowledge. “Education” Society of Azerbaijan Republic.Series Business: 3–13 (2005) 15. Aliyarov, R.Y., Gardashova, L.A., Hasanli, N.I.: Predicting porosity through fuzzy logic based methods from south caspian basin data. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 268–274. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_33 16. Ercan, O.: Artificial neural network based modelling of the Marshall Stability of asphalt concrete. Expert Syst. Appl. 38(5), 6025–6030 (2011). https://doi.org/10.1016/j.eswa.2010. 11.018 17. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 18. Gardashova, L.A.: Z-Set based inference using ALI-2 implication for control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 75–84. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-92127-9_14 19. Aliyeva, K.R.: Demand forecasting for manufacturing under Z information. Procedia Comput. Sci. 120, 509–514 (2017). https://doi.org/10.1016/j.procs.2017.11.272

Logical-Linguistic Model for Reactor Cleaning from Impurities E. A. Melikov(B)

, T. M. Magerramova , and A. A. Safarova

Azerbaijan State Oil and Industry University, Baku, Azerbaijan [email protected], [email protected]

Abstract. The study of one chemical-technological complexes class as a control object and the analysis of the solving state the problem of these complexes optimal control shows that one of the most important tasks is the automating problem the control of the catalytic apparatus that is part of these complexes. Thus, the main and complex apparatus of the chemical-technological complex for the propylene production is the reactor for the hydrogenation of acetylene compounds. It is a complex physicochemical system in which a multiphase, multicomponent, inhomogeneous continuous medium is distributed within the working volume of the catalytic apparatus and changes in time, at each point of which and at the phase boundary there is a transfer of mass, momentum, energy. The operation of the apparatus under study in incomplete information conditions and the complexity of constructing optimal control trajectories leads to the need to develop a reactor control system based on a logical-linguistic current situations description. Due to the variability of the non-stationary process physicochemical characteristics in the reactor, as well as the incompleteness of the rules linguistic table, due to the impossibility of taking into account all possible situations, the article presents a fuzzy control algorithm. It is implemented as a fuzzy logic controller with structural and parametric adaptation, with self-learning elements, which provides an adequate display of the control strategy. This facilitates the effective control of the process under study and ensures the required quality of the resulting propane-propylene fraction at the reactor outlet, and hence commercial propylene at the considered chemical-technological complex outlet. Keywords: Management · Uncertainty · Fuzzy set · Affiliation function · Oil and gas industry · Numerical methods · Static models · Dynamic models

1 Introduction The main difficulty in the management of chemical-technological complex in propylene production is associated with determination of the optimal control trajectory for the process of selective methylacetylene and propadiene hydrogenation. The causes of these complications are as listed: the complexity of identifying the equations describing the physicochemical transformations (these transformations become sophisticated because of short contact time and the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 321–329, 2023. https://doi.org/10.1007/978-3-031-25252-5_44

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variable content of situational characteristics distribution in the reaction zone of the apparatus as well as contributions due to temperature of acetylene compound hydrogenation process and the active surface of the catalyzer in the reactor); high costs and in some cases impossibility of carrying out experiments. Additionally, the speed at which characteristics of technological processes exacerbates their full compatibility and even, if possible, leads to drastic overcomplication of the apparatus control system with respect to the static error in adequacy.

2 Statement of the Problem In numerous existing scientific works, to identify the internal processes of such contact reactors, preference was given to mathematical models based on the kinetic representation of catalytic transformations, as well as mixed models. The reason for this is search for reliable mathematical models for solving the issue of controlling the reaction apparatus. This model comprehensively describes the work surface and accounts for catalyst activeness loss. However, considering the lack of information on physicochemical transformations in the operating catalytic apparatus, difficulty of determining catalyst activeness, numerous situational variables and presence of complex relationships among them regime parameters and loadings complexity of determining the rate of elementary reactions in the catalytic reactor, the wide range of quantitative and qualitative characteristics variation of the raw materials leads to utilizing impossibility universal regression analysis models. Because of this there is an issue of describing the operation of acetylene hydrogenation reactor through utilizing the information on quality by using the summarization of the staff knowledge and experience. It is worth mentioning that sometimes automatic process control systems specialists need to consider factors that may be impossible or difficult to formalize. The degree of complexity of such technological processes is so high that the application of deterministic and stochastic mathematical models describing their operation fails to give desired characteristics. In these cases, to identify the operating modes of the complex under consideration, it is important to use the apparatus of the theory of fuzzy sets [1–5]. In other words, the construction of adequate mathematical models for control systems can be based on fuzzy set theory, which allow for projection and synthesis of these systems [6]. The preparation of such intellectual control systems is based on logical-linguistic description of technological processes occurring in them. The control of the process in these systems is undertaken through use of fuzzy controllers. What lays in the intellectual fuzzy controllers application basis is using presenting and researching knowledge ways to generate “knowledge”. Thus, the industrial fuzzy controllers creation lately has been relying on the artificial intelligence principles which are undergoing active improvement in the cybernetics field. The essence of fuzzy controller synthesis is the ability to make use of its knowledge base (KB). KB is put forward as a collection of fuzzy control rules and it is presented in a form of fuzzy conditions statements.

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During generation of a KB the fuzzy controller[7–10] is given an objective, ensuring the desired control system transition characteristics, and the information on the control object and technological process. Fuzzy controllers capable of gathering the preliminary regulations collect the knowledge independently without an expert through method of trial and error whilst operating in a form of limited KB. The fuzzy logic control (FLC) synthesis is undertaken via these methods of self-organization. Below the automatic control system of a reactor incorporating use of fuzzy controllers based on fuzzy models and control algorithm application that are shown to be robust and trustable in practice is discussed. The control system of the catalytic apparatus is shown on Fig. 1. The control object operation description in these algorithms and models is done IN /Q IN OUT through both qualitative and quantitative information use. Here QH C3 H4 and TPPF 2 OUT is situational variable, F IN , Q IN , Q IN are control variables, QH PPF C3 H4 C3 H6 are disturbances 2 OUT and QC3 H4 is regulating quantity.

Fig. 1. Acetylene compound hydrogenation reactor control system

Linguistic variables (LV) used to describe the quantity and quality of raw material entering the reactor, regime parameters and quality requirements to final product are utilized in preparing the logical-linguistic description of the reactor. −

IN , Q IN IN Furthermore, Xj 1t (j1 =1, 3) correspond to LV FPPF C3 H4 and QC3 H6 describing OUT describing state, V corresponds to LV Q OUT disturbance, Yt corresponds to LV QH t C3 H4   2 − IN /Q IN OUT describing quantity; Uj 2t j2 =1, 2 correspond to LV QH C3 H4 and TPPF describing 2   − IN OUT controls; Uj 3t j3 =1, 2 correspond to LV (QIN H2 /QC3 H4 ) and TPPF describing

variations of control. Each one of Xj 1t , Yt , Vt , Uj 2t and Uj 3t LV Xj 1t , Yt , Vt , Uj 2t and Uj 3t was specified in the universal set. Then each was transfered to fuzzy divison which defines how many terms there are in the term set. The strength of input space term sets defines the maximum number of fuzzy control rules in the KB. Usually trial and error heuristic procedure is used to select the optimal fuzzy division.

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Here the term sets of LV components are defined as follows: T(Xj 1t ) = T(Yt ) = T(Vt ) = T(Uj 2t ) = T(Uj 3t ) = {NB, NM, NS, VNS, ZE, VPS, PS, PM, PB}. As follows, NB is negative big, NM is negative medium, NS is negative small, VNS is very negative small, ZE is zero, VPS is very positive small, PS is positive small, PM is positive medium, PB is positive big. The membership functions based on research of the discussed technological process are generated according to LV term sets. In addition, an expert specialists group is involved in the work, estimating the values of this process membership functions. The membership function is presented as shown below: μA (u) =

n 

ai /ui

i=1

Chainlike membership function allowing for its manipulation through fuzzy calculations is used here: μ(x) = e−a(x−b) , 2

where a is width, b is the angle coordinate of bell shape form. The possible situations description is given in a linguistic table form based on the formalization of the expert knowledge and information coming from the control object and through using LV term sets. The linguistic table of these regulations presented as collection of these linguistic rules is defined as follows: IF disturbance is χt , the control object position is γt , regulating quantity is νt and controls are ωt−1 , THEN the controls variations ωt−1 . Here χt = (χ1t , χ2t , χ3t ), γt , νt , ωt = (ω1t , ω2t ) and ωt = (ω1t , ω2t ) Xt = (X1t , X2t , X3t ), Yt , Vt , Ut = (U1t , U2t ) and Ut = (U1t , U2t ) are corresponding values of LV at the instance t. Each logical regulation defines a situation that may occur in the control object. The linguistic table based on experience and corresponding technological personnel knowledge is shown below (Table 1). When the next state vector of the control object arrives at the FLC input, the linguistic rules values describing the required control actions are determined using the Zadeh compositional rule and transferred to the control object as controls: ωt = χt ◦ γt ◦ νt ◦ ωt−1 ◦ Rt Rt is the current value of the relationship table, “°” means the max-min composition.

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Table 1. Logical-linguistic rules X1t

X2t

X3t

Yt

1

PS

2

PS

3

Vt

U1t ,

U2t

U1t

U2t

PS

PM

PS

PS

PS

PM

PS

ZE

PM

PM

ZE

VPS

PM

PS

PS

ZE

PS

PM

PM

ZE

PB

PM

PM

PS

ZE

4

PM

PM

PM

ZE

PM

PS

PM

ZE

PS

5

PS

PS

PM

PM

PB

PS

PM

ZE

PS

6

PM

PIS

PM

PM

PS

PM

PM

ZE

PS

7

PB

PM

PB

ZE

PS

PB

PS

ZE

PS

8

PS

PM

PM

ZE

VPS

PM

PM

ZE

NS

9

PM

PS

PM

ZE

PS

PM

PM

ZE

NS

10

PM

PM

PM

PM

PB

PS

PM

ZE

PM

11

PB

PB

PM

PS

PS

PS

PS

ZE

PM

12

PM

PM

PS

PS

VPS

PM

PS

NS

ZE

13

PB

PM

PM

PM

VPS

PM

PM

NS

ZE

14

PS

PM

PS

ZE

PS

PM

PM

VNS

VPS

15

PS

PM

PM

ZE

PB

PS

PS

PM

ZE

16

PB

PB

PM

ZE

PM

PS

PS

PS

PM

17

PM

PB

PS

PS

PS

PS

PB

NS

PS

18

PS

PM

PS

ZE

PM

PM

PS

PM

NS

19

PB

PM

PM

ZE

VPS

PB

PM

NS

NM

20

PM

PB

PM

ZE

PS

PS

PS

VNS

PS

21

PM

PB

PS

ZE

VPS

PM

PS

VNS

ZE

22

PB

PB

PM

ZE

VPS

PM

PM

VPS

VPS

23

PM

PS

PS

PM

VPS

PS

PB

NM

VPS

3 Fuzzy Control Algorithm Consider the proposed fuzzy control algorithm that describes the human experience of controlling the reactor under study, implemented on the basis of the developed logicallinguistic model in the form of a FLC with structural-parametric adaptation elements. At stage I, the actual fuzzy controller is implemented, which is determined by a set of rules (1). By  introducing a composite variable that is the input vector of the control system At = Xj , Yt , Vt , Ut−1 and, assuming that some vector at comes to its input, the logical inference rule for the FLC in in terms of the membership function is written in the form:   μωt = ∨ . . . ∨ ∨ ( ∨ μαt (at ) ∧ μRjt (at × ut ) , a1t ∈A1t

a6t ∈A6t ut ∈U t j∈P

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here μRjt (at × ut ) describes the mapping corresponding to the j-th LCR of the form (1). Here μRjt = ( ∧ μrjit (ait )) ∧ ( ∧ μrjkt (ut )), μαt (at ) = ∧ μαit (ait ), rjit - relation i∈I

i∈I

k∈K

table elements, I = {1, . . . , n}, P = {1, . . . , p}, K = {n + 1, . . . , n + k}. Further, at stage II, the analysis of the obtained solution is carried out. Moreover, if the resulting solution is approximated as undetermined and μαt (at ) ≈ 0 or μαt (at )  μRjt (at × ut ), ∀j ∈ P, then the output FLC is connected to the parametric adaptation block, thus forming a set It of all indexes i, for which μαt (at ) = μωt . If μωt is a unimodal function that allows full interpretation of the fuzzy correspondence ωt , then the output of the fuzzy controller is connected to the control object, otherwise the transition to the structural adaptation block is performed. At stage III, it is checked whether the response of the object νt fell into the allowable region (νt ∈ ϕt ). If this condition is met, then the transition to stage I is carried out (the output of the control object under consideration is closed with a fuzzy controller / ϕt and for the and a control corresponding to the current situation is generated). If νt ∈ term-sets introduced by the operator of the desired control changes ωt the inequality holds: μωt (μt ) ≤ ε, νt (μt−1 + μt ) ∈ ϕt ) then the transition to stage IV (parametric adaptation stage) is carried out. In this case, a set of all indices k is formed, for which:   μj0 kt (μt ) ≤ ε, j0 = arg max μat (at ) ∧ μRjt (at × μt ) . j∈P

/ ϕt and μωt (ut ) > ε, then the transition to stage V (the structural adaptation If νt ∈ stage) is carried out. It should be noted that the parametric adaptation of the FLC is implemented at stage IV. The transition to this stage from stage III means that the parametric assignment of / It does not match to the changed knowledge base of the decision the terms ait , ∀i ∈ / It is taken. maker. If the solution is approximated as undefined, then μαt (at ) ≈ 0, ∀i ∈ In this case, the parameters of the membership function are changed so that: μαt (at ) = c0 , where c0 is chosen in such a way that the fuzzy matching approximation ωt with the adapted membership function parameters is no worse than that obtained at stage I. As one of the options for choosing the parameter c0 , we used:   c0 = min μait (ait ) . If the transition is carried out from stage III, then it is necessary to solve the following system of equations:

μrjo kt (μt ) = c0 , ∀k ∈ / It . At the same time, structural adaptation is carried out when the current situation on the technological control object does not exist in the relationship table. In this case, μαt (at )

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does not prevent the fuzzy matching interpretation ωt (μαt (at ) > μωt ), however, the solution is approximated by contamination of several or all terms from T(Ur ) (transition from stage II). When moving from step III, the row for which μRt was the maximum is replaced. Replacement is carried out with the consent of the person making the decision. The issue of controlling the methylacetylene and propadiene hydrogenation reactor is governed by stabilization of propane-propylene fraction quality indices obtained at the catalytic reactor exit. These are shortly and fairly described above. Table 2. A fragment of the linguistic rules table obtained as a FLC self-learning result X1t

X2t

X3t

Yt

Vt

U1t ,

U2t

U1t

U2t

24

PM

PS

PS

PM

VPS

PS

PB

NM

VPS

25

PB

PB

PM

ZE

PS

PS

PS

PS

VPS

26

PM

PM

PS

PS

VPS

PM

PS

PM

VNS

27

PM

PS

PM

PS

PS

PM

PS

PM

VNS

28

PB

PS

PB

PS

PS

PM

PS

VNS

VNS

29

PB

PS

PB

PM

PM

PB

PS

VNS

VNS

30

PB

PB

PB

PS

PB

PM

PB

NB

VNS

31

PS

PM

PM

PM

PB

PB

PM

NB

VNS

32

PM

PS

PB

PS

PB

PB

PS

NM

VNS

33

PB

PB

PB

PS

PB

PM

PM

NB

NB

34

PB

PB

PM

PS

PM

PM

PS

NB

VNS

35

PS

PM

PM

PS

PB

PM

PM

NS

NS

36

PM

PS

PB

PM

PB

PB

PS

VNB

VNS

37

PM

PS

PB

PS

PB

PB

PS

NS

VNS

38

PB

PS

PB

PS

PM

PM

PS

ZE

VNS

39

PB

PM

PB

PS

PB

PB

PS

ZE

ZE

40

PB

PS

PB

PS

PB

PB

PS

ZE

NS

41

PB

PB

PM

PM

PM

PM

PS

NM

VNS

42

PM

PB

PB

PM

PB

PM

PM

NM

NS

43

PS

PS

PS

PS

PB

PB

PS

NM

ZE

44

PB

PB

PB

PM

PB

PB

PM

NB

ZE

Due to the variability of the physicochemical non-stationary process in the reactor (in particular, the drop in catalyst activity), as well as the incompleteness of the rules linguistic table, due to the impossibility of taking into account all possible situations, the logical-linguistic description becomes inadequate to the process described by it. It is clear that it is necessary to make changes to the logical-linguistic model, which are associated both with the need to clarify the parametric definition of the components linguistic variables term sets, and with the relationship table structure addition based on

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new knowledge of the technological personnel. In this regard, in the developed reaction apparatus control system with self-learning elements, an adaptive controller is proposed, which is a FLC with structural-parametric adaptation elements. Moreover, this controller consists of a fuzzy controller itself, output feedback blocks, structural adaptation, parametric adaptation, solution analysis, a memory device, as well as a fuzzy-to-clear value converter block. It should be noted that the table of relations at the first 60 steps of the regulator operation was supplemented with 20th rows. The corresponding correction of membership functions parameters a and b for linguistic variables term sets elements has been carried out. In addition, five lines in the rules linguistic table have been replaced. A fragment of the rules linguistic table obtained as a FLC self-learning result is presented in Table 2.

4 Conclusion Thus, the developed and presented logical-linguistic model, developed using the technological personnel knowledge and experience and the relevant measuring instruments readings, makes it possible to quite easily and effectively control the reactor for the selective hydrogenation of acetylene compounds in the propane-propylene fraction. For this, software has been developed that describes the algorithm proposed above for controlling the methylacetylene and propadiene hydrogenation reactor under study in a self-learning and self-configuring automatic control system for this catalytic apparatus, based on a logical-linguistic description of technological situations that arise in the control process. It should be noted that the control of the catalytic apparatus, observed using a FLC with structural-parametric adaptation based on the above logical-linguistic rules table and a fuzzy control algorithm, provides better (optimal) results compared to traditional quality indicators of the propane-propylene fraction, obtained at the reactor outlet, and reduces the low-quality commercial propylene amount to 0.5 ÷ 0.8% of the total volume. Approbation of the developed algorithm and control system in industrial conditions that confirmed their performance and efficiency was carried out.

References 1. Peng, X.T.: Generating rules for fuzzy logic controllers by function. Fuzzy Sets Syst. 36(83– 89), 98–105 (1990) 2. Dushdurova, N.I., Mammadkhanova, S.A.: Modeling of dehydrogenation and oxidative dehydrogenation of isopropyl alcohol over Ti-V-O catalyst. Adv. Intel. Syst. Comput. 1323, 596–603 (2021) https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104847314&doi= 10.1007%2f978-3-030-68004-6_7 3. Aliyeva, A.Z., Mamedova, N.A.: Two-stage catalytic process for producing unsaturated esters of naphthenic acids in ionic liquids. Theor. Exp. Chem., 136–141 (2020). https://doi.org/10. 1007/s11237-020-09647-1 4. Gardashova, L.A.: Synthesis of fuzzy terminal controller for chemical reactor of alcohol production. Adv. Intel. Syst. Comput. 1095 (2020). https://doi.org/10.1007/978-3-030-352493_13 5. Khalafova, I.A.: Research of the composition of gases produced in the catalytic cracking process under the influence of magnetic field. Process. Petrochem. Oil Refin. 1(1), 61–72 (2022)

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6. Melikov, E.A.: Principles of optimizing the control of propylene purification process from acetylene derivatives. In: The 7-th International Conference on Control and Optimization with Industrial Applications – COIA-2020, Azerbaijan, Baku, 26–28 August 2020, pp. 272–274 (2020) 7. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., M., Jamshidi, Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 8. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 9. Aliev, R., Aliev, F., Babaev, M.: Fuzzy process control nd knowledge engineering in petrochemical and robotic manufacturing. Verlag TUV Rheinland, Koln (1991) 10. Adilova, N.E.: Construction of fuzzy control system rule-base with predefined specificity. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 901–904. Springer, Cham (2019). https://doi.org/10.1007/978-3-03004164-9_119

Quantitative Assessment of the Risk of Failure and Vulnerability of Oil and Gas Pipelines at Underwater Crossings I. A. Habibov(B)

and S. M. Abasova

Azerbaijan State Oil and Industry University, Azadliq Streed 20, Baku, Azerbaijan [email protected]

Abstract. Currently, several routes are used to transport Azerbaijani energy resources, including the Baku-Novorossiysk, Baku-Supsa, Baku-Tbilisi-Ceyhan oil pipelines and the Baku-Tbilisi-Erzurum and TANAP gas pipelines. In addition, to meet the needs of the population and industrial enterprises within the country, there is a wide branching of the gas transmission system, the total length of which is more than 4,500 km for the transportation of high-pressure gas and about 40,000 km for low and medium pressure gas pipelines. All gas pipelines run along complex routes, including near sea shores, above and below rivers, mountain, steppe, forest and other places. The most dangerous sections of the routes are the places where rivers and sea shores intersect. Failures and damages of gas pipelines are largely determined by technical, technological, operational, geographical and other factors. At the same time, the problem of ensuring the safe functioning of gas pipelines when they cross rivers is of particular relevance. The situation is particularly difficult in mountainous and foothill areas, where the number of pre-emergency situations has recently increased due to the exposure of pipes as a result of general and lateral erosion. Forecasting the depression of the bottom in the cross sections of watercourses by pipelines for various purposes is one of the important tasks in the design of underwater pipeline crossings. This task is still far from being solved due to insufficient knowledge of riverbed erosion. Based on the above, the work is devoted to solving the problem of predicting the process of general erosion and exposure of gas pipelines at underwater crossings, taking into account the time to reach the maximum depth of erosion using linear stochastic differential equations. Keywords: Unified gas supply system · Gas pipeline · Forecasting · Exposure and depth of pipe erosion

1 Introduction The problem of ensuring the safe functioning of oil and gas pipelines when they cross rivers has become particularly relevant in recent years. The situation is particularly difficult in mountainous and pre-mountainous regions, where the number of pre-emergency © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 330–337, 2023. https://doi.org/10.1007/978-3-031-25252-5_45

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situations has increased recently due to the exposure of pipes, due to general and lateral erosion. Forecasting the lowering of the bottom in the intersections of watercourses by pipelines for various purposes is one of the important tasks in the design of pipeline underwater crossings. This task is still far from being solved due to the insufficient degree of knowledge of the erosion of riverbeds. A deeper analysis of the problem and the creation of adequate forecast models are needed to design the structures in question safe, taking into account the reasonable risk of pipeline exposure. The poor reproducibility of the phenomenon of erosion and exposure of gas pipelines, as well as their relationship with the variability of soil characteristics and long-term fluctuations in river flow, makes it appropriate to use probabilistic models and the theory of random process releases [1, 2]. Despite the well-known successes of hydrology in predicting the flow of rivers [3, 4], as well as studies on the permissible non-erosive velocities of the water flow, sediment movement, erosion and other factors (see [5, 6]), the deepening of the pipeline in the underwater crossing are considered too simplistic. When choosing the depth of laying, the risk degree of an unfavorable condition of the pipeline (exposure and rupture), accompanied by significant material [13–16] damage and significant environmental violations, is not taken into account. The main reason for the unreasonable choice of the depth of the pipeline should be considered an incomplete account of the random nature of the process of erosion - exposure of the pipeline. Thus, when choosing a depth margin and determining the risk of an unfavorable (failure) condition, one should first of all take into account the random statistical nature of the erosion (which is a classic example of a random process) and the variable nature of the flow of physical, mechanical and other processes during the erosion of the riverbeds, as well as the responsibility of the object under consideration for the damage caused in case of failure [7]. New opportunities for further risk reduction in assessing the resistance to erosion of riverbeds are hidden in the disclosure of the random nature of the deformation of riverbeds and the factors that cause it.

2 Modeling of the Process of General Erosion Solution of the problem of predicting the process of general erosion and exposure of gas pipelines at underwater crossings, taking into account the time to reach the maximum depth of erosion using linear stochastic differential equations. One of the important tasks in the study of erosion processes is the prediction of the time (period) of its stabilization. Due to the complexity of the process, the prediction of gaps in time has not been fully studied. Only for cohesive soils there is an expression for an approximate time prediction, derived on the basis of the fatigue theory of erosion [8, 9]. To describe changeable random processes of erosion, the methods of the theory of Markov processes, the so-called processes without memory, seem to be the most effective. These include, in particular, stochastic kinetic equations used in physics to study diffusion and other similar processes. In [10], the stochastic differential equation (SDE) was used to describe the erosion process dy = m0 dt + σ dx(t)

(1)

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where y(t) is the defining parameter (in this case, the depth of the fracture); m0 , σ respectively, the average rate of change of the determining parameter and its standard deviation; x(t) is a random component of the Gaussian process. The main task of the analysis of the erosion process is to determine the distribution of time until the greatest depth of the total erosion is reached. This problem is similar to the problem of the first achievement by process (1) of the upper boundary of the region. Obviously, it can be solved if the conditional probability density of the transition of process (1) from one state to another is known. The conditional transition density for a Markov process of diffusion type is described by the Fokker-Planck-Kolmogorov (FPK) equation, which for process (1) is written as σ 2∂ 2P ∂P ∂P + m0 − =0 ∂t ∂y 2∂y2

(2)

The solution of this equation under the boundary conditions corresponding to the case of the monotonic nature of the realizations of the process (1)   P(y, t)y=−∞ = P(y, t)y=+∞ = 0 (3) and initial condition P(y, t)|t=o = δ(y)

(4)

where δ(y) – delta function, makes it possible to determine the density f (t) of the distribution of the time of the first achievement by the process of a given threshold H, which is expressed as H f (t) = −∞

∂P ∂y ∂t

(5)

The distribution function of the time of the first achievement by the process (1) of the given boundary H is represented as   μ−t (6) P(t) =  √ , αμ t where α - is the significance level; μ = H/m0 ; F(Z) - probability integral given tabularly in reference manuals on mathematical statistics. The value of the time t of the first achievement of the process (1) is obtained by resolving the equation with respect to t μ−t √ , in this case, the value of Z is determined from the equality F(Z) = P g , where Z = αμ t Pg - specified acceptable level of non-failure operation (usually Pg = 0,9 is accepted). In the case when the realizations of the random process y(t) are nonmonotonic curves, instead of (6) we have the equality       t+μ μ−t 2  − √ . P(t) =  (7) √ − exp 2 α μ αμ t αμ t

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However, in practice, the values m0 and σ generally depend on t and y, i.e., the erosion process is described by the stochastic differential equation (SDE) dy = a(t, y)dt + b(t, y)dW (t),

(8)

where a(t, y) and b(t, y) are nonrandom functions; W(t) is the standard Wiener process, dW(t) = V(t)dt, where V(t) is white noise with intensity ν(t) [11]. We will consider a linear SDE, i.e., Eq. (8), in which a(t, y) = α0 + α1 y, b(t, y) = β0 + β1 y

(9)

In this case, Eq. (8) has a unique solution. Under condition (9) and the restriction β1 = const = 0

(10)

the solution of Eq. (8) obeys the normal distribution law. Let’s indicate by U(t) the solution of Eq. (8) under condition (9) and consider the problem of determining the distribution law for the residence time of a Markov random process U(t) in a given region (u1 , u2 ). Let us introduce into consideration the probability density w(τ , y) that at time τ the ordinate of the random function U(t) will be in the interval (y, y + dy) provided that in the time interval (t, t + T) the value of the ordinate has never gone beyond the boundaries of the region (u1 , u2 ), i.e. Let us consider the probability density w(τ, y) that at the moment of time the ordinate of the random function U(t) will be in the interval (y, y + dy) provided that in the time interval (t, t + T) the value ordinate has never gone beyond the boundaries of the region (u1 , u2 ), i.e. u1 ≺ U (t) ≺ u2

(11)

during the time interval (t, τ ), τ = t + T. Then the probability W(τ) of not reaching the boundaries of the region (11) by the time τ = t + T is determined by the equality u2 W (τ ) =

w(τ, y)dy.

(12)

u1

Let’s denote by ƒ 0 (θ ) the probability density of the time of the function U(t) in a given area. Obviously, if by the time τ the ordinate of the function has never reached the forbidden boundaries u1 and u2 , then this means that the time θ of staying in the allowable ∞ area will be at least (τ − t) and the probability of this event is equal to fθ (θ )d θ. On the other hand, this probability is determined by formula (12). Hence ∞

u2 fθ (θ )d θ =

τ −t

τ −t

w(τ, y)dy u1

(13)

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Here, by differentiation with respect to τ we get u2 f0 (θ ) = − u1

 ∂w(τ, y)  ∂W (τ ) |τ =t+θ τ =t+θ dy = − ∂τ  ∂τ

(14)

When the moment of crossing the boundary of the region (11) (u1 or u2 ) is taken as the initial moment of time, formula (14) gives the law of time distribution between two successive crossings of the boundaries of the region, i.e. the residence time of the random function U(t) in the allowed area from the moment of entry into this area until the moment of exit. Having a probability density ƒθ (θ), it is possible to calculate the mathematical expectation of the residence time of the function U(t) in the given area: ∞ θ = M (θ ) =

θ fθ (θ )d θ .

(15)

0

Integrating by parts and taking into account that W(∞) = 0, W(t) = 1, we obtain ∞ θ=

W (τ )d τ .

(16)

t

Since under the condition (9) a(t,y) = a(y) and b(t, y) = b(y), then U(t) is a stationary Markov process. In this case w(τ , y) will not depend on t and τ separately, but only on the difference (τ -t) and, therefore, ∂w ∂w =− ∂t ∂τ

(17)

On the other hand, until the boundary of the allowed region is reached, the function w must satisfy the first Kolmogorov equation ∂w 1 2 ∂ 2 w ∂w + a(x) + b (x) 2 = 0 ∂t ∂x 2 ∂x

(18)

where x is the value of U at time t. After simple transformations, taking into account (16) and the condition that the functions a and b are independent of time, from (18) we obtain the equation: d 2θ dθ = q(x) + p(x) 2 dx dx where indicated p(x) = 2a(x)/b2 (x), q(x) = −2/b2 (x). The general integral of Eq. (19) will be [1]: ⎧ x3 x3 x ⎪ p(x1 )dx1 ⎨x3 p(x1 )dx1  }dx3 + c2 θ(x) = e x 2 x2 q(x2 )dx2 + c1 ex ⎪ ⎩  x

x

(19)

(20)

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where x is any value of U taken as the initial value, and the constants c1 and c2 are determined from the boundary conditions θ (u1 ) = θ (u2 ) = 0

(21)

expressing the fact that if at first the ordinate of the random process was equal to one of its maximum allowable values, then the residence time of the random function inside the allowable region is equal to zero. Putting in (20) x = u1 and taking into account (21), we obtain u2 x3 c1 = −



ex

x3 p(x1 )dx1

· q(x2 )dx2 dx3

u1 u1

u2

c2 = 0,

−

e

x2

(22) p(x1 )dx1

u1

dx2

u1

Under conditions (9)–(10) p(x) =

2 (α + α1 x), q(x) β02 0

= − β22 and θ(x) is calculated 0

by formulas (20) and (22) using two-dimensional quadrature formulas [12]. In particular, when α1 = 0 formulas (20) and (22) have analytical expressions:       2α 2α 2 − 20 (x−x ) − 20 (x−x ) β 1 β0 2 1 θ (x) = 1 − e β0 − (x − x1 ) + c1 0 1 − e β0 , (23) 2 α0 a 2α0  2α c1 =

2 β02

−

1 α0

1−e

1−e

−

−

0 (u −u ) 2 1 β02

2α0 (u2 −u1 ) β02

(24)

We apply formulas (23) and (24) to solve the example from [10].

3 Application of the Model Let’s consider an example where it is required to determine how long it will take for an underwater pipeline to become exposed when crossing a river. The limiting depth of erosion H = 2 m and the level of non-failure operation Pg = 0.9 are set. There are data on the estimated depth of erosion (in meters) obtained from observations of the maximum flow of the river: 2000 - 1.35; 2004 - 0.89; 2008 - 1.15; 2012 - 0.90; 2016 1.20. Let’s assume x  = 0.89, x = 0.9, u1 = x  = 0.89, u2 = 2. By formula (24) we find c1 = 2211.97. Substituting c1 into (23), we get θ (x) = 10.33. Since the initial data are given with a countdown of 4 years, then 10.33 × 4 ≈ 41 years, starting from t = 2012 (which corresponds to x = 0.9). Therefore, the time required to expose the pipeline during washout is 38 years. For comparison, it should be noted that approximately the same time (35.95 years) was obtained from the calculations in [10]. However, the calculations in [10] were made according to the simplified formula Pg = F(z), which is valid only in the case when the process realizations are monotonic curves. In the case

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of non-monotonic realizations of the process (this is the case we are dealing with in the considered example), the required time t will be determined from Eq. (7) at P(t) = Pg . The formulas for calculating the maximum rupture depth H are given in [9] both for cohesive soils and non-cohesive soils, heterogeneous in size and for foundations made of rocks. Satisfactory agreement between the calculated maximum depths of the erosion funnel and the observed ones indicates the acceptability of the H calculation schemes given in [9] and some (not quite strict) assumptions made in this case.

4 Conclusions Thus, designing the depth of oil and gas pipelines at underwater crossings requires the study of the random statistical nature of river erosion. For this purpose, the problem of predicting the process of general erosion is solved in this work, taking into account the time to reach the limiting depth of erosion using linear stochastic differential equations. The proposed assessment of the degree of risk of the onset of an unfavorable state of the pipeline (exposure and rupture) at underwater crossings will contribute to the development and rapid deployment of systems for preventing and eliminating emergency situations. A similar methodology based on the use of stochastic kinetic equations can be used to predict the vulnerable state of territories and objects under the impact of mudflows.

References 1. Sveshnikov, A.A.: Applied Methods of the Theory of Random Functions. 3rd edn, 463 p. Lan, St. Petersburg (2011). (in Russian) 2. Kovyazin, V.F.: Applied Methods of the Theory of Random Functions: Study Guide, 464 p. Lan, St. Petersburg (2016). (in Russian) 3. Ratkovich, D.Ya.: Actual problems of stochastic hydrology. Water Resour. 27(6), 645–654 (2000). (in Russian). https://doi.org/10.1023/A:1026609817870 4. Naidenov, V.I., Shveikina, V.I.: Nonlinear models of fluctuations in river flow. Water Resour. 29(1), 62–67 (2002). https://doi.org/10.1023/A:1013801308608. (in Russian) 5. Begam, L.T., Lishtvan, L.L., Muromov, V.S.: Deformations of Bridge Beds (Ed. “Transport”), p. 200 (1970) 6. Zhuravlev, M.M.: Local erosion at the bridge supports. “Transport”, p. 113 (1984) 7. Mirtskhulava, Ts.E.: Prediction of General Erosion in Bridge Crossings and in Places Where Oil and Gas Pipelines Cross Rivers, Taking into Account Time, p. 39. Academy of Sciences of Georgia, Tbilisi (2001) 8. Grishanin, K.V., Degtyarov, V.V., Seleznev, V.M.: Waterways. Transport, p. 400 (1986) 9. Mirtskhulava, Ts.E.: Fundamentals of Physics and Mechanics of Channel Erosion. Gidrometeoizdat, p. 304 (1988) 10. Mirtskhulava, Ts.E.: Assessment of the risk of failure and vulnerability of oil and gas pipelines at river crossings. Oil Ind. 3, 96–99 (2005) 11. Pugachev, V.S., Sinitsyn, I.N.: Stochastic Differential Systems. Nauka, p. 560 (1985) 12. Kahaner, D., Mowler, K., Nash, S. Numerical Methods and Software. Mir, p. 575(1998)

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13. Aslanov, J.N., Sultanova, A.B., Huseynli, Z.S., Mustafayev, F.F.: Determination of radial strains in sealing elements with rubber matrix based on fuzzy sets. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 765–773. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-921279_101 14. Gasanova, N.A.: Definition of mechanical indicators of plastic details of the oil field equipment. Int. J. Innov. Res. Comput. Sci. Technol. 8(4), 313–314 (2020). https://doi.org/10. 21276/ijircst.2020.8.4.11 15. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 16. Babanli, M.B.: Fuzzy Logic-based Material Selection And Synthesis, World Scientific Publishing Company (2019). ISBN 9813276584, 9789813276581 17. Sultanova, A.B.: Development of an automatic parking algorithm based on fuzzy logic. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW-2021. LNNS, vol. 362, pp. 428–436. Springer, Cham (2022). https://doi.org/10. 1007/978-3-030-92127-9_58

Prediction of Energy Consumption in Residential Buildings Using Type-2 Fuzzy Wavelet Neural Network Rahib Abiyev1(B)

and Sanan Abizada2

1 Department of Computer Engineering, Near East University, Lefkosa, North Cyprus

[email protected]

2 Department of Electrical and Electronic Engineering, Near East University, Lefkosa,

North Cyprus [email protected]

Abstract. Residential buildings use a significant part of the total energy of the countries. The utilisation of energy is defined by consumer occupancy, construction materials used in buildings. The timely changes of these factors lead to vague and imprecise representations of energy consumption prediction. Fuzzy logic is a more suitable approach for modelling this problem. In this paper, type-2 fuzzy wavelet neural networks (T2-FWNN) is proposed for modelling the energy consumption prediction of residential buildings. The system implements type-2 fuzzy reasoning using wavelet neural network technology. A gradient descent algorithm using a cross-validation approach has been applied for the construction of T2FWNN system. The learning of T2-FWNN system is based on an adaptive procedure that adjusts learning rates for stabilisation of training. The constructed system is used for the prediction of energy demand in residential buildings of Northern Cyprus. The presented comparative results prove the effectiveness of the constructed T2-FWNN model and the suitability of the T2-FWNN in the prediction of energy demand. Keywords: Type-2 fuzzy sets · Energy prediction · Wavelet neural networks

1 Introduction Residential buildings utilize a significant part of the total electricity. Due to lack of financial incentives, this sector is not studied well in comparison to other industrial sectors [1, 2]. Various factors affect energy utilization in residential buildings. Human occupancy, the characteristics of residential buildings and the locations of energy stations have strongly influenced energy utilization. The buildings’ characteristics which are the size of the house, size of rooms, size of windows, number of rooms, number of windows, materials’ type used in the construction of the house are important variables that influence the energy consumption [2]. Also, economical factors such as the income of consumers, the price of energy, the frequency of using electrical appliances are important variables affecting energy consumption. As can be seen, the variables that affect the energy demand © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 338–345, 2023. https://doi.org/10.1007/978-3-031-25252-5_46

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in the building are different and also, the impacts of these factors on energy usage are vague and uncertain. The existence of uncertainties and imprecise information allows the use of fuzzy technology in evaluating the appropriate value of energy consumption. In this paper, we are considering the design of energy consumption using fuzzy set theory. Various approaches were used for the energy load prediction of residential buildings. They can be conditionally divided into physical modelling and data-driven methods [1, 2]. Physical models use thermodynamic rules for energy modelling. These are DOE-2 [3], EnergyPlus [4], ESp-r [5], DeST [6], TRNSYS [7], which can estimate the energy load of buildings. These programs allow to evaluate the effect of physical parameters on energy load. But these programs have a complex structure and need detailed information about residential buildings for the appropriate design of the model. Obtaining the physical parameters is difficult and sometimes substantial differences may occur between predicted model output and actual values [1, 7]. Nowadays, data-driven approaches based on computational intelligence techniques are actively used for modelling and control of industrial and non-industrial processes. These models use historical statistical data for the evaluation of the energy load. Various computational intelligence techniques were implemented for the prediction of energy load. These are ANNs [8], SVM [9], SVR [10]. The integration of different computational intelligence techniques was used to improve the performance of the prediction system [11, 12]. As shown above, energy consumption depends on the characteristics of residential buildings, locations of energy stations and it has strongly influenced by economical and demographic factors. The impacts of these factors on energy consumption are uncertain and vague. To handle these uncertainties, type-2 fuzzy logic is applied. Because type-2 fuzzy logic uses a fuzzy membership function (MP), it can handle uncertainties that existed in the rule base of the problem. Type-2 fuzzy logic was invented by Zadeh [13] and future improved by Mendel [14]. Type2 fuzzy sets are applied to solve many industrial and nonindustrial problems[15–20]. These are time-series forecasting [15, 16], channel equalizations [17], dynamic plant control [18, 19], servo system control [20], credit rating [21]. The development of the type-2 rule base is important for the design of the type-2 fuzzy system. In this paper, we are considering the integration of wavelet neural network (WNN) technology and type-2 fuzzy sets for the construction of the rule base. The design of such hybrid system decreases the design time of the system. In addition, WNN can model the local detail of nonlinear processes [22]. The integration of WNN and fuzzy sets were used for time-series prediction [16], dynamic plant control [19]. In this study, type2 fuzzy sets and WNN are integrated for modelling the energy demands of residential buildings. The paper is written as follows. Section 2 proposes T2-FWNN model used for the buildings’ energy demand. Section 3 describes the simulation of the T2-FWNN prediction system. The conclusions are given in Sect. 4.

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2 T2-FWNN Model for Energy Consumption In the paper, we are using TSK type rules, NN and wavelet technology for the design of T2-FWNN. Wavelet functions with different translation and dilation coefficients can describe various essential behaviors and features of the used nonlinear model. The rule number is also decreased because of this property. The used if-then rules are as follows: If x1 is A˜ j1 and . . . and xm is A˜ jm Then y1 is wjk

m

(1 − zij2 )e− i=1

2 zij 2

(1)

where, zij = (xi −bij )/aij , , (i = 1,..,m; j = 1,…,r). Aij and bij are dilation and translation. A˜ ji are type-2 membership functions (MFs), wij are coefficients, x 1 , x 2 , …, x m and y1 , y2 , …, yr are inputs and outputs, correspondingly. m is the number of inputs, r is the rules’ number, correspondingly. Figure 1 presents T2-FWNN system structure. As shown T2-FWNN consists of six layers. The first layer distributes inputs, the second layer presents MFs. In the paper, Gaussian is used for describing membership functions(mf). We used Gaussian mf with an uncertain mean. The Gaussian MFs μj (x i ) used in this paper are described as μj (xi ) = e

−

(xi −cij )2 σij2

(2)

where, x is the input signal with uncertain mean c ∈ [c1 ,c2 ], cij and σij are the centers and widths of the Gaussians, respectively. The second layer of T2-FWNN calculates upper μj and lower μj membership degrees using interval type-2 fuzzy sets and α-cut. _

  μA˜ j (xk ) = μA˜ j (xk ), μA˜ j (xk ) = [μj , μj ] k

k

(3)

k

In rule layer 2, the t-norm operation is utilised to find the fuzzy firing strange of each rule.

Fig. 1. T2-FWNN model

Prediction of Energy Consumption in Residential Buildings

  fj = min μA˜ (x1 ), μA˜ (x2 ), . . . μA˜ (xm ) ; m 1 2   f j = min μA˜ 1 (x1 ), μA˜ 2 (x2 ), . . . μA˜ m (xm )

341

(4)

j

where f and f j are upper and lower mfs, correspondingly. In the next layer using input signals the output of wavelet functions is calculated for each fired neuron. Here the number of rules is denoted as r and this value is equal to the number of wavelet functions used Ψj (z) =

 zij2  m  − 1  aij  2 1 − z 2 e− 2 ; yj = wj j (z) ij

(5)

i=1

where zij = (xi − bij )/aij . In the next fourth and fifth layer, the type-reduction and defuzzification operations [18, 19] is performed in order to find the output uk (k = 1,..,n) of the network.       r r r r (6) uk = p f j yjk / fj + q f j yjk / fj j=1

j=1

j=1

j=1

where yjk = wjk ·Ψ j (z), p and q are used to update the upper and lower portions. The design of the T2-FWNN system includes finding the proper values of c1ij , c2ij , sij , wjk , aij , bij , p, q (k = 1,..,n, i = 1,..,m, j = 1,..,r,) variables of the system. In this study, fuzzy clustering and gradient descent algorithms are applied to design T2-FWNN.

3 Simulations The T2-FWNN system is used for modelling energy consumption in residential buildings. For modelling, we used statistical monthly data, between 2004–2020 years, about the energy consumption in the residential building. The data was taken from Kib-Tek electricity company of North Cyprus. Using T2-FWNN model the design of the prediction model is accomplished. The cross-validation approach, gradient algorithms and fuzzy clustering are used for the training of the system. The performance of the designed system is measured using root mean square error (RMSE) and also mean square error (MSE).

2 2 1 N  d 1 N  d Yi − Yi ; RMSE = Yi − Yi (7) MSE = i=1 i=1 N N The solving of electricity consumption allows to plan electricity production in advance and prevent electricity deficiency problems. Using the dataset we organised training, validation and testing data. At first we used x(t), x(t − 2), x(t − 3), x(t − 8) and x(t − 9) in order to predict three-step ahead prediction x(t + 3). As seen 5-dimensional input vector is used to predict one-dimensional output vector. 10-fold crassvalidation and 200 epochs were used for simulation. Five, eight and ten rules are used for simulation purposes. The training division has been plotted in Fig. 2. With 10 rules, the error values

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of training, validation and testing were obtained as 0.052754, 0.052858 and 0.051163 respectively. Figure 3 depicts the results of the T2-FWNN system. Here solid line depicts the actual, dashed line depicts 3-step ahead prediction result of the T2-FWNN system. Figure 4 depicts a plot of RMSE for test division. Comparison has been done in order to demonstrate the efficiency of T2-FWNN model. Using the same statistical data, the design of the prediction system is implemented using neural networks (NN) and fuzzy neural networks (FNN). Table 1 describes the comparison of the prediction models using different rule numbers. In the second stage, the T2-FWNN system is used for one-step ahead prediction. Input signal was five-dimensional vector that included x(t), x(t − 1), x(t − 4), x(t − 5) and x(t − 11) items, output was x(t + 1). The results were obtained using 10-fold crossvalidation and 200 learning epochs. The RMSE values for training, testing and validation data were determined as 0.05825, 0.059 and 0.05747 correspondingly (Table 2).

Fig. 2. Training division

Fig. 3. Test division. 3-step ahead prediction. Solid line-actual output, dashed line-predicted output

The T2-FWNN model results are compared with the results of NN and fuzzy NN based prediction models. Table 2. Shows the comparative results. The obtained results indicate the efficiency of using T2-FWNN in the prediction of electricity consumption.

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Fig. 4. The error plot

Table 1. Comparative results Rules

MSE

RMSE

Training

Evaluation

Testing

Training

Evaluation

Testing

NN

10

0.00559

0.00613

0.00597

0.07482

0.07831

0.07727

Fuzzy NN

10

0.00471

0.00474

0.00419

0.06865

0.06886

0.06478

T2-FWNN

5

0.00414

0.00416

0.00407

0.06434

0.06450

0.06380

8

0.00304

0.00305

0.00299

0.05515

0.05526

0.05467

10

0.00278

0.00279

0.00262

0.05275

0.05285

0.05116

Table 2. The results of comparisons. MSE

RMSE

Train

Evaluation

Testing

Training

Evaluation

Testing

NN

0.00524

0.00532

0.00523

0.072415

0.072941

0.072334

Fuzzy NN

0.00477

0.00483

0.00471

0.069086

0.69526

0.068672

T2-FWNN

0.00339

0.003482

0.00330

0.058245

0.059007

0.057475

Comparisons of the different models were done in order to prove the efficiency of the proposed T2-FWNN. Multilayer Perceptron that uses backpropagation for learning (MLP), least media Lazy Kstar, squared linear regression(LeastMedSq), Linear regression, Radial basis function networks (RBF) that uses K-means clustering algorithm, radial based function network that uses supervised training, Support vector machine (SMOReg), Random Forest, NN, Fuzzy NN and T2FWNN. The simulations were done for 3- and 1-step ahead predictions (Table 3). Here NN, Fuzzy NN and T2FWNN were simulated using 10 hidden neurons. The results obtained from the comparisons indicate the suitability of using T2-FWNN in the prediction of electricity demand.

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R. Abiyev and S. Abizada Table 3. Comparative results. 3 ahead prediction

1-ahead prediction

MAE

RMSE

MAE

RMSE

Random Forest

0.0575

0.0783

0.0588

0.082

Bagging

0.0603

0.0834

0.0585

0.0821

Lazy Kstar

0.0636

0.0867

0.0651

0.0927

Linear Regression

0.0593

0.0811

0.0553

0.0766

RBF

0.0836

0.1022

0.0787

0.1001

RBF Regressor

0.0574

0.0779

0.0562

0.0774

SMOReg

0.0562

0.0801

0.0537

0.0775

LeastMedSq

0.0563

0.0798

0.0549

0.0773

MLP

0.07

0.0931

0.0672

0.0917

M5Rules

0.06

0.0821

0.0553

0.0766

NN

0.005971

0.077275

0.00523

0.072334

Fuzzy NN

0.004197

0.064787

0.00471

0.068672

T2FWNN

0.002628

0.051163

0.00286

0.057475

4 Conclusions The paper proposes T2-FWNN model for the energy consumption prediction in residential buildings. The design of the system is implemented using fuzzy classification and gradient descent algorithms. The cross-validation approach is applied to organise learning division. The designed system is applied for energy prediction in residential buildings of North Cyprus. The development of T2-FWNN is performed using statistical data for three- and one-step-ahead prediction. For the comparative purpose, the design of other techniques including NN and FNN is implemented. The comparisons of different models indicate the suitability of using T2-FWNN in the prediction of energy consumption.

References 1. Amasyali, K., El-Gohary, N.M.: A review of data-driven building energy consumption prediction studies. Renew. Sustain. Energ. Rev. 81, 1192–1205 (2018). https://doi.org/10.1016/ j.rser.2017.04.095 2. Tsanas, A., Xifara, A.: Accurate quantitative estimation of energy performance of residential buildings using statistical machine learning tools. Energy .ings 49, 560–567 (2012). https:// doi.org/10.1016/j.enbuild.2012.03.003 3. Simulation Research Group, Lawrence Berkley National Lab, Overview of DOE 2.2 (1998). http://ww.doe2.com/ 4. Crawley, D.B., et al.: EnergyPlus: creating a new-generation building energy simulation program, Energ. Build. 33(4), 319–331 (2001). https://doi.org/10.1016/S0378-7788(00)001 14-6

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5. Strachan, P.A., Kokogiannakis, G., Macdonald, I.A.: History and development of validation with the ESP-r simulation program. Build. Environ. 43(4), 601–609 (2008). https://doi.org/ 10.1016/j.buildenv.2006.06.025 6. Yan, D., Xia, J., Tang, W., Song, F., Hang, X.Z., Jiang, Y.: DeST—an integrated building simulation toolkit part I: fundamentals. Build. Simul. 1(2), 95–110 (2008). https://doi.org/10. 1007/s12273-008-8118-8 7. Fumo, N.: A review on the basics of building energy estimation. Renew. Sustain. Energ. Rev. 31, 53–60 (2014). https://doi.org/10.1016/j.rser.2013.11.040 8. Kumar, R., Aggarwal, R., Sharma, J.: Energy analysis of a building using artificial neural network: a review. Energ. Build. 65, 352–360 (2013). https://doi.org/10.1016/j.enbuild.2013. 06.007 9. Li, Q., Meng, Q., Cai, J., Yoshino, H., Mochida, A.: Applying support vector machine to predict hourly cooling load in the building. Appl. Energ. 86, 2249–2256 (2009). https://doi. org/10.1016/j.apenergy.2008.11.035 10. Hong, W.C.: Electric load forecasting by support vector model. Appl. Math. Model 33(5), 2444–2454 (2009). https://doi.org/10.1016/j.apm.2008.07.010 11. Abiyev, R.H.: Fuzzy wavelet neural network for prediction of electricity consumption. AIEDAM: Artif. Intell. Eng. Des. Anal. Manuf. 23(2), 109–118 (2009). https://doi.org/10. 1017/S0890060409000018 12. Abiyev, R., Abiyev, V.H., Ardil, C: Electricity consumption prediction model using neurofuzzy system. World Acad. Sci. Eng. Technol. 8 (2005) 13. Zadeh, L.H.: The concept of linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5 14. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic System: Introduction and New Directions, 2nd edn, 684 p. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-51370-6 15. Karnik, N.N., Mendel, J.M.: Application of Type-2 fuzzy logic systems to forecasting of time-series. Inf. Sci. 120, 89–111 (1999). https://doi.org/10.1016/S0020-0255(99)00067-5 16. Abiyev, R.H.: A Type-2 fuzzy wavelet neural network for time series prediction. In: GarcíaPedrajas, N., Herrera, F., Fyfe, C., Benítez, J.M., Ali, M. (eds.) IEA/AIE 2010. LNCS (LNAI), vol. 6098, pp. 518–527. Springer, Heidelberg (2010). https://doi.org/10.1007/9783-642-13033-5_53 17. Abiyev, R.H., Kaynak, O., Alshanableh, T., Mamedov, F.: A Type-2 neuro-fuzzy system based on clustering and gradient techniques applied to system identification and channel equalization. Appl. Soft Comput. 11(1), 1396–1406 (2011). https://doi.org/10.1016/j.asoc. 2010.04.011 18. Abiyev, R.H., Kaynak, O.: Type-2 fuzzy neural structure for identification and control of timevarying plants. IEEE T. Ind. Electron 57(12), 4147–4159 (2010). https://doi.org/10.1109/TIE. 2010.2043036 19. Abiyev, R.H., Kaynak, O., Kayacan, E.: A type-2 fuzzy wavelet neural network for system identification and control. J. Franklin Inst.-Eng. Appl. Math. 350(7), 1658–1685 (2013). https://doi.org/10.1016/j.jfranklin 20. Kayacan, E., Oniz, Y., Aras, A.C., Kaynak, O., Abiyev, R.: A servo system control with time-varying and nonlinear load conditions using Type-2 TSK fuzzy neural system. Appl. Soft Comput. 11(8), 5735–5744 (2011). https://doi.org/10.1016/j.asoc.2011.03.008 21. Abiyev, R.H: Credit rating using Type-2 fuzzy neural networks. Math. Probl. Eng. (2014). https://doi.org/10.1155/2014/460916 22. Thuillard, M.: Wavelets in Softcomputing. World Scientific Press, Singapore (2001)

Modeling the Interaction of Components of a Distributed Information and Communication Environment Nodirbek Yusupbekov1(B)

, Nargiza Usmanova2

, and Shukhrat Gulyamov1

1 Tashkent State Technical University, 2 University Street, 100095 Tashkent, Uzbekistan

[email protected] 2 Tashkent University of Information Technologies named after Muhammad Al-Khorezmi,

108 Amir Temur Street, 100200 Tashkent, Uzbekistan

Abstract. The work is devoted to the development of scientific and methodological foundations for improving the efficiency of distributed computing networks and systems by organizing an info-communication network environment for transmitting and processing information. The concept of the study of information processes in network structures based on the principles of the organization of the intermediate software environment, which allows you to explore various mechanisms of intra-system and intersystem information exchange between system components. The principles of development and implementation of associative interaction components of info-communication network structures are proposed. They allow achieving intellectualization of their behavior. A methodological approach to the study and analysis of info-communication network structures and their capabilities is proposed, based on the application of the principles of creating a program description and allowing to determine of a set of objects (distributed elements) under the modes of function and processes of functioning of a distributed information environment from a detailed analysis of the principles and mechanisms for the interaction of services and resources of a distributed networks and ensure effective interplay of network and system components of info-communication systems both for the distributed architecture of the network itself and for interacting resources, services, and interfaces. Keywords: Associative interactions of components · Info-communication network structures · Distributed information environment · Intelligent agents · Distributed information system

1 Introduction A distributed system, which is of fundamental importance in various fields and areas of ICT, is today the object of research by many groups of the world community. These studies are stimulated by the ever-increasing role and the ever-wider development of various networks and technologies (such as the semantic Web, Grid computing, cloud computing, the Internet of things, and others), each of which has its principles and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 346–353, 2023. https://doi.org/10.1007/978-3-031-25252-5_47

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implementation features. But in general, all these technologies are based on creating a single environment that allows the user to receive services anywhere and anytime. However, in many areas, the capabilities of computing tools are limited due to the nature of information processing and the development of computer system control (for example, in the field of pattern recognition, problem-solving with incomplete information, predicting the results of an intended action and generating control, with real-time process dynamics, etc.). The possibilities of information technology that exist today involve the implementation of new approaches to information processing, united by the general properties of associative or intuitive information processing, which make it possible to process knowledge, carry out logical inference and, thereby, allow the intellectualization of computing systems [1, 2]. To date, despite the existence of enough solid theoretical and practical foundations for studying distributed systems, there are still insufficiently developed tools for describing the evolution in time of both the distributed systems themselves and the populations of programs operating in their structures; this is due to several reasons, among which, first of all, the heterogeneity of the composition and the dynamics of the behavior of the components, including the presence of unpredictably changing structures. Existing methods for describing and studying distributed systems, as an analysis of modern domestic and foreign works shows, are mostly unable to answer many questions in this direction, in particular, how software structures operating in distributed systems and networks can be formed for effective interaction. Components and creating a single distributed environment. In this regard, it is necessary to solve the problems of effective organization of distributed computing, expanding the corresponding functionality and improving the mechanisms for the interaction of many elements (components), taking into account functional processes of an intra- and inter-system nature, as well as complex infrastructure links due to network and system architectures [3, 4].

2 Conceptual Representation of a Behavioral Model of a Distributed Information Space The decomposition of the functional architecture of distributed systems takes into account the component construction of software (in the context of the software architecture, in which various structures are distinguished corresponding to certain aspects of the interaction of components, i.e. class structures, deployment structures, possible interaction scenarios, etc.) of a computing system, properties of components and relations between them. A distributed state information space represents a set of objects associated with or related to processes. At the same time, methodologically, the decomposition in relation to the components and the representation of the state space for various components is carried out in such a way that connections can be defined in the model at one level or another (Fig. 1). Such a representation allows you to define and detail a set of internal structures of a distributed environment, its components, their connections, and possible interactions between components, including the properties of these components, by specifying the corresponding structural elements identified by the interaction interface at various levels

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of abstraction (for example, through the structure software classes, possible scenarios for the interaction of components, etc.) [5]. Along with this, in a distributed space, the implementation of the application is carried out through a set of autonomous processes, it’s represented by a multi-agent system and is supported by the underlying environment, i.e. the proper degree of functionality can be provided at the required level of consideration, which makes it possible through the behavioral model of the distributed environment (space) to move to the programming model, and, accordingly, to the software architecture (SW) or modification of the process of its development. Considering that the behavior of an agent in a multi-agent system is identified by its control system, an agent control scheme is considered, the development of which is an important part of solving the problem.

Fig. 1. Conceptual representation of the behavioral model of the distributed space and its relationship with the model of the environment.

The agent control scheme in the conceptual representation of the distributed space behavioral model is shown in Fig. 2. In the distributed space, depending on the task, a set of objects is formed, the behavior of objects, their properties, the establishment of relations between objects, the interfaces for each object and the implementation of the object are specified. It is important to substantiate the fact that in OOP the computational process is understood as a system assembled from modules that interact with each other and have their own ways of processing incoming messages [6]. Based on sound modeling principles, the implementation of the relevant blocks of the above scheme and the optimization of the behavior of agents takes into account the following factors when modeling: 1. Evolutionary search: a module of communication with other agents (highlighted in the diagram by a dash-dotted line) - a model of an associative environment. 2. Individual learning and action choice: goal and evaluation module - Hopfield neural network model and tensor transformation. 3. Exchange of experience between agents as a result of communications: effective interaction of components in a distributed environment - a model of a multi-agent system based on fuzzy sets.

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At the same time, the implementation of the modeling principles for each of them is determined by the corresponding model, taking into account the principles of multidimensional decomposition.

Fig. 2. Agent control scheme in the conceptual representation of the behavioral model.

Modeling of evolutionary search. Under the provisions of the theory of intelligent systems, the implementation of information processing and control technologies, and, consequently, the organization of the computational process largely depends on the implemented principle of organizing the system in each specific case, on the basis of which models of dynamic objects and processes are presented, as well as from a number of other factors. At the same time, changes occurring as a result of information interactions between sets of elements of the same hierarchy level can be both quantitative and qualitative. The former is characterized by changes within information systems, the latter by changes in the hierarchical structure, as well as changes in relationships and interconnections between sets of information systems at different levels of the hierarchy. For quantitative analysis of information processes, determination of the effective configuration of the interaction of network components, and a detailed assessment of the functioning of information systems, a systematic approach is used that makes it possible to describe information processes based on associative links [7]. The associative environment plays the role of a communication system (Fig. 1); association or associative connection - the establishment of similarity/difference relations between the representations of two or more objects or events, and the defining characteristic of the space of a multi-coordinate associative environment is the implementation in it of the chosen measure of similarity, interpreted as the distance between the analyzed information objects, presented in the form of ordered sets of elements of some sets, based on the introduced space metric. Using the possible manifestations of the properties of

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information objects in the network, based on the concepts of associative environments, one can determine [8]: – information field Q as a set of information about the state space of the information system; – hierarchy level of the information field QL (L- hierarchy level) - information from the information field Q, which can be reflected by information systems of a certain level of organization of the level  model in all sets ofcells of the corresponding L-th (not higher) hierarchy level U PK(L) K = 1..Z..X – the layer of the hierarchy level of the information field QJ (L) (J -layer index) - information available to a separate subset of information systems levelof the hierar   of a certain chy of sets of elements of the L-th hierarchical level U PK(L) k = 1..Z , U (PK(L) ) . The above provisions are applicable when modeling information processes: when modeling a network graph G(V , R(V )) can be represented by a set of all possible pairs of nodes D0 : D0 = {(s, d )|s, d ∈ V , s = d }, where the first element of the pair will correspond to the source node that initiates some information flow, and the second to the recipient node. Thus, any task associated with information transformation can be described as a set of tasks for the interaction of virtual elements HK(L) , DK(L) and UK(L) of the corresponding network nodes. If V1 are network nodes, represented by a set of virtual objects, characterizing information interactions of information systems of different levels V1 , (V1 ⊂ HK(L) , DK(L) , KK(L) ):     N N N c c s s d d min c ∈ Pc i,j=1 Uij Cij + i,j=1 Hij Cij + i,j=1 Dij Cij , i=j

s∈Ps

i=j

d ∈D

i=j

where: N - set of elements of the same level; Pc - processes of the source node; Ps - processes of the receiving node; Cijx - the conditional cost of communication when requesting an information object on element j from element i. It is obvious that the value of Cijx will be determined by the efficiency of management processes for heterogeneous components (objects) in a distributed environment formed by info-communication network structures. The conditions for the execution of this expression can be restrictions on access to a resource, features of the application implementation, etc. It is important to note that in such a representation, two concepts are used to describe the task of information interaction of objects in a distributed environment: data (as a result of information exchange) and calculations (as a process), which are different for different applications. The efficiency of a distributed environment is determined by and depends on the results of managing the processes associated with providing data and performing calculations. The data is described by the attributes of the entities in the environment, and the calculations are related to the behavior of the entities [9]. A formalized description of the system-network connections between the components of a distributed system based on the concepts of associative environments allows, therefore, the most complete mutual mapping of various network architectures, to represent the interaction of network elements, and also to describe the application functionality of various scenarios and solutions for the implementation of services (applications).

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A distributed application is considered to consist of many processes (programs, computing resources, operating systems, and other processes) performing a task, while a communication network passes messages between processes in a coordinated manner to exchange data and information). The functionality of a distributed environment, and, accordingly, its functional architecture, is completely determined by the needs of application processes in the transfer of various types of information. The system model is described by a graph, the vertices of which represent processes, and the edges are directed communication channels. A distributed application (according to the distributed application model and the system model for a software component proposed in the third chapter) consists of a set of p1 , p2 , pi , ..., pn processes that interact via mij message exchange. In general, the set of states of processes and communication channels is the state of distributed computing. For process pi , event x is received as eix ; for message m send and receive events - send (m) and rec(m) respectively. If events occur, this leads to changes in the corresponding processes and channels and a change in the state of the system: an internal event changes the state of the process to which it refers. Events for any process are linearly ordered as they occur: the execution of process   pi is a sequence of events ei1 , ei2 , ..., eix , eix+1 , ... denoted as Si , i.e. Si = (si → i), where si is the set of events initiated by process pi , and the relation → i determines the linear sequence of these events [10]. The execution of a distributed application is a set of distributed events (processes), i.e. S = ∪i si . The → relationship between events in distributed computing determines the  order of events S = (S, →), that occur depending on the distributed algorithm, as well as the cause-and-effect dependence of the processes involved in distributed computing (the occurrence of events). In general, one can write: ⎧ y ⎪ eix → ei , ⎨ y y y eix →msg ei , ∀eix , ∀ei ∈ S, eix → ej ⇔ ⎪ ⎩ ∃ez ∈ S : ex → ez ∧ ez → ey , j i k k k Using of such relationships, can be written various procedures for the functioning of a distributed object from the point of view of information exchange. For the purpose of modeling a distributed space, the so-called internal model of an agent is developed as a representative of an object (or group of objects) in terms of object-oriented programming. Modeling individual learning and action selection in a distributed environment. To describe the behavior of elements and components of a distributed environment (space), objects (entities) with variable parameters and discrete time are introduced into consideration, on the basis of which certain properties of objects can be studied. In addition, such objects, from the point of view of the mathematical description, are introduced into the neural network space as its nodes interacting according to certain rules and algorithms, depending on the functional purpose of the object in the state space. Such a representation of the structure of the associative environment is close to a model organized according to the object principle. The justification for the transition to such an organization should be the concretization of the concept of an element of the environment, i.e. its states, input and output signals (depending on functions) [11, 12]. Then the associative element of the environment will be the minimum structural element with respect to which the associative environment appears to be homogeneous. At the level of objects, in a structurally

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homogeneous associative environment, functional nodes and blocks can be formed (for example, these can be blocks of basic associative cells). For a distributed associative environment, links between associative elements organize structures of another level. These can be, for example, structures for managing, storing and processing data; the number of internal states of an associative element must be sufficient to implement the functions of memory, interaction, comparison, etc. Associative elements make it possible to implement in the associative environment all the basic functions that the base associative cell has, and if the base associative cell realizes its capabilities due to the presence of functional nodes, then the associative elements implement these capabilities as part of the objects of the associative environment.

3 Conclusion Concepts, principles, and scientific and methodological foundations for solving the theoretical and applied aspects of the implementation of associative interaction in modern info-communication network structures of computer systems have been developed in the work. The proposed and substantiated methodology for the study of info-communication network structures allows, based on a single framework concept, to describe complex functional and information connections of an inter- and intra-system nature and confirms the validity of the initial hypothesis of the study: methods and algorithms of software engineering when fulfilling the postulate of separation and sharing of the potential of distributed information and computing resources in the area of their coordination and coordination, allow for effective interaction of nodes and components of info-communication network structures and optimal real-time control of computing resources, significantly expanding the potential of automated control and expanding the functionality of computing systems. For a formalized description of complex relationships in the organizational structure of an associative environment, the apparatus of neural networks can be used: the process of functioning of an associative environment is described on the basis of the Hopfield network, for which there are two modes: learning and classification; in the learning mode, based on the known vectors, the weight coefficients of the network are selected; in the classification mode, with fixed values of weights and input of a specific initial state of neurons, a transient process occurs. This network can be trained according to various rules; in this case, the training vectors are repeatedly presented until the values of the weights stabilize. Further, the vectors representing the vertices of a distributed network environment are studied on the basis of the concepts of a tensor, which is a multidimensional vector in a certain basis, the directions of the component axes of which are specified by the coordinates of the multidimensional space.

References 1. Soumitra, D., Benat, B.-O.: INSEAD, the global information technology report, 2012: living in a hyperconnected world. INSEAD and the World Economic Forum, Geneva (2012). https:// www3.weforum.org/docs/Global_IT_Report_2012.pdf

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2. Insights to drive stronger performance. http://www.gartner.com/technology/home.jsp. 3. Usmanova, N.: Featuring self-organization in distributed systems: the way to converge toward desired structure/ubiquitous computing and internationalization. Korea 4(1), 1–6 (2012) 4. Usmanova, N.B.: Determination of the optimal structure of telecommunications networks in the context of the introduction of new technologies. J. Prob. Inf. Energy 3, 26–32 (2001) 5. Yusupbekov, N.R., Aliev, R.A., Aliev, R.R., Yusupbekov, A.N.: Intelligent Control Systems and Decision Making. Uzbekiston Milliy Encyclopedia, Tashkent (2014) 6. Akimova, G.P., Soloviev, I.A., Tarkhanov, I.A.: Modeling the reliability of distributed information systems. IT CS 3, 79–86, (2019). 1014357/207186321190307 7. Kasymov, S.S., Usmanova, N.B.: On developing the environment for multiagent system of distributed computing: using the associations. J. Chem. Tech. Cont. Manag. 3, 72–76 (2015) 8. Weiss, G.: Multiagent Systems: A Modern Approach to Distributed Artificial Intelligence. The MIT Press, Cambridge (2000) 9. Moser, T., Mordinyi, R., Winkler, D., Melik-Merkumians, M., Biffl, S.: Efficient automation systems engineering process support based on semantic integration of engineering knowledge. In: International Conference on Emerging Technologies and Factory Automation, pp. 1–8. IEEE Press, New York (2011). https://doi.org/10.1109/ETFA.2011.6059098 10. Broy, M.: A model of dynamic systems. In: Bensalem, S., Lakhneck, Y., Legay, A. (eds.) ETAPS 2014. LNCS, vol. 8415, pp. 39–53. Springer, Heidelberg (2014). https://doi.org/10. 1007/978-3-642-54848-2_3 11. Liang, T.-Y., Shieh, C.-K., Zhu, W.: Task mapping on distributed shared memory systems using Hopfild neural network. In: Proceedings of the Communication Networks and Distributed Systems Modeling and Simulation (1997) 12. Yusupbekov, N.R., Igamberdiev, H.Z., Mamirov, U.F.: Adaptive control system with a multilayer neural network under parametric uncertainty condition. CEUR Workshop Proc. 2782, 228–234 (2020)

Fuzzy Approach to Analysis of the Temporal Variability of the Vegetation in a Specific Area Elchin Aliyev(B)

and Fuad Salmanov

Institute of Control Systems of ANAS, B. Vahabzadeh str. 9, AZ1141 Baku, Azerbaijan {elchin,fuad.salmanli}@sinam.net

Abstract. Existing remote monitoring technologies provide farmers with useful information about the current health status of crops. The ability of remote sensors to detect subtle differences in vegetation makes them indispensable tools for precision farming, providing a quantitative assessment of crops in a particular area of the field. Multispectral data from such sounding allows farmers to obtain the vegetation maps, reflecting the current state of crops. Such vegetation maps allow to analyze the state of plants in dynamics, as well as to predict yields. In precision agriculture, for the numerical interpretation of multispectral data, vegetation indices are used. These indices are obtained empirically, i.e., by conducting experiments with different wavelength ranges in the electromagnetic spectrum. The given article considers the annual dynamics of the development of the plant culture in a particular field by analyzing the corresponding time series of a particular vegetation index. The possibility of predicting the yield of a particular crop based on fuzzy modeling of such time series is considered. Keywords: Multispectral data · Vegetation index · Vegetation map · Fuzzy time series · Forecasting

1 Introduction Most sown crops are distinguished by successive changes in development phases, which are fixed by means of the spectral-reflective features of plants. One of the ways to study seasonal changes in the spectral-brightness characteristics of crops is the vegetation indices for each pixel of the vegetation map, which make it possible to quantify the features of the vegetation cover and the patterns of its change in the dynamics of development. Precision agriculture uses standard algorithms for predicting crop yields based on the analysis and modeling of the dynamics of the spectral-reflective properties of plants, which, as a rule, work with “crisp” averaged multispectral remote sensing data. At the same time, averaging the results of measurements of spectral ranges for calculating vegetation indices is one of the most common empirical operations in systems for collecting and processing multispectral data. However, multispectral remote sensing data, or, more specifically, the wavelength ranges in the electromagnetic spectrum,

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 354–363, 2023. https://doi.org/10.1007/978-3-031-25252-5_48

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should be considered weakly structured, that is, those that are known to belong to a certain interval [1]. For example, the maximum reflection of the cellular structures of plants is fixed in the wave range from 750 nm to 900 nm, which is the near infrared region of the electromagnetic spectrum. However, more adequate ways of reflecting such ranges of the electromagnetic spectrum are evaluative concepts, such as the terms “high”, “low”, etc., which can be formally described by appropriate fuzzy sets [1, 2]. Based on this paradigm, the importance and relevance of studying methods for predicting seasonal changes in the spectral-brightness characteristics of crops using fuzzy time series (FTS) that reflect the dynamics of the vegetation index and the corresponding plant reflection coefficients become obvious.

2 Problem Definition As a rule, the calculation of vegetation indices is based on two ranges of the electromagnetic spectrum of vegetation reflectivity [3]: on the reflection of plants in the red region (RED) of the spectrum (620 nm, 750 nm), which illustrates the greatest absorption of solar radiation by chlorophyll of higher vascular plants, and on the reflection of plants in the near infrared region (NIR) of the spectrum (750 nm, 900 nm), where the region of greatest reflection of the cellular structures of the leaf is concentrated. In the theory of precision farming, the most common indicator for assessing the state of vegetation is the NDVI (Normalized Difference Vegetation Index), which is established by the following formula NDVI =

NIR − RED NIR + RED

(1)

where NIR and RED are the reflection coefficients, which are calculated by mapping the red and infrared regions onto a unit segment [0, 1] by trivial equalities: RED = (λ1 − 620)/(750 − 620), NIR = (λ2 − 750)/(900 − 750), where λ1 ∈ (620, 750) and λ2 ∈ (750, 900). The task is to implement a fuzzy method for predicting seasonal changes in the spectral-reflective characteristics of crops based on the TS of plant reflection coefficients obtained by processing multispectral data for each pixel of the vegetation map. To test the fuzzy approach, appropriate TS were chosen as an example, which, on the scale of one fixed pixel, reflect the temporal variability of the spectral ranges RED and NIR (see Table 1 and Fig. 1) obtained from MODIS images (see Fig. 2) area in Jonesboro (USA, Arkansas) with geographic coordinates (−90.16, 35.81) [4]. Table 1 also summarizes the appropriate NDVI values calculated by (1).

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Fig. 1. NDVI TS as a reflection of the temporal variability of the RED and NIR coefficients.

Table 1. Temporal variability of NDVI. №

Date

NIR

RED

NDVI

№

Date

NIR

RED

NDVI

1

18.02.2000

0.2036

0.0958

0.3599

16

25.06.2000

0.8565

0.1452

0.7101

2

26.02.2000

0.3175

0.1445

0.3745

17

02.07.2000

0.8651

0.1453

0.7124

3

05.03.2000

0.3639

0.1523

0.4099

18

11.07.2000

0.8702

0.1455

0.7135

4

15.03.2000

0.3623

0.1623

0.3812

19

20.07.2000

0.3357

0.1256

0.4554

5

21.03.2000

0.2219

0.1025

0.3680

20

27.07.2000

0.1125

0.0678

0.2479

6

29.03.2000

0.1717

0.0835

0.3457

21

02.08.2000

0.3666

0.1348

0.4623

7

06.04.2000

0.1676

0.0845

0.3296

22

12.08.2000

0.6051

0.1245

0.6587

8

15.04.2000

0.1407

0.0765

0.2957

23

20.08.2000

0.5828

0.1463

0.5987

9

22.04.2000

0.1106

0.0659

0.2535

24

28.08.2000

0.4628

0.1354

0.5473

10

29.04.2000

0.1214

0.0689

0.2759

25

03.09.2000

0.3492

0.1158

0.5019

11

08.05.2000

0.1502

0.0815

0.2966

26

13.09.2000

0.3523

0.1233

0.4815

12

15.05.2000

0.1529

0.0813

0.3058

27

20.09.2000

0.3450

0.1389

0.4259

13

24.05.2000

0.1664

0.0855

0.3211

28

29.09.2000

0.2457

0.1125

0.3719

14

09.06.2000

0.4084

0.1324

0.5104

29

07.10.2000

0.2173

0.1045

0.3505

15

15.06.2000

0.5890

0.1356

0.6257

30

15.10.2000

0.2058

0.1056

0.3217

3 FTS: Initial Steps for Building a Predictive Model The existing approaches to modeling and forecasting the FCS imply the sequential implementation of the following steps: 1) construction of a universe covering all data of the TS; 2) TS data fuzzification; 3) identification of internal fuzzy relations and their grouping; 4) establishment of fuzzy outputs (forecasts) of the applied model and their defuzzification. One of the methods for constructing the universe and establishing the optimal number of qualitative criteria for evaluating weakly structured data was proposed in [5]. The essence of this approach is the sequential implementation of the following procedures. Step 1. Assorting all data {x t }t=1÷n into the ascending sequence {x p(i) }, where p is a permutation that sorts the data under condition: x p(t) ≤ x p(t+1) .

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Step 2. Determination of the average (AD) for all pairwise distance between any two consecutive values x p(i) and x p(i+1) (d i = |x p(i) – x p(i+1) |) by following formula: AD(d1 , d2 , ..., dn ) =

n−1 i=1

|xp(i) − xp(i+1) |/(n − 1)

and standard deviation σ AD by following formula  n−1 σAD = (di − AD)2 /(n − 1) i=1

(2)

(3)

Step 3. Identification of existing anomalies to be eliminated. For this purpose, the average distance and standard deviation values set in the previous step are applied. Pairwise distances that do not satisfy condition (4) must be removed. AD − σAD ≤ di ≤ AD + σAD .

(4)

Step 4. Recalculation the average AD for the remaining pairwise distance d i . Step 5. Determination the appropriate universe in the form U = [D1 , D2 ], where D1 = Dmin – AD; D2 = Dmax + AD; Dmax is the maximum among the TS data; Dmin is the minimum among the time series data. Step 6. Determination the appropriate number of qualitative criteria for evaluating the TS data by following equality m = [D2 − D1 − AD]/[2 · AD].

(5)

4 Modeling the NDVI FTS Based on the above procedures for the TS relative to NIR and RED reflectance (see Table 1), the final average distance ADNIR = 0.0144 and ADRED = 0.0022 were be established. Then, the universes for each TS are obtained in the form: • U NIR = [0.1106 − 0.0144, 0.8702 + 0.0144] = [0.0962, 0.8846], where 0.8702 and 0.1106 are the maximum and minimum among the NIR TS data, respectively. • U RED = [0.0659 − 0.0022, 0.1623 + 0.0022] = [0.0637, 0.1645], where 0.1623 and 0.0659 are the maximum and minimum among the RED TS data, respectively. Based on the application of formula (5), the optimal values of the number of evaluation criteria for estimation the NIR and RED reflection coefficient were obtained as: mNIR = [0.8846 − 0.0962 − 0.0144]/[2 · 0.0144] = 26.9158 ≈ 27, mRED = [0.1645 − 0.0637 − 0.0022]/[2 · 0.0022] = 22.2444 ≈ 22.

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Fuzzification of NIR and RED reflections is carried out by following trapezoidal membership function ⎧ ⎪ 0, x < akj ⎪ ⎪ x−aj1 ⎪ ⎪ ⎪ ⎨ aj2 −aj1 , aj1 ≤ x ≤ aj2 , μAj (x) = 1,aj2 ≤ x ≤ aj3 , (6) ⎪ aj4 −x ⎪ ⎪ , a ≤ x ≤ a , ⎪ j4 ⎪ aj4 −ak3 j3 ⎪ ⎩ 0, x > aj4 , the corresponding parameters of which are satisfied to following equations: aj2 – aj1 = aj3 – aj2 = aj4 – aj3 (j = 1 ÷ m) and presented in Table 2. As a result, obtained fuzzy analogues for all NIR and RED data are presented in Table 3. The modeling of the FTS provides for the detection of internal relationships, which in our case are reflected in the form of fuzzy implications “If , then ”. Internal fuzzy relationships are grouped by the following rule: • if the fuzzy set Ak is prerequisite for one or more fuzzy sets in the FTS, then the so-called 1st order group is localized relative to Ak ; • if the bunch of fuzzy sets Ai , Ai+1 is prerequisite for one or more fuzzy sets in the FTS, then the so-called 2nd order group is localized relative to Ai , Ai+1 . Groups of the 1st and 2nd orders of identified internal relationships for the NIR and RED TS are presented in Tables 4 and 5, respectively. Table 2. Fuzzy sets as qualitative criteria for evaluation of NIR and RED reflections. NIR TS

RED TS

Fuzzy set Membership function parameters

Fuzzy set Membership function parameters

ai1 A1

ai2

ai3

ai4

bi1

bi2

bi3

bi4

0.0637 0.0659 0.0681 0.0703

A2

0.0962 0.1106 0.1250 0.1394 B1 0.1250 0.1394 0.1537 0.1681 B2

A3

0.1537 0.1681 0.1825 0.1969 B3

0.0726 0.0748 0.0770 0.0792

A4

0.0770 0.0792 0.0814 0.0836

…

0.1825 0.1969 0.2112 0.2256 B4 …

A24

0.7576 0.7720 0.7864 0.8007 B19

0.1435 0.1457 0.1479 0.1501

A25

0.1479 0.1501 0.1524 0.1546

A26

0.7864 0.8007 0.8151 0.8295 B20 0.8151 0.8295 0.8439 0.8582 B21

A27

0.8439 0.8582 0.8726 0.8846 B22

0.1568 0.1590 0.1612 0.1645

0.0681 0.0703 0.0726 0.0748

0.1524 0.1546 0.1568 0.1590

Various approaches are used to determine “crisp” (defuzzified) predicts. The essence of one of them is as follows [6]. If the data for the i-th day is described in the form of the

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Table 3. FTS of reflection coefficients NIR and RED. №

NIR TS

№

RED TS

NIR

FS

RED

FS

1

0.2036

A4

0.0958

B7

2

0.3175

A8

0.1445

3

0.3639

A10

4

0.3623

A10

5

0.2219

6 7 8

NIR TS

RED TS

NIR

FS

RED

FS

16

0.8565

A27

0.1452

B19

B18

17

0.8651

A27

0.1453

B19

0.1523

B20

18

0.8702

A27

0.1455

B19

0.1623

B22

19

0.3357

A9

0.1256

B14

A5

0.1025

B9

20

0.1125

A1

0.0678

B1

0.1717

A3

0.0835

B5

21

0.3666

A10

0.1348

B16

0.1676

A3

0.0845

B5

22

0.6051

A18

0.1245

B14

0.1407

A2

0.0765

B3

23

0.5828

A17

0.1463

B19

9

0.1106

A1

0.0659

B1

24

0.4628

A13

0.1354

B16

10

0.1214

A1

0.0689

B1

25

0.3492

A9

0.1158

B12

11

0.1502

A2

0.0815

B4

26

0.3523

A9

0.1233

B14

12

0.1529

A2

0.0813

B4

27

0.3450

A9

0.1389

B17

13

0.1664

A3

0.0855

B5

28

0.2457

A5

0.1125

B11

14

0.4084

A11

0.1324

B16

29

0.2173

A4

0.1045

B9

15

0.5890

A17

0.1356

B16

30

0.2058

A4

0.1056

B10

Table 4. Internal relationships of the 1st order. NIR TS

RED TS

G1 : A1 ⇒ A2 , A10 , A11

G9 : A11 ⇒ A17

G1 : B1 ⇒ B1 , B4 , B16 G9 : B14 ⇒ B1 , B17 , B19

G2 : A2 ⇒ A1 , A2 , A3

G10 : A13 ⇒ A9

G2 : B3 ⇒ B1

G3 : A3 ⇒ A2 , A3 , A11

G11 : A17 ⇒ A13 , A27 G3 : B4 ⇒ B4 , B5

G4 : A4 ⇒ A4 , A8

G12 : A18 ⇒ A17

G4 : B5 ⇒ B3 , B5 , B16 G12 : B18 ⇒ B20

G5 : A5 ⇒ A3 , A4

G13 : A27 ⇒ A9 , A27

G5 : B7 ⇒ B18

G13 : B19 ⇒ B14 , B16 , B19

G6 : A8 ⇒ A10

G6 : B9 ⇒ B5 , B10

G14 : B20 ⇒ B22

G7 : A9 ⇒ A1 , A5 , A9

G7 : B11 ⇒ B9

G15 : B22 ⇒ B9

G8 : A10 ⇒ A5 , A10 , A18

G8 : B12 ⇒ B14

G10 : B16 ⇒ B12 , B14 , B16 , B19 G11 : B17 ⇒ B11

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E. Aliyev and F. Salmanov Table 5. Internal relationships of the 2nd order.

NIR TS

RED TS

G1 : A1 , A1 ⇒ A2 G2 : A1 , A2 ⇒ A2

G15 : A9 , A5 ⇒ A4 G1 : B1 , B1 ⇒ B4 G16 : A9 , A9 ⇒ A9 , A5 G2 : B1 , B4 ⇒ B4

G15 : B14 , B17 ⇒ B11 G16 : B14 , B19 ⇒ B16

G3 : A1 , A10 ⇒ A18

G17 : A10 , A5 ⇒ A3

G3 : B1 , B16 ⇒ B14

G17 : B16 , B12 ⇒ B14

G4 : A2 , A1 ⇒ A1 G5 : A2 , A2 ⇒ A3

G18 : A10 , A10 ⇒ A5 G19 : A10 , A18 ⇒ A17

G4 : B3 , B1 ⇒ B1 G5 : B4 , B4 ⇒ B5

G18 : B16 , B14 ⇒ B19 G19 : B16 , B16 ⇒ B19

G6 : A2 , A3 ⇒ A11

G20 : A11 , A17 ⇒ A27

G6 : B4 , B5 ⇒ B16

G20 : B16 , B19 ⇒ B19

G7 : A3 , A2 ⇒ A1 G8 : A3 , A3 ⇒ A2

G21 : A13 , A9 ⇒ A9 G22 : A17 , A13 ⇒ A9

G7 : B5 , B3 ⇒ B1 G8 : B5 , B5 ⇒ B3

G21 : B17 , B11 ⇒ B9 G22 : B18 , B20 ⇒ B22

G9 : A3 , A11 ⇒ A17 G10 : A4 , A8 ⇒ A10

G23 : A17 , A27 ⇒ A27 G24 : A18 , A17 ⇒ A13

G9 : B5 , B16 ⇒ B16 G10 : B7 , B18 ⇒ B20

G23 : B19 , B14 ⇒ B1 G24 : B19 , B16 ⇒ B12

G11 : A5 , A3 ⇒ A3

G25 : A27 , A9 ⇒ A1

G11 : B9 , B5 ⇒ B5

G25 : B19 , B19 ⇒ B19 , B14

G12 : A5 , A4 ⇒ A4

G26 : A27 , A27 ⇒ A27 , G12 : B11 , B9 ⇒ B10 A9

G26 : B20 , B22 ⇒ B9

G13 : A8 , A10 ⇒ A10

G13 : B12 , B14 ⇒ B17 G27 : B22 , B9 ⇒ B5

G14 : A9 , A1 ⇒ A10

G14 : B14 , B1 ⇒ B16

fuzzy set Ak , which has only relationship within the FTS, say Ak ⇒ Aj , then the fuzzy predict for the next (i + 1)-th day will be the set Aj . If there is a group of fuzzy relations, for example, of the form Ak ⇒ Aj1 , Aj2 , …, Ajp , then the union of fuzzy sets Aj1 ∪ Aj2 ∪ … ∪ Ajp is the fuzzy predict for the (i + 1)-th day. So, the defuzzified value of predict Ak is the abscissa of the middle of the upper base of the k-th trapezoid. For example, for the fuzzy predict A4 , described by the trapezoidal membership function with the parameters indicated in Table 2, the numerical analogue is the abscissa of the middle of the upper base: (0.1969 + 0.2112)/2 = 0.20405. Really, according to the fuzzy set point estimate rule [2], the following formula is used: F(A) =

1 αmax

α max

M (Aα )d α,

(7)

0

where Aα = {u|μA (u) ≥ α, u ∈ U} is the α-level set (α ∈ [0, 1]); M (Aα ) =

1 n

n t=1

ut (uk

∈ Aα ) is the cardinal number of the corresponding α-level set. For the fuzzy output A4 = {0/0.1825, 1/0.1969, 1/0.2112; 0/0.2256} (see Table 2) we have: 0 < α < 1, α = 1, A4α = {0.1969, 0.2112}, M (A4α ) = (0.1969 + 0.2112)/2 = 0.20405.

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Then, according to (7), the defuzzified value of the A4 is follows 

1

F(A4 ) =

M (A4α )d α = M (A4α ) · α = 0.20405.

0

According to [6], for fuzzy relation Ak ⇒ Ai , Aj , At the numerical predict is obtained as the arithmetical mean value. In particular, the fuzzification of fuzzy output for the date 15.03.2000, which is described as union A1 ∪ A2 ∪ A3 (see Table 2), is provided as following F = [(0.1106 + 0.1250)/2 + (0.1394 + 0.1537)/2 + (0.1681 + 0.1825)/2]/3 = 0.14655. Thus, considering the internal fuzzy relations of the 1st and 2nd orders for the FTS of the NIR and RED, the corresponding predictive models were obtained. Further, desire predictive model for NDVI TS is restored by application of the empirical formula (1) for each day according to the corresponding forecast data NIR and RED, which are obtained on the base of 1st and 2nd order models (M1 and M2). These models are interpreted in the form of Table 6 and Fig. 2. Table 6. NDVI FTS models. №

Date

NDVI

M1

M2

№

Date

NDVI

M1

M2

1 18.02.2000 0.3599

16 25.06.2000 0.7101

0.6722

0.7099

2 26.02.2000 0.3745 0.2951

17 02.07.2000 0.7124

0.6360

0.7099

3 05.03.2000 0.4099 0.4269 0.4269 18 11.07.2000 0.7135

0.6360

0.6343

4 15.03.2000 0.3812 0.4337 0.4034 19 20.07.2000 0.4554

0.6360

0.6343

5 21.03.2000 0.3680 0.5964 0.3887 20 27.07.2000 0.2479

0.3301

0.2748

6 29.03.2000 0.3457 0.3287 0.3482 21 02.08.2000 0.4623

0.5356

0.4765

7 06.04.2000 0.3296 0.4240 0.3482 22 12.08.2000 0.6587

0.5138

0.6591

8 15.04.2000 0.2957 0.4240 0.3177 23 20.08.2000 0.5987

0.6626

0.5948

9 22.04.2000 0.2535 0.3724 0.2748 24 28.08.2000 0.5473

0.6622

0.5523

10 29.04.2000 0.2759 0.5356 0.2748 25 03.09.2000 0.5019

0.4553

0.5005

11 08.05.2000 0.2966 0.5356 0.2920 26 13.09.2000 0.4815

0.3026

0.4724

12 15.05.2000 0.3058 0.2795 0.2920 27 20.09.2000 0.4259

0.3301

0.3094

13 24.05.2000 0.3211 0.2795 0.3482 28 29.09.2000 0.3719

0.3530

0.4028

14 09.06.2000 0.5104 0.4240 0.5045 29 07.10.2000 0.3505

0.2985

0.3314

15 15.06.2000 0.6257 0.6323 0.6247 30 15.10.2000 0.3217

0.4638

0.3124

MSE

0.0137

0.0021

MAPE (%)

25.5716

5.9490

MPE (%)

−0.1161 −0.0182

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Fig. 2. 1st and 2nd order models for NDVI TS forecasting.

As can be seen from the results of NDVI forecasting by the 2nd method, the error value according to the MSE criterion is quite low (0.0137 for M1, and 0.0021 for M2), which cannot be said about the error value according to the MAPE criterion (25.5716 for M1 and 5.9490 for M2). The MPEs for the 1st and 2nd order predictive models are (−0.1161) and (−0.0182), respectively, reflecting a slight bias below the 5% threshold.

5 Conclusion The paper discusses one of the tools of precision farming methodology related to the applying of the NDVI, which allows to identify crop volumes and more accurately estimate the current state of growing. The last statement is relative since the index itself does not reflect the absolute values of plant volumes. Nevertheless, regarding the obtained multispectral data, it is possible to estimate the development of growing plants and predict their perspective yield. It is necessary to consider that the NDVI changes throughout the entire vegetation cycle, that is, during the period of initial growth, the period of flowering and maturation, its indicators differ significantly, in fact, as evidenced by the dynamics of NDVI on the example of given pixel (see Fig. 1). The practice of precision farming has shown that the most active increase in the NDVI occurs during the growing season, during the flowering period, the growth of the crop slows down and halts, and in the process of crop maturation, the index gradually decreases. The fuzzy approaches to forecasting the temporal variability of NDVI proposed in the article can be easily extrapolated onto the processing of multispectral data obtained for all pixels of the corresponding vegetation maps. If vegetation maps used in precision farming allow only visually determining differences in the state of plants, then owing to digitalization it becomes possible to interpret the color range of vegetation from light tones with a low index to dark color with high NDVI.

References 1. Rzayev, R.R.: Analytical Support for Decision-Making in Organizational Systems. Palmerium Academic Publishing, Saarbruchen (2016). (in Russian) 2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning–I. Inf. Sci. 8(3), 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90017-1

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3. Andreichikov, A., Andreichikova, O.: Analysis, Synthesis, Planning Decisions in the Economy. Finance and Statistics, Moscow (2000). (in Russian) 4. Vegetation Indices 16-Day L3 Global 250 m MOD13Q1 (LPDAAC). https://goo.gl/maps/YAd domuoXsD4QQN36. Accessed 11 Feb 2022 5. Ortiz-Arroyo, D., Poulsen, J.R.: A weighted fuzzy time series forecasting model. Indian J. Sci. Tech. 11(27), 1–11 (2018). https://doi.org/10.17485/ijst/2018/v11i27/130708 6. Chen, S.M.: Forecasting enrollments based on high-order fuzzy time series. Cybern. Syst. Int. J. 33, 1–16 (2002). https://doi.org/10.1080/019697202753306479

Application of Fuzzy TOPSIS in Server Selection Problem V. H. Salimov(B) Azerbaijan State Oil and Industry University, Baku Azadliq Street 20, Baku, Azerbaijan Republic [email protected]

Abstract. The paper is devoted to the application fuzzy technologies for solving multi-criteria decision making problems. In the information technology era the computer servers play key role. The effectiveness of function information processing centers depends on adequate server selection. The modern servers are characterized by many attributes. There are various methods for solving this problem. One of most used method is TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution). TOPSIS method is based on the ideal point approach. All stages of the servers selection problem solving on base of TOPSIS method are presented. Keywords: Fuzzy number · Decision making · TOPSIS method

1 Introduction Multi Criteria Decision making (MCDM) [1, 2] is permanently important problem in system analysis. MCDM can be considered as vector optimization problem. MCDM problems can be solved on the basics of preferences of decision makers. There are many methods for solving this problem. These methods can be classified in 2 categories: the methods based on the aggregation of criteria into single criterion and methods based on pairwise comparisons of alternatives. The WGP (weighted average product), WGA (weighted average sum) and their variations [3, 4] are included in first category, AHP, PROMETHEE, ELECTRE, TOPSIS [5–13] are included in second category. The information about popularity of different methods is presented in article [3]. The original TOPSIS has been developed by Hwang for certain data. In 2000 Chen developed fuzzy TOPSIS [4–21] method for problem with uncertain data. The paper is devoted to application of fuzzy TOPSIS method in server selection problem. In the information technology era the computer servers play key role. The effectiveness of functioning of information processing centers depends on adequate server selection. The modern servers are characterized by many attributes. There are various methods for solving multiattribute decision problem. One of most used method is TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution). TOPSIS method is based on the ideal point approach. All stages of the servers selection problem solving on base of TOPSIS method are presented.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 364–371, 2023. https://doi.org/10.1007/978-3-031-25252-5_49

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2 Fuzzy TOPSIS Method MCDM problem can presented as a linguistic matrix m – alternative’s number n - criteria’s number (Table 1), where X˜ ij = (aij , bij , cij , dij ) is a representation of linguistic terms by fuzzy trapezoidal numbers. Table 1. MCDM problem representation. C1

C2

C3

…

Cn

X˜ 12 X˜ 22

X˜ 13 X˜ 23

…

A2

X˜ 11 X˜ 21

…

X˜ 1n X˜ 2n

A3

X˜ 31

X˜ 32

X˜ 33

…

X˜ 3n

…

… X˜ m1

… X˜ m2

… X˜ m3

…

… X˜ mn

A1

Am

…

The fuzzy TOPSIS method’s stages are presented below: 1. In first stage the linguistic variables for decisions and weights of criteria are presented with fuzzy trapezoidal numbers (Tables 2 and 3).

Table 2. The linguistic variables for the importance of criterion weights. Linguistic Variables

Trapezoidal Fuzzy Numbers

Very Low (VL)

(0, 0.1, 0.2.0.3)

Low (L)

(0.1, 0.3, 0.45, 0.7)

Medium (ML)

(0.4, 0.5, 0.7, 0.8)

High (H)

(0.5, 0.6, 0.75, 0.85)

Very High (VH)

(0.6, 0.7, 0.8, 0.9)

A normalized matrix R˜ = (rij ), i = 1, 2, . . . m; j = 1, 2, . . . n is calculated. The calculation of the normalized matrix is realized by following formulas:   aj∗ aj∗ aj∗ aj∗ aij bij cij dij , , , = ( , , , ), j ∈ J1 , j ∈ J , r ˜ r˜ij = ij dj∗ dj∗ dj∗ dj∗ dij cij bij aij dj∗ = maxi dij , j ∈ J , aj∗ = mini aij , j ∈ J1 where J and J1 present the set of maximization criteria and set of minimization criteria respectively.

366

V. H. Salimov Table 3. The linguistic variables for the decisions. Linguistic Variables

Trapezoidal Fuzzy Numbers

Very Poor (VP)

(0, 1, 2, 3)

Poor (P)

(1, 3, 4.7)

Medium Poor (MP)

(4, 5, 7, 8)

Good (G)

(7, 8, 9.9.25)

Very Good (VG)

(9, 9.25, 9.5, 10)

  2. Calculate of the weighted decision matrix V˜ = vij , i = 1, 2, . . . m; j = 1, 2, . . . n ∼

where v˜ ij =rij ⊗w˜ j ,i = 1, 2, . . . m; j = 1, 2, . . . n, and w˜ j are weights of criteria. 3. Determine of positive and negative ideal solutions: A+ = (˜v1+ , v˜ 2+ , v˜ 3+ , . . . . . . .˜vn+ ), A− = (˜v1− , v˜ 2− , v˜ 3− , . . . . . . .˜vn− ), where v˜ 1+ = (1, 1, 1, 1), v˜ 1− = (0, 0, 0, 0). 4. The distances between positive and negative ideal solutions and actual decisions are calculated by formulas:   di+ = nj=1 d (˜vij+ , v˜ j+ ), di− = nj=1 d (˜vij− , v˜ j− ), j = 1,2,……m, where the distance is calculated by formula:   1 ˜ ˜ [(a1 − b1 )2 + (a2 − b2 )2 + (a3 − b3 )2 + (a4 − b4 )2 D A, B = 4 5. Calculate closeness coefficient for all alternatives:

CC i =

di−

di− + di+

, i = 1, 2, . . . .m

6. Determine acceptance level of decisions (Table 4). Table 4. Acceptance criteria. Closeness Coefficient(CCi)

Evaluation

CC i ∈ [0, 0.2)

Not recommended

CC i ∈ [0.2, 0.4)

Recommended with high risk

CC i ∈ [0.4, 0.6)

Recommended with low risk

CC i ∈ [0.6, 0.8)

Acceptable

CC i ∈ [0.8, 1.0)

Accepted and preferred

Application of Fuzzy TOPSIS in Server Selection Problem

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7. The decision with maximum of closeness coefficient is selected.

3 Server Selection Problem Solving The are many papers where server selection problems are considered [21, 22]. In this paper we consider this problem with 9 criteria. Some of them are objective criteria so are measurable. The used objective criteria are as follows: • • • • •

Price RAM capacity (GB) Processor speed (GHz) Number of cores Hard disk capacity (TB).

The subjective criteria aren’t measurable like objective ones. They are defined based on human expertise. Subjective criteria: • • • •

Reliability Security Scalability Usability.

The selection problem is implemented in 2 stages: in first stage on base of objective criteria are selected group of acceptable by capacity servers, in second stage are selected optimal server according to subjective criteria. Assume that first stage is completed and the set of acceptable alternatives were formed. In this paper we consider implementation of second stage. The Linguistic decision matrix is shown in Table 5. Table 5. Linguistic decision matrix. C1 , ML

C2 , H

C3 , VH

C4 , H

A1

VG

G

VG

MP

A2

MP

G

G

VG

A3

G

VG

MP

G

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The trapezoidal fuzzy numbers-based values are presented below (Tables 6 and 7): Table 6. The results of conversion linguistic data into trapezoidal fuzzy numbers. C1

C2

C3

C4

A1

(9, 9.25, 9.5, 10)

(7, 8, 9.9.25)

(9, 9.25, 9.5, 10)

(4, 5, 7, 8)

A2

(0.4, 0.5, 0.7, 0.8)

(7, 8, 9.9.25)

(4, 5, 7, 8)

(9, 9.25, 9.5, 10)

A3

(7, 8, 9.9.25)

(9, 9.25, 9.5, 10)

(4, 5, 7, 8)

(7, 8, 9.9.25)

Table 7. Weights of criteria. (0.4, 0.5, 0.7, 0.8)

(0.5, 0.6, 0.75, 0.85)

(0.6, 0.7, 0.8, 0.9)

(0.5, 0.6, 0.75, 0.85)

The results of computations are given in Tables 8, 9, 10 and 11. Table 8. The results of calculations of normalized matrix by corresponding formulas. C1

C2

C3

A1

(0.40, 0.42, 0.43, 0.44)

(0.70, 0.80, 0.90, 0, 93)

(0.9, 0.93, 0.95, 1)

C4 (0.4, 0.5, 0.7, 0.8)

A2

(0.5, 0.57, 0.8, 1)

(0.70, 0.78, 0.88, 1)

(0.7, 0.8, 0.9, 0.93)

(0.9, 0.925, 0.95, 1)

A3

(0.43, 0.44, 0.5, 0.57)

(0.90, 0.74, 0.76, 0.78)

(0.4, 0.5, 0.7, 0.8)

(0.7, 0.8, 0.9, 0.925)

Table 9. The results of weighted matrix. C1

C2

A1

(0.16, 0.21, 0.3, 0.36)

(0.35, 0.48, 0.68, 0.79) (0.54, 0.65, 0.76, 0.9)

C3

A2

(0.2, 0.29, 0.56, 0.8)

(0.35, 0.48, 0.68, 0.79) (0.42, 0.56, 0.72, 0.83) (0.45, 0.56, 0.71, 0.85)

A3

(0.17, 0.22, 0.35, 0.46) (0.45,0.56,0.71,0.85)

(0.24.0.35, 0.56, 0.72)

C4 (0.20, 0.30, 0.53.0.68) (0.35, 0.48, 0.68, 0.79)

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Table 10. The results of calculation distance between decisions and the ideal solutions.

d (A1 , A+ ) d (A2 , A+ ) d (A3 , A+ ) d (A1 , A− ) d (A2 , A− ) d (A3 , A− )

C1

C2

C3

C4

0.75

0.73

0.49

0.99

0.95

0.73

0.62

0.62

1.22

0.62

0.92

0.73

0.52

1.16

1.37

0.92

1.02

1.16

1.25

1.26

0.62

1.26

0.98

1.16

Table 11. The results of closeness coefficients calculations. di+

di−

CC i

Ranking

A1

2.67

4.59

0.63

1

A2

3.02

4.52

0.60

2

A3

3.09

4.46

0.59

3

All alternatives are determined as “Acceptable” (Table 4). The analysis of closeness coefficients shows that optimal decision is alternative A1 .

4 Conclusion Today the computer servers play very important role. The paper is dedicated to the problem of computer server selection. The problem is defined as MCDM. All criteria is divided in two groups: objective and subjective. The selection problem for subjective criteria was solved on base of fuzzy TOPSIS method. All stages of implementation are presented in details.

References 1. Hwang, C.L., Yoon, K.: Multiple Attribute Decision Making: Methods and Applications. Springer- Verlag, New York (1981). https://doi.org/10.1007/978-3-642-48318-9 2. Mardani, A., Jusoh, A., Khalil M.D., Nor, Z., Khalifah, N., Zakwan, A.: Valipour Multiple criteria decision-making techniques and their applications - a review of the literature from 2000 to 2014, ISSN: 1331–677X (Print) (2015) 3. Taha, R.A., Daim, T.: Multi-criteria applications in renewable energy analysis, a literature review. In: Daim, T., Oliver, T., Kim, J. (eds.) Research and Technology Management in the Electricity Industry, pp. 17–30. Springer, London (2013). https://doi.org/10.1007/978-14471-5097-8_2 4. Wu, H.Y., Chen, J.K., Chen, I.S., Zhuo, H.H.: Ranking universities based on performance evaluation by a hybrid MCDM model. Measurement 45(5), 856–880 (2012). https://doi.org/ 10.1016/j.measurement.2012.02.009

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5. Beccali, M., Cellura, M., Ardente, D.: Decision making in energy planning: the ELECTRE multicriteria analysis approach compared to a fuzzy-sets methodology. Energy Conv. Manag. 39(16–18), 1869–1881 (1998). https://doi.org/10.1007/0-387-23081-5_21 6. Rogers, M., Bruen, M.: Using ELECTRE III to choose route for Dublin port motorway. J. Transp. Eng. 126(4), 313–323 (2002). https://doi.org/10.1061/(ASCE)0733-947X(2000)126: 4(313) 7. Srdjevic, B., Medeiros, Y.D.P.: Fuzzy AHP assessment of water management plans. Water Res. Manag. 22(7), 877–894 (2008). https://doi.org/10.1007/s11269-007-9197-5 8. Meixner, O.: Fuzzy AHP group decision analysis and its application for the evaluation of energy sources. In Proceedings of the 10th International Symposium on the Analytic Hierarchy. Network Process, Pittsburgh, PA, USA, vol. 29 (2009) 9. Srichetta, P.: Thurachon: applying fuzzy analytic hierarchy process to evaluate and select product of notebook computers. Int. J. Model. Optim. 2(2), 168 (2012). https://doi.org/10. 7763/IJMO.2012.V2.105 10. Azadeh, A., Shirkouhi, S.N., Rezaie, K.: A robust decision-making methodology for evaluation and selection of simulation software package. Int. J. Adv. Manuf. Tech. 47, 381–393 (2010). https://doi.org/10.1007/s00170-009-2205-6 11. Karaarslan, N., Gundogar, E.: An application for modular capability-based ERP software selection using AHP method. Int. J. Adv. Manuf. Tech. 42, 1025–1033 (2009). https://doi. org/10.1007/s00170-008-1522-5 12. Smirlis, Y.G., Zeimpekis, V., Kaimakamis, G.: Data envelopment analysis models to support the selection of vehicle routing software for city logistics operations. Oper. Res. 12, 399–420 (2012). https://doi.org/10.1007/s12351-010-0100-4 13. Ma, J., Lu, J., Zhang, G.: Decider: a fuzzy multi-criteria group decision support system. Knowl.-Based Syst. 23(1), 23–31 (2010). https://doi.org/10.1016/j.knosys.2009.07.006 14. Perez, I.J., Cabrerizo, F.J., Herrera-Viedma, E.: Group decision making problems in a linguistic and dynamic context. Expert Syst. Appl. 38(3), 675–1688 (2011). https://doi.org/10. 1016/j.eswa.2010.07.092 15. Xu, Z.S.: Approaches to multi-stage multi-attribute group decision making. Int. J. Inf. Tech. Decis. Mak. 10(1), 121–146 (2011). https://doi.org/10.1142/S0219622011004257 16. Aliev, R.A., Pedrycz, W., Guirimov, B.G., Huseynov, O.H.: Clustering method for production of Z-number based if-then rules. Inf. Sci. 520, 155–176 (2020) https://www.sciencedirect. com/science/article/abs/pii/S0020025520300657 17. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Fahreddin, M., Sadikoglu, F. (eds.) 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018, pp. 42–50. Springer International Publishing, Cham (2019). https://doi.org/ 10.1007/978-3-030-04164-9_10 18. Aliyeva, K.: Multifactor personnel selection by the fuzzy TOPSIS method. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 478–483. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_64 19. Aliyeva, K.: Fuzzy type-2 decision making method on project selection. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 180–185. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_23 20. Jabbarova, K., Hasanova, N.: An application of the VIKOR method to decision making in investment problem under Z-valued information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 499–506. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_67

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21. Sarika, S.: Server Selection by using Weighted Sum and Revised Weighted Sum Decision Models. G.G.S. IP University, Dwarka, New Delhi (2012) 22. Vesna, C.: Considering interactions among multiple criteria for the server selection. J. Inf. Organ. Sci. 34(1), 55–65 (2010)

Fuzzy Inference Based Quadcopter Flight Regulation Under Overland Monitoring Tunjay Habibbayli1,2(B)

and Murad Aliyev3

1 Institute of Control Systems of ANAS, Vahabzadeh Street 9, AZ1141 Baku, Azerbaijan

[email protected]

2 Institute of Information Technology of ANAS, Vahabzadeh Street 9, AZ1141 Baku, Azerbaijan 3 Intelpro LLC, Jabbarly Street Globe Center 609, AZ1065 Baku, Azerbaijan

Abstract. Some territories where economic activity is carried out are characterized by the presence of mountain and forest tracts. To provide information support for the development of infrastructure and agriculture in these areas, in some cases overland monitoring using unmanned technologies is required. In this regard, an algorithm for the formation of a 3D trajectory of a quadcopter during overland piloting in a mountainous and wooded landscape is proposed, which implies autonomous maneuvering to overcome possible obstacles. As a basic model, it is proposed to use a fuzzy inference system with input characteristics in the form of linguistic variables that reflect fuzzy sectors of space, within which the presence of obstacles and the distance to them are interpreted verbally, that is, in the form of terms of corresponding input linguistic variables. Overcoming obstacles is supposed to be performed based on fuzzy conclusions of the proposed system, formulated as terms of output linguistic variables, which reflect changes in the angle of rotation in the horizontal plane, flight altitude and traverse speed of the quadcopter. The given paper analyzes the results of the model behavior for different scenarios of the terms of the input linguistic variables. Keywords: Quadcopter · Overland monitoring · Fuzzy set · Membership function · Fuzzy inference

1 Introduction The current level of unmanned technologies actualizes the use of drones for overland monitoring of infrastructure and agriculture, characterized by large mountainous and forested areas. For overland monitoring of various objects, it is preferable to use rotarywing drones (quadcopters) [1], which are the most popular among researchers despite their own limitations. The advantage of the quadcopter is that each of its four propellers provides raising force and high flight stability. Nevertheless, as a rather complex technical device, a quadcopter is characterized by flight dynamics that are difficult to formalize due to its “sensitivity” to the influence of external factors [1, 2]. Therefore, solving the problem of controlling a quadcopter for overland monitoring in the presence of natural

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 372–381, 2023. https://doi.org/10.1007/978-3-031-25252-5_50

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obstacles in a mountainous-wooded landscape and hard-to-reach places is interesting both from scientific and practical points of view. In this regard, of particular interest are the technological solutions of DJI, which produces compact quadcopters with intelligent flight modes [3].

2 Problem Formulation In the absence of the necessary information support and, as a result, the impossibility of constructing an accurate mathematical model, the application of fuzzy logic methods in quadcopter control is specified by the capabilities, which provide for compiling heuristic knowledge and using intuitive data. Currently, fuzzy approaches to solving problems of automatic control are considered in two aspects. The first is related to the creation of a classifier of situations that forms the goals and objectives of the functioning of a dynamic system. The second approach involves direct fuzzy regulation of the variables of the control object. Based on these prerequisites, it becomes obvious the importance and actuality of developing software for the autonomous movement of the quadcopter under overland piloting in mountainous and wooded areas, including automatic maneuvering to bypass possible obstacles. In the context of the foregoing, an algorithm is proposed for creating a “smart” obstacle avoidance system for quadcopter autopiloting, based on the use of the fuzzy inference.

3 Fuzzy Inference System for Quadcopter Autopilot Regulation The DJI Mavic 2 quadcopter is equipped with six sensors for detecting obstacles in all directions, which ensures high-quality drone performance even in the most difficult situations. Thanks to the Flight Autonomy autopilot system, all data are transmitted and processed permanently in real time. In [4], an algorithm for forming the flight path of a quadcopter was proposed using a fuzzy inference system based on expert and empirical data analysis. It provides overland autopiloting of a quadcopter equipped with obstacle detection sensors in five frontal viewing sectors (Fig. 1).

Fig. 1. Obstacle visibility sectors: a) side view, b) top view

To form the schedule for overland autopiloting of the quadcopter in five directions, a bounded set of logically consistent rules is considered in the form of the information fragments such as:

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d 1 : “If any obstacle is not detected on the flight path of the quadcopter or it is too far away, then there is no need to change direction, height and to reduce speed”; d 2 : “If the sensor detects an obstacle at a medium distance along the flight path of the quadcopter and the sector on the left is free, then it is necessary to lose velocity to an average value and to turn slightly to the left without changing the height”; d 3 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter and the sector on the left is free, then it is necessary to lose velocity to a minimum, and to turn sharply to the left without changing the height”; d 4 : “If the sensor detects an obstacle at a medium distance along the flight path of the quadcopter, there is also an obstacle in the left sector at a not remote distance and the sector on the right is free, then it is necessary to lose velocity to an average value, and to turn slightly to the right without changing the height”; d 5 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, there is also an obstacle in the left sector at a not remote distance and the sector on the right is free, then it is necessary to lose velocity to a minimum, and turn sharply to the right without changing the height”; d 6 : “If the sensor detects an obstacle at an average distance along the flight path of the quadcopter, there are also obstacles in the left and right sectors at a not remote distance, and the upper sector is free, then it is necessary to lose velocity to an average value, and slightly increase the flight altitude (pitch-up) without yaw”; d 7 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, there are also obstacles in the left and right sectors at a not remote distance, and the upper sector is free, then it is necessary to lose velocity to a minimum, and sharply increase the flight altitude without yaw”; d 8 : “If the sensor detects an obstacle at an average distance along the flight path of the quadcopter, there are also obstacles in the left, right and upper sectors at a non-remote distance, and the lower sector is free, then it is necessary to lose velocity to an average value, and slightly reduce the flight altitude (dive) without yaw”; d 9 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, there are also obstacles in the left, right and upper sectors at a not remote distance, and the lower sector is free, then it is necessary to lose velocity to a minimum, and sharply reduce the flight altitude without yaw”; d 10 : “If the sensor detects an obstacle at an average distance along the flight path, and an obstacle is also detected at an average distance to the left, obstacles are detected at a not remote distance to the right, below and above, then it is necessary to lose velocity to an average value while maintaining the course and flight altitude”; d 11 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, and an obstacle is also detected at an average distance to the left, obstacles are detected at a not remote distance to the right, below and above, then it is necessary to lose velocity to a minimum and turn sharply to the left without changing the height”;

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d 12 : “If the sensor detects an obstacle at a medium distance along the flight path of the quadcopter, and an obstacle is detected a close distance to the left, an obstacle is detected at an average distance to the right, and obstacles are detected at a not remote distance from below and above along the course, then it is necessary to lose velocity to an average value and turn sharply to the left without changing the course and height”; d 13 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, and an obstacle is also detected at a close distance to the left, an obstacle is detected at an average distance to the right, and obstacles are detected from below and above along the course at a not remote distance, then it is necessary to lose velocity to minimum and turn sharply to the right without changing the height”; d 14 : “If the sensor detects an obstacle at a medium distance along the flight path, an obstacle is detected at a close distance to the left, an obstacle is also detected at a close distance to the right, an obstacle is detected at an average distance from above, and an obstacle is detected at a not remote distance from below, then it is necessary to lose velocity to an average value and turn sharply to the right without changing the course and height”; d 15 : “If the sensor detects an obstacle at close distance along the flight path of the quadcopter, the obstacles are detected at an average distance to the left and to the right, as well as an obstacle is detected at a not remote distance from above, then it is necessary to lose velocity to a minimum and sharply increase flight altitude without yaw”; d 16 : “If the sensor detects an obstacle at a medium distance along the flight path, obstacles are detected at a close distance to the left, right and higher along the course, and an obstacle is detected at an average distance below the course, then it is necessary to lose velocity to an average value without changing the course and height”; d 17 : “If the sensor detects the obstacles at close distance along the flight path of the quadcopter, as well as to the left, right and above, however, an obstacle is detected at an average distance below the course, then it is necessary to lose velocity to a minimum, sharply reduce the flight altitude without yaw”; d 18 : “If an obstacle is detected at a medium distance along the flight path, obstacles are detected at a close distance to the left, right, above and below the course, then it is necessary to lose velocity to an average value without changing the course and height”; d 19 : “If in all sectors of the view the detected obstacles are at a close distance, then it is necessary to lose velocity to a minimum and turn sharply to the left without changing the height”. Maneuvering to the left (or to the right, which is also appropriate) from the frontal impasse caused by the presence of obstacles in all five sectors of view (Rule d19), the quadcopter continues to move and, thereby, creates a new flight path for itself in accordance with the regulations established by rules d 1 ÷ d 19 . Thus, analysis of all possible scenarios of collision with obstacles made it possible to form a complete set of linguistic variables (Table 1) and rules for forming a Fuzzy Inference System (FIS) that regulates the behavior of a quadcopter during overland piloting.

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T. Habibbayli and M. Aliyev Table 1. Input and output linguistic variables of the FIS and their terms.

Inputs Symbol

Variable name

Universe

Term set

x1

The remoteness of the obstacle in the direction of flight

[0, 1]

{X 11 = significant, X 12 = average, X 13 = unsignificant}

x2

The remoteness of the obstacle to the left of the direction

[0, 1]

{X 21 = significant, X 22 = average, X 23 = unsignificant}

x3

The remoteness of the obstacle to the right of the direction

[0, 1]

{X 31 = significant, X 32 = average, X 33 = unsignificant}

x4

The remoteness of the obstacle to the higher of the direction

[0, 1]

{X 41 = significant, X 42 = average, X 43 = unsignificant}

x5

The remoteness of the obstacle to the lower of the direction

[0, 1]

{X 51 = significant, X 52 = average, X 53 = unsignificant}

y1

Airspeed

[0, 1]

{Y 11 = full, Y 12 = average, Y 13 = zero}

y2

Yaw

[−0.5, 0.5]

{Y 21 = sharply to the left, Y 22 = slightly to the left, Y 23 = is absent, Y 24 = slightly to the right, Y 25 = sharply to the right}

y3

Pitch

[−0.5, 0.5]

{Y 31 = sharply up, Y 32 = slightly up, Y 33 = is absent, Y 34 = slightly down, Y 35 = sharply down}

Outputs

The corresponding FIS is formed by the following rules in symbolic form: d 1 : (x 1 =X 11 ) ⇒ (y1 =Y 11 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 2 : (x 1 =X 12 ) & (x 2 =X 21 ) ⇒ (y1 =Y 12 ) & (y2 =Y 22 ) & (y3 =Y 33 ); d 3 : (x 1 =X 13 ) & (x 2 =X 21 ) ⇒ (y1 =Y 13 ) & (y2 =Y 21 ) & (y3 =Y 33 ); d 4 : (x 1 =X 12 ) & (x 2 =¬X 21 ) & (x 3 =X 31 ) ⇒ (y1 =Y 12 ) & (y2 =Y 24 ) & (y3 =Y 33 ); d 5 : (x 1 =X 13 ) & (x 2 =¬X 21 ) & (x 3 =X 31 ) ⇒ (y1 =Y 13 ) & (y2 =Y 25 ) & (y3 =Y 33 ); d 6 : (x 1 =X 12 ) & (x 2 =¬X 21 ) & (x 3 =¬X 31 ) & (x 4 =X 41 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 34 ); d 7 : (x 1 =X 13 ) & (x 2 =¬X 21 ) & (x 3 =¬X 31 ) & (x 4 =X 41 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 35 ); d 8 : (x 1 =X 12 ) & (x 2 =¬X 21 )& (x 3 =¬X 31 )& (x 4 =¬X 41 )& (x 5 =X 51 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 32 ); d 9 : (x 1 =X 13 )&(x 2 =¬X 21 )& (x 3 =¬X 31 ) & (x 4 =¬X 41 ) & (x 5 =X 51 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 31 ); d 10 : (x 1 =X 12 ) & (x 2 =X 22 ) & (x 3 =¬X 31 )& (x 4 =¬X 41 )& (x 5 =¬X 51 )⇒ (y1 =Y 12 )& (y2 =Y 23 ) & (y3 =Y 33 );

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d 11 : (x 1 =X 13 ) & (x 2 =X 22 )& (x 3 =¬X 31 )& (x 4 =¬X 41 )& (x 5 =¬X 51 )⇒ (y1 =Y 13 ) & (y2 =Y 21 ) & (y3 =Y 33 ); d 12 : (x 1 =X 12 ) & (x 2 =X 23 )& (x 3 =X 32 ) & (x 4 =¬X 41 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 13 : (x 1 =X 13 ) &(x 2 =X 23 ) & (x 3 =X 32 ) & (x 4 =¬X 41 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 13 ) & (y2 =Y 25 ) & (y3 =Y 33 ); d 14 : (x 1 =X 12 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 42 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 15 : (x 1 =X 13 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 42 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 35 ); d 16 : (x 1 =X 12 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 43 ) & (x 5 =X 52 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 17 : (x 1 =X 13 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 43 ) & (x 5 =X 52 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 31 ); d 18 : (x 1 =X 12 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 43 ) & (x 5 =X 53 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 19 : (x 1 = X 13 ) & (x 2 = X 23 ) & (x 3 = X 33 ) & (x 4 = X 43 ) & (x 5 = X 53 ) ⇒ (y1 = Y 13 ) & (y2 = Y 21 ) & (y3 = Y 33 ) To implement the FIS that provides autopiloting of the quadcopter according to the formalized schedule, it is necessary to reflect the introduced linguistic variables to the set of their corresponding real numbers by setting membership functions, that is, fuzzify the terms of all input and output linguistic variables. For this purpose, the advantage of one element over another relative to the property of the given fuzzy subset of the discrete universe U = {0, 0.1, 0.2, …, 1} is estimated. According to the Saaty’s 9-point scale [5], for example, the matrix of paired comparisons of the elements of the universe for identifying the membership function of the fuzzy set “unsignificant” as one of the terms of the input linguistic variable “Remoteness of obstacles” (Table 1) is presented as follows.

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where, if the preference of the i-th number over the j-th has one of the presented values, then the assessment of the preference of the j-th number over the i-th has the inverse value (i, j = 0, 1, 2, …, 10). Finding the eigenvector (μ0 , μ1 , …, μ10 ) from the equation (X 13 – λE)·μ = 0, the values of the membership function μ(ui ) of the fuzzy set X 13 are obtained, which are summarized in Table 2. Each such membership function can be approximated as given in a tabular form and obtain a graphical representation of the corresponding fuzzy set. Table 2. The values of the membership function of the fuzzy set unsignificant. Remoteness 0 0.1 0.2 0.3 μ(ui )

1 1

1

0.4

0.5

0.6

0.7

0.8

0.9

1

0.9865 0.0113 0.0098 0.0064 0.0035 0.0021 0.0008 0.0002

In MATLAB\FIS notation, all membership functions were established empirically. In particular, the input and output characteristics of the model are shown in Fig. 2 and Fig. 3, respectively.

Fig. 2. Terms of input linguistic variable “The remoteness of the obstacle in the course”

Fig. 3. Terms of output linguistic variables: y1 – airspeed, y2 – yaw, y3 – pitch.

As a result, using the interactive window of the graphical interface of the MATLAB\FIS editor (Fig. 4), it was possible to generate the products, which are summarized in Table 3, and different flight scenarios, which is presented in Table 4.

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Table 3. The products generated by MATLAB\FIS editor. №

Inputs

Outputs

x1

x2

x3

x4

x5

y1

y2

y3

1

0.95

0.50*

0.50

0.50

0.50

0.855

0

0

2

0.50

0.95

0.50

0.50

0.50

0.350

−0.200

0

3

0.10

0.90

0.50

0.50

0.50

0.013

−0.411

0

4

0.50

0.50

0.90

0.50

0.50

0.350

0.200

0

5

0.10

0.50

0.90

0.50

0.50

0.013

0.411

0

6

0.50

0.50

0.50

0.90

0.50

0.350

0

0.200

7

0.10

0.50

0.50

0.90

0.50

0.013

0

0.411

8

0.50

0.50

0.50

0.50

0.90

0.350

0

−0.200

9

0.10

0.50

0.50

0.50

0.90

0.013

0

−0.411

10

0.50

0.50

0.40

0.40

0.40

0.350

0

0

11

0.10

0.50

0.50

0.50

0.50

0.013

−0.411

0

12

0.50

0.10

0.50

0.50

0.50

0.350

0

0

13

0.10

0.10

0.50

0.50

0.50

0.013

0.411

0

14

0.50

0.10

0.10

0.50

0.50

0.350

0

0

15

0.10

0.10

0.10

0.50

0.50

0.013

0

0.411

16

0.50

0.10

0.10

0.10

0.50

0.350

0

0

17

0.10

0.10

0.10

0.10

0.50

0.013

0

−0.411

18

0.50

0.10

0.10

0.10

0.10

0.350

0

0

19

0.10

0.10

0.10

0.10

0.10

0.013

−0.411

0

* The absence of obstacles determines the use of the average value 0.5 on the universe [0, 1].

Table 4. Obstacle maneuvering scenarios for quadcopter autopiloting. №

Inputs

Outputs

x1

x2

x3

x4

x5

y1

y2

y3

1

0.433

0.291

0.628

0.076

0.961

0.350

0.055

2

0.611

0.824

0.460

0.862

0.855

0.380

−0.194

0.000

3

0.374

0.622

0.139

0.750

0.702

0.337

−0.154

0.215

4

0.712

0.738

0.568

0.438

0.469

0.854

0.000

0.000

5

0.922

0.535

0.320

0.107

0.102

0.855

0.000

0.000

30

0.605

0.961

0.766

0.756

0.306

0.367

−0.196

0.000

31

0.702

0.644

0.219

0.000

0.740

0.851

−0.001

−0.190

… −0.001 (continued)

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T. Habibbayli and M. Aliyev Table 4. (continued)

№

Inputs x1

x2

x3

x4

x5

y1

32

0.433

0.629

0.741

0.405

0.838

0.350

0.144

0.000

33

0.465

0.793

0.395

0.745

0.086

0.350

−0.200

0.000

34

0.065

0.004

0.789

0.553

0.318

0.013

0.411

0.000

35

0.026

0.245

0.480

0.651

0.787

0.014

0.000

−0.195

Outputs y2

y3

Fig. 4. Graphical interface of the MATLAB\FIS editor for viewing rules.

4 Conclusion Complexity, multicoupling, nonlinearity, the presence of uncertain parameters of such technical objects as a quadcopter necessitates the search for ways to solve control problems alternative to the well-known classical P, PI, PID controllers. The result of the expert-empirical research carried out in this article is to get an idea of how to control quadcopters under overland monitoring of the area, the features of their practical application, advantages, and disadvantages. It seems to us that the improvement of results should be achieved using neural and neuro-fuzzy modeling methods. For example, any membership function given at key points obtained using the Saaty’s 9-point scale can be easily approximated using a three-layer feedforward neural network. Based on the scenarios presented in Table 4, it is possible to form a neuro-fuzzy controller capable of providing overland autopiloting of a quadcopter under different obstacles.

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References 1. Michael, D.S.: Simulation, and control of a quadrotor unmanned aerial vehicle (2011). http:// uknowledge.uky.edu/gradschool_theses/93 2. Sharma, A., Barve, A.: Controlling of quadrotor UAV using PID controller and fuzzy logic controller (2012). https://researchtrend.net/ijeece/pdf/8%20ASTHA%20LNCT.pdf 3. DJI drones: types and capabilities of the brand’s aircraft. https://korabelov.info/2021/11/220 373/drony-dji-vidy-i-vozmozhnosti-letatelnyh-apparatov-brenda/. (in Russian) 4. Neretina, V.V., Nafikov, I.R.: Formation of the UAV trajectory during overland monitoring of forest ecosystems based on the apparatus of fuzzy logic. https://apni.ru/article/845-formirova nie-traektorii-dvizheniya-bpla 5. Saaty, T.L., Vargas, L.G.: The Logic of Priorities. Kluwer Nijhoff Publishing, Massachusetts (1982)

Fuzzy Logic Analysis of Parameters Affecting Students’ Satisfaction with Their Life at University M. A. Salahli1(B)

, T. Gasimzade2 , V. Salahli3 and A. Guliyev4

, F. Alasgarova4

,

1 Department of Computer and Instructional Technology Education, Çanakkale Onsekiz

Mart University, Canakkale, Turkey [email protected] 2 Department of Instrument Making Engineering, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ 1010 Baku, Azerbaijan 3 Department of Computer Engineering, Odlar Yurdu University, Koroglu Rehimov Street, 13, AZ 1072 Baku, Azerbaijan 4 Department of Information Technology and Natural Sciences, Management University, Koroglu Rehimov Street, 822/23, AZ 1072 Baku, Azerbaijan

Abstract. There has been a rapid increase in the number of universities in recent years. This situation causes an increase in the competition among universities in terms of attracting students. Since the factors that express the satisfaction of the students with the university they are studying have a very serious effect on the university preference, studies on the analysis of these factors are of great importance. In this study, the factors affecting students’ satisfaction with their university life were investigated. These factors are divided into 3 groups as department-related, university-related and city-related factors. In the study, using fuzzy logic methods, the effect of various satisfaction factors on the general satisfaction value of the students was determined. The weight of the factors in the formation of satisfaction levels is expressed with fuzzy values. Fuzzy inference method was applied to determine the relationships between the factors. Keywords: University life of students · Student’s satisfaction · Satisfaction factors · Fuzzy inference rules

1 Introduction With the increase in the number of universities, the competition between universities is also increasing. In this respect, it is very important for universities to increase their opportunities to attract students. One of the ways to increase the attractiveness of universities is to increase students’ satisfaction with the university they attend. In the study [1], 6 satisfaction factors were determined in a scale developed to evaluate student satisfaction. These are satisfaction with social and cultural activities; satisfaction with the management of research and development activities; Satisfaction © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 382–390, 2023. https://doi.org/10.1007/978-3-031-25252-5_51

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with education monitoring, evaluation and quality management; Satisfaction with educational process and practices; Satisfaction with education and instructional design; and Satisfaction with the educational environment and resources. The study [2] examines the role of satisfaction on students’ academic performance and investigates the relationship between satisfaction of students and academic performance and explores other factors that contribute academic performance. The study found that there is strong relationship between satisfaction of students and academic performance, and satisfaction promotes both academic achievement and student retention. The factors affecting student satisfaction analysed in [3]. In the study, the relationship between student satisfaction and teacher-student relationship, teachers’ academic preparation, campus facilities and the experiences provided by the institute to students were investigated. In a study investigating the satisfaction levels of students of a faculty [4], it was determined that the most important factors affecting student satisfaction were equipment and infrastructure, academic staff, catering services and location. Researches have also been conducted on the analysis of various dimensions of student satisfaction. In the [5] the differences in life satisfaction dimensions between on-campus and off-campus indicators related to student housing were analysed and it was determined how life satisfaction factors were formed. The relationship between education service quality and student satisfaction in state universities was investigated in [6]. The results of the study [7] showed that only four factors had a significant positive effect on foreign students’ satisfaction with their higher education. These four factors are: education, security, the image and prestige of the institution and student’s preparation before going abroad. Qualitative assessments are mostly used for satisfaction factors. For this reason, it is seen that fuzzy logic methods, which are quite suitable for qualitative evaluations [8, 9], are widely used in studies to determine the satisfaction levels of students with university life. In the study of [10], the degree of satisfaction of international students with the chosen educational environment was determined by Fuzzy Importance-Performance Analysis. A descriptive analysis of student satisfaction was conducted in [11] to discover the main variables affecting the overall online teaching-learning process using classification trees and fuzzy inference methods. The study [12] aimed to determine the quality level of academic services to students by measuring the satisfaction levels of students with academic services. Mamdani fuzzy inference method was used for the analysis of academic services.

2 Research Problem It is important in several ways to learn the satisfaction levels of university students from the educational institution they study. As said above, the increase in the number of higher education institutions has led to an increase in competition among them. Good education alone is not enough to attract more students. The socio-cultural opportunities of the campuses, where students spend a few years of their lives, and the service facilities they offer are important factors in the school preferences of the students. Investigation of student satisfaction can give important clues about the school choice of students. The results of learning about student satisfaction can give important ideas for increasing the morale and motivation of students. The good psychological state, morale and

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motivation of the students also have a positive effect on their education. It is not possible to think of the university life of the students separately from the city where the university is located. Especially in small cities, students have a great impact on the social and commercial life of the city. Many factors such as the social-cultural structure of the city, quality of life, transportation, rented house prices also have a significant impact on students’ satisfaction. Learning these effects is important for the management of cities. Studies show that the level of satisfaction varies according to personality traits. These features may differ depending on the environment in which the student grew up, family situation, economic conditions, and circle of friends. Another group of factors that determine students’ satisfaction levels is related to the department the student is studying. Having to choose the department that he does not want according to his score, the opportunity to find a job suitable for his branch after graduating from school, the level of communication with the department teachers affects the level of satisfaction. In conclusion, we can say that the concept of satisfaction is a complex concept that can be evaluated by the city of the student, the social, economic, cultural characteristics of the university, the department and the personal characteristics of the student. The aim of this study is to determine the satisfaction levels of the students of the Computer and Teacher Technologies Education Department of the Canakkale Onsekiz Mart University. The study takes into account the characteristics of CEIT departments, having some specific characteristics. Changing the score type in student admissions to CEIT departments, increasing the lower limit of entrance scores to the department, and reducing the quota for appointment of teachers for the field of educational technologies decreased the preference for CEIT departments. CEIT department is not in the first preference list for the majority of department students. Many students chose CEIT because their scores were not enough for the more prestigious computer engineering branch. Of course, this forced choice affects their motivation, indirectly their satisfaction with the department. Computer-oriented courses in CEIT departments are not much easier than Computer Engineering Department courses. Despite this, it is very difficult for CEIT graduates to find a job at the same rate as Computer engineering graduates. The fear of not being able to find a job in the future has a negative impact on the satisfaction levels of CEIT students. The fact that there are no questions about the field in the exams for teacher appointments causes the students to lose their interest in the field courses. They cannot find an answer to the question “If my computer knowledge is not necessary, why should I learn the field courses (for example, programming course) that are more difficult”. This leads to a decrease in student satisfaction.

3 Data Collection and Data Analysis As mentioned above, many factors affect students’ satisfaction levels. It is difficult to consider and analyse all these factors in a study. In this sense, in this study, we tried to consider the factors specific to the CEIT department of Çanakkale OnSekiz Mart University. The effect of the city’s characteristics on the satisfaction levels of university students was evaluated within the scope of the research. We can divide the satisfaction factors considered in the study into 3 groups: The first group of factors is related to the CEIT department and includes: The effect of the department not being one of the students’ first preferences (FD1); Fear of being able

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to find a job in the future(FD2); Computer laboratories and internet (FD3); Prestige of the branch (FD4); Syllabus and course content are difficult for students (FD5); Attitude of department staff to students (FD6); The teaching staff have sufficient knowledge and experience (FD7); Attracting students to participate in projects and scientific activities (FD8). The second group of factors is related to the University and includes: Prestige of the University (FU1); University location (FU2); University staff-student relations (FU3); Library facility (FU4); Cafeteria, canteen, recreation facilities (variety, quality, price, and accessibility) (FU5); Student-oriented activities (FU6). The third group of factors is related to the city and includes: Safety (FC1); Accommodation (dormitory and rental facilities, price, distance from school, accessibility) (FC2); Transport (FC3); Sightseeing, entertainment, social interaction, sportive, cultural activity opportunities (FC4): Service (variety, price, quality, accessibility (FC5). A questionnaire containing these factors was prepared and distributed to the 74 students of the CEIT department. For evaluation. Students were asked to make the following evaluations: – Student satisfaction for each factor (SSF); – Weight of each factor in determining student satisfaction level (WSF); – Students’ level of satisfaction with university life (overall satisfaction value-OS). Students were asked to evaluate the parameters of SSF, WSF and OS in the range of [0, 10]. A value 0 for SSF indicates the lowest satisfaction by factor and 10 indicates the highest. A value of 0 for WSF indicates that the factor is very unimportant and 10 is very important. A value 0 for the OS parameter indicates very low overall satisfaction, and 10 indicates very high overall satisfaction. The values of these parameters were converted to fuzzy values for the application of the fuzzy logic method a given in Figs. 1, 2 and 3.

Fig. 1. Fuzzy expressions of parameters SSF Fig. 2. Fuzzy expressions of parameters WSF

Tables 1 and 2 show that the majority of students were satisfied with the factors FD3, FD6, FD7, and FC1. We can interpret these results as follows. Students can do their homework and research without any problems in the computer laboratories of the department during and outside of class hours. The technical and software facilities of the computers ensure that the courses are carried out effectively. High-speed wired

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Fig. 3. Fuzzy expressions of parameters OS

Table 1. Number of students for each satisfaction score and weight value for the factor group 1. Factor name Factor’s satisfaction score (number of students)

Factor’s weight value (number of students)

Satisfied (S) Not be satisfied Very important Important (I) Less (NS) (VI) Important(LI) FD1

51

23

13

32

29

FD2

20

54

44

29

5

FD3

68

6

32

24

18

FD4

33

41

26

33

14

FD5

15

59

34

26

14

FD6

69

4

26

28

20

FD7

65

9

31

30

13

FD8

32

42

38

32

4

internet and Wi-Fi are available for students to access at the university. In this sense, it is reasonable for the students to give mostly positive answers about the FD3 factor. The data related to the FD6 factor show that the student-academic relations are at a good level in the department. The data on the FD7 factor proves that the academic staff have sufficient knowledge and experience. The fact that it is possible to walk around the city safely at any time of the day, and that negative cases are rarely encountered, showed that the students were highly satisfied with the FC factor. Regarding the FD2 factor, the students mostly expressed their dissatisfaction. The thought that they may have problems in finding a job in the future has a negative effect on the education process of the students. This negatively affects the university life of the students. Students stated that they were not satisfied with the curriculum and course content, so the course content was difficult (factor FD5). This is not because the course content is difficult or incomprehensible. The reason why students give negative answers is that most of them do not have sufficient high school knowledge. The majority of the students expressed their satisfaction with the public transportation in the city. This is due to the expensiveness of public transport and the long waiting times (factor FC3). The

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Table 2. Number of students for each satisfaction score and weight value for the factor group 3. Factor name Factor’s satisfaction score (number of student)

Factor’s weight value (number of students)

Satisfied (S) Not be satisfied Very important Important (I) Less (NS) (VI) important(LI) FC1

71

3

65

9

0

FC2

26

48

32

41

1

FC3

18

56

26

18

30

FC4

36

38

26

18

30

FC5

49

25

29

30

15

answers given by the students to the question “Are you satisfied with your university life” were as follows: 21 students stated that they were very satisfied, 30 students were moderately satisfied, and 23 students were not satisfied.

4 The Analysis Process of Satisfaction Values Using Fuzzy Logic The steps of the analysis process of satisfaction values are shown in the Fig. 4.

Fig. 4. The process of analysis of satisfaction factors values with fuzzy logic

We have explained the first 3 steps shown in Fig. 5 in the previous section. In this section, we will try to explain the next steps. Our aim in the analysis of satisfaction parameters using fuzzy logic is to determine the effect of satisfaction factors on the overall satisfaction value. Concretely, it was aimed to investigate the correlation between the satisfaction levels (SSFF), the weights of the factors (WSF), the overall satisfaction value (OS) and the effect of student evaluation on the overall satisfaction value by the SSFF factor (FS). For this purpose, the Apriori algorithm, which is one of the association rule methods, was used [13]. The method finds items that are frequently used together. Using the Apriori algorithm, we tried to answer the following question: Which value combinations of SSFF, WSF, OS and FS are more common in survey responses? For example, the combination of SSFF = “Satisfied”, WSF = “Very Important”, OS = “High”, and FS =” High” values is frequently encountered. In this case, we can say that if SSFF = “Satisfied”, WSF = “Very Important” and OS = “High”, the probability of FS getting the value of “High” is high.

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We used the results of applying the Apriori algorithm for the fuzzy logic inference method expressed by the IF THEN rules [14–16] as follows: FR1i : If SSF i = Satisfied AND WSF i = Very Important AND OS = High THEN FS i = High FR2i : If SSF i = Satisfied AND WSF i = Very Important AND OS = Medium THEN FS i = High FR3i : If SSF i = Satisfied AND WSF i = Very Important AND OS = Low THEN FS i = Low FR4i : If SSF i = Satisfied AND WSF i = Important AND OS = High HEN FS i = High FR5i : If SSF i = Satisfied AND WSF i = Important AND OS = Medium THEN FS i = High FR6 i : If SSF i = Satisfied AND WSF i = Important AND OS = Low THEN FS i = LOW FR7 i : If SSF i = Satisfied AND WSF i = Less Important AND OS = High THEN FS i = Medium FR8i : If SSF i = Satisfied AND WSF i = Less Important AND OS = Medium THEN FS i = Medium FR9i : If SSF i = Satisfied AND WSF i = Less Important AND OS = Low THEN FS i = Low FR10i : If SSF i = Not satisfied AND WSF i = Very Important AND OS = High THEN FS i = Low FR11i : If SSF i = Not satisfied AND WSF i = Very Important AND OS = Medium THEN FS i = Low FR12i :If SSF i = Not satisfied AND WSF i = Very Important AND OS = Low THEN FS i = High FR13i : If SSF i = Not satisfied AND WSF i = Important AND OS = High THEN FS i = Low FR14i : If SSF i = Not satisfied AND WSF i = Important AND OS = Medium THEN FS i = Low FR15i : If SSF i = Not satisfied AND WSF i = Important AND OS = Low THEN FS i = High FR16 i : If SSF i = Not satisfied AND WSF i = Less Important AND OS = High THEN FS i = Low FR17 i : If SSF i = Not satisfied AND WSF i = Less Important AND OS = Medium THEN FS i = Low FR18i : If SSF i = Not satisfied AND WSF i = Less Important AND OS = Low THEN FS i = Medium. The implementation of fuzzy inference rules on the FisPro application is given in Fig. 5. FisPro (Fuzzy Inference System Professional) application [17] was used to create fuzzy inference rules. FisPro is an open source portable software. It allows to create fuzzy inference systems and to use them for reasoning purposes. In accordance with the sample values in the Fig. 5, if the student’s satisfaction factor is 5, the weight of this factor is 3.8, and the overall satisfaction is 5, the overall satisfaction effect of this factor will be 4.432.

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Fig. 5. The implementation of fuzzy inference rules on the FisPro application (screen shoot)

5 Conclusion In the study, a questionnaire was applied to determine the satisfaction of the students from their university life in a university department. Parameters affecting satisfaction were expressed with fuzzy values. By applying fuzzy inference rules, satisfaction factors, the weight of the factors and the effect of these factors on overall satisfaction were investigated. For this purpose, fuzzy inference open source software application FisPro was used. Student opinions about a concrete university, department and city were reflected in the survey data. In this sense, it is possible to come up with completely different results within the scope of another research. The results of the research can help university, faculty and department managers and academicians to pay more attention to which subjects to increase student satisfaction and to take measures in this direction.

References 1. Sim¸ ¸ sek, H., Islim, Ö.F., Öztürk, N.: Student satisfaction as an indicator of quality in higher education: a scale development study. Trakya J. Education 9(3), 380–395 (2019). https://doi. org/10.24315/tred.441397 2. Dhaqane, M.K., Afrah, N.A.: Satisfaction of students and academic performance in Benadir University. J. Edu. Pract. 7(24), 59–63 (2016). https://doi.org/10.7176/JEP 3. Siming, L., Gao, J., Xu, D., Shaf, K.: Factors leading to students’ satisfaction in the higher learning institutions. J. Edu. Pract. 6(31), 114–118 (2015). https://doi.org/10.7176/JEP 4. Bakır, N.O., Arslan, F.M., Gegez, A.E.: Factors affecting satisfaction levels of university students: a research on marmara university business administration faculty students. Marmara Uni. J. Econ. Adminis. Sci. 38(1), 93–125 (2016). https://doi.org/10.14780/iibd.69451 5. Muslim, M.H., Karim, H.A., Abdullah, I.C.: Satisfaction of students’ living environment between on-campus and off-campus settings: a conceptual overview. Procedia - Social Behav. Sci. 68, 601–614 (2012). https://doi.org/10.1016/j.sbspro.2012.12.252 6. Muchiri, K.A., Tanui, E.K., Kalai, J.M.: Quality of academic resources and students’ satisfaction in public universities in Kenya. Int. J. Learn., Teach. Educ. Res. 15 (2016). https:// doi.org/10.26803/ijlter

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7. Ngamkamollert, T., Ruangkanjanases, A.: Factors influencing foreign students’ satisfaction toward international program in Thai universities. Int. J. Inf. Edu. Tech. 5, 170–178 (2015). https://doi.org/10.7763/ijlet.2015.v5.497 8. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II – Singapore: World Sci., p. 692 (2019) 9. Aliev, R.A.: Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-34895-2 10. Wang, R., Wang, R., Tseng, M.: Evaluation of international student satisfaction using fuzzy importance-performance analysis. Procedia - Social Behav. Sci. 25, 438–446 (2011). https:// doi.org/10.1016/j.sbspro.2012.02.055 11. Cervero, A., Castro-Lopez, A., Álvarez-Blanco, L., Esteban, M., Bernardo, A.: Evaluation of educational quality performance on virtual campuses using fuzzy inference systems. Plos One 15(5), e0232802 (2020). https://doi.org/10.1371/journal.pone.0232802 12. Nababan, D., Simarmata, J.E.: Analysis of student satisfaction with academic services using fuzzy mamdani method. Solid State Technol. 63(3), 5069–5075 (2020) 13. Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.I.: Fast discovery of association rules. In: Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.) Advances Knowledge Discovery and Data Mining, pp. 307–328. AAAI Press, Menlo Park (1996) 14. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 15. Mirzakhanov, V.E., Gardashova, L.A.: The incrementality issue in the Wu-Mendel approach for linguistic summarization using IF-THEN rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 293–300. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_40 16. Aliev, R.A., Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization of information granules in fuzzy IF-THEN rules. In: 10th World Conference Intelligent Systems for Industrial Automation, WCIS-2018, Tashkent, Uzbekistan, pp. 52–55 (2018) 17. FisPro: An open source portable software for fuzzy inference systems FisPro. https://www. fispro.org/download/documentation/fispro36inline.pdf

Investigation of Submarine Pipeline Failure Accidents in Deepwater Based on the Fuzzy Analytical Hierarchy Process Hajar Ismayilova1

, Mansur Shahlarli2

, and Fidan Ismayilova1(B)

1 Azerbaijan State Oil and Industry University, Azadlig 20, Baku AZ1010, Azerbaijan

˙ [email protected], [email protected] 2 SOCAR, “OIL GAS SCIENTIFIC RESEARCH PROJECT” Institute, H. Zardabi 88a,

Baku AZ1012, Azerbaijan

Abstract. Offshore pipelines perform crucial role in energy industry. The safe exploitation of subsea pipelines is one of the most important issues. Therefore, it is necessary to minimize technological risks in order to avoid undesirable situations resulting from oil and gas spills in subsea pipelines. Ensuring the safety of subsea pipelines is one of the most important factors. As about 2/3 of the world is under deep-water, the main energy sources are also under water. The paper investigates the causes of accidents (corrosion, natural disaster, material, operation process) in subsea pipelines. The purpose of the study is to investigate the most common accidents in subsea pipelines, to identify the main risk factors, to develop an algorithm and to calculate its weight factors in accordance with the triangular Fuzzy AHP (Analytical Hierarchy Process). A special algorithm was developed to determine the risk factors in four categories. Then, according to the algorithm, evaluation index system, relative importance language scale, judgement matrices was established and calculations were performed with the fuzzy analytical hierarchy process, degree of possibility and relative criteria weight factors were shown. As a result, risk weight factors were shown in 4 categories and the most affected factor was determined. The result of the study was that the potential source of accidents on subsea process lines was investigated. Keywords: Fuzzy · Weight vectors · Risk factors · Judgement matrix · Subsea pipeline algorithm

1 Introduction Safety of subsea pipelines significantly affects oil and gas industry. As a result of the research, it was found that accidents on underwater pipelines as a result of technological risks led to a shutdown of the technological process, environmental pollution, economic losses and material losses. Studies show that most accidents occur in the Gulf of Mexico. Pipeline spills can be caused by factors such as corrosion, equipment failure, external forces, severe weather, or human error [1]. Overall statistics on accident frequency by risk factor (weight coefficients) are different (Table 1.) [2]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 391–398, 2023. https://doi.org/10.1007/978-3-031-25252-5_52

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Table 1. Total statistics on accident stopping frequencies by factors (weight coefficients) №

Types of factors

1

Human impacts

0,20

2

Corrosion factors

0,10

3

Quality and features of pipes production

0,05

4

Quality of construction and installation works

0,10

5

Constructive design technological parameters

0,10

6

Natural impacts

0,10

7

Exploitation factors

0,05

8

Defects in welding seams and pipe connections

0.30

Coefficients

The main learning objectives of the paper are: - Determining the factors affecting failure of deep-water pipelines. - Analysis of key risk factors. - Proposed guidelines for effective inspection and maintenance of offshore oil and gas pipelines. The major factors to be considered in the article are as follows: 1. 2. 3. 4.

Corrosion Natural disasters Material Operation process.

Considering the fact that, the main pipelines are considered a potential source of fear, thus, an assessment of pipeline risks is a foundation for developing priority measures in order to increase their safe operation [3].

2 Materials and Methods Fuzzy Analytical Hierarchy Process Based on Triangular Number. Three Numbers - l, M, U (Where l ≤ m ≤ u) Are Used to Denote a Fuzzy Event. Evaluation system: Step 1: Establish the hierarchy system (Fig. 1). Step 2: Appoint the membership functions of triangular fuzzy numbers (Fig. 2). Step 3: Establishment of the judgement matrix. Step 4: Consistency text. Step 5: Calculation of weights for risk factors. Step 6: Compare the risk factors. -Step 1. In this research we will consider 4 risk factors: Corrosion, Natural disaster, Material, and Operation. Each factor has four sub-factors illustrated in Fig. 1.

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Fig. 1. Establishing of the hierarchical structure system

-Step 2. Establishing language scale.

Fig. 2. Relative importance languages scale table

Fuzzy linguistic scale methods for risk factors are followings [4, 5]: (Table 2). Table 2. The mean of fuzzy number Lingustic scale definition

TFN( Triangular fuzzy number)

The Inverse of triangular fuzzy scale

Equally

1, 1, 1

1, 1, 1

Moderate

1/2, 1, 3/2

2/3, 1, 2

Weakly

1, 3/2, 2

1/2, 2/3, 1

Strongly

3/2, 2, 5/2

2/5, 1/2, 2/3

More serious

2, 5/2, 3

1/3, 2/5, 1/2

Extremely

5/2, 3, 7/2

2/7, 2/5, 1/3

Triangular fuzzy number (P = (l, μ, m)) can be determined according to the Fig. 3 [6, 7].

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Fig. 3. Triangular fuzzy number (P)

The membership function is determined as Eq. 2 ⎧ ⎪ 0(x < l), ⎨ x−l μ(x) = m−l , l ≤ x < m ⎪ ⎩ μ−x , m ≤ x < μ μ−m

(1)

-Step 3: Creating of the judgement matrix: numerical quantity of judgement matrix is related to the relative importance language scale [8]. (Table 3). Table 3. Risk factors in general Risk factors

Corrosion factor-1

Natural disaster factor-2

Material factor-3

Operation factor-4

Corrosion factor-1

(1, 1, 1)

(5/2, 3, 7/2)

(2/7, 1/3, 2/5)

(1, 3/2, 2)

Natural disaster factor-2

(2/7, 1/3, 2/5) (1, 1, 1)

(3/2, 2, 5/2)

(1, 3/2, 2)

Material factor-3

(5/2, 3, 7/2)

(3/2, 1/2, 2/3)

(1, 1, 1)

(2/5, 1/2, 2/3)

Operation factor-4

(1/2, 2/3, 1)

(1/2, 2/3, 1)

(3/2, 2, 5/2)

(1, 1, 1)

-Step 4. Checking of consistency: Initially, calculation of the maximum value (λmax ) of the fuzzy matrix, test according to the consistency checking equation [9]: CI = (λmax − n)/(n − 1) CR =

CI RI

(2) (3)

CI- indicator of consistency, n-matrix order, RI- random index value, CR- Consistency random index. The values of random index are given in the table 4 [10]. -Step 5: Calculation of weights for risk factors.

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Table 4. Definition of values for consistency checking n

2

3

4

5

6

7

8

9

10

RI

0

0.58

0.90

1.12

1.24

1.32

1.41

1.45

1.49

Fig. 4. Triangular fuzzy number (P1, P2)

Fuzzy AHP (Analytic Hierarchy Process) is one of the fuzzy ranking methods using pair-wise comparison criteria [11]. Determination of triangular fuzzy numbers P1 = (l1m1u1) and P2 = (l2m2u2) graphically can be shown as Fig. 4.

Si =

m

j M j=1 gi

×

 n

m

j M j=1 gi

i=1

−1 (4)

where: m 

j

Mgi = (

m 

j=1

i=1

m

j M j=1 gi

−1

m 

j=1

and  n

lj ,

=

mj ,

j=1

1

m

j=1 uj

1

, m

j=1 mj

1

, m

j=1 lj

 (5)

Degree of possibility: Applying Chang’s extent analysis to determine the degree of possibility Sb ≥ Sa . V(Sb ≥ Sa ) = 1, if mb ≥ ma 0, if la ≥ ub la − ub , otherwise (mb − ub ) − (ma − la ) V(Sb ≥ Sa ) = hight(Sb ∩ Sa ) = μSa

(6)

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-Step 6: The relative criteria weight: V (Si ≥ S1 , . . . .., Sk ) = minV (Si ≥ Sk ) = w (Si )

(7)

3 Solution of the Problem Through calculation (5–9), the 4 categories of failure elements in the corrosion, natural disaster, material and operation process are shown as follows: Corrosion - SF1 = (0.1983, 0.2915, 0.3946), Natural disaster - SF2 = (0.1569, 0.2415, 0.3374), Material damages - SF3 = (0.2236, 0.25, 0.3335), Operation process (by Human Error) - SF4 = (0.1449, 0.2165, 0.3146), The minimum possible degree is obtained with these vectors as: V(S1 ≥ S2) = 1.00 V(S2 ≥ S1) = 0.73558963 V(S1 ≥ S3) = 1.00 V(S3 ≥ S1) = 0.76513865 V(S1 ≥ S4) = 1.00 V(S4 ≥ S1) = 0.60794563 V(S2 ≥ S4) = 1.00 V(S4 ≥ S2) = 0.27584397 V(S2 ≥ S3) = 1.00 V(S3 ≥ S2) = 0.93431855 V(S3 ≥ S4) = 1.00 V(S4 ≥ S3) = 0.15917439 V(S1 ≥ S2, S3, S4) = 1 V(S2 ≥ S1, S3, S4) = 0.73558963 V(S3 ≥ S1, S2, S4) = 0.76513865 V(S4 ≥ S1, S2, S3) = 0.15917439 In our previous studies [2], the final vectors for individual expert and expert group based on Table 3 are followings. [0.18, 0.37, 0.59], [0.18, 0.31, 0.53], [0.18, 0.37, 0.59], [0.18, 0.36, 0.58]. According to previous investigations, these indicators do not differ much from each other and the level of technological risk resulting from oil spills for oil pipelines is not very high, mainly can be assessed “weak” risks. Finally, the weight factor of 4 categories risk factors in process are obtained (9). w = (1, 0.73558963, 0.76513865, 0.15917439)T Through the normalization of equation, we have obtained the weight vectors for each factor (FI, F2, F3 and F4): W = (0.375953606, 0.276547574, 0.287656634, 0.059842186)T

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Table 5. Weights of criteria of risk factors Criteria

Weights of criteria

Si

C-1

0.375953606

0.1983, 0.2915, 0.3946

C-2

0.276547574

0.1569, 0.2415, 0.3374

C-3

0.287656634

0.2236, 0.25, 0.3335

C-4

0.059842186

0.1449, 0.2165, 0.3146

After normalization, we can classify the weights of criteria as following (Table 5). The weight vectors obtained in this article are shown on a scale of [0, 1]. According to the assessment, the main cause of accidents in subsea pipelines is corrosion.

4 Conclusion In the paper, it was shown fuzzy linguistic scale for fuzzy number and was established special algorithm for calculation of weight factors for risks. The evaluation index system and relative importance language scale graphic was analyzed. Based on judgement matrices for risk factors, the weight risk factors were calculated and determined.

References 1. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: An introduction to the arithmetic of Z-numbers by using horizontal membership functions. Procedia Comput. Sci., Elsevier, Netherlands, 120, 349–356, (2017) https://www.sciencedirect.com/science/article/pii/S1877050917324614 2. Ismayilova, H.G., Farzalizada, Z.I., Damirova, J.R., Alakbarov, Y.Z., Shahlarli, M.E.: Fuzzy Assessment of Technological Risks in the Main Oil Pipeline. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 127– 131. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_16 3. Muhibauer, W.K.: Pipeline Risk Managament Manual. Guff Publishing Company, p. 256 (1992) 4. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 5. Kahraman, T.: Ertay: A fuzzy optimization model for QFD planning process using analytic network approach”. Europ. J. Operat. Res. 171, 390–411 (2006) 6. Aliev, R.A., Pedrycz, W., Fazlollahi, B., Alizadeh, A.V., Guirimov, B.G., Huseynov, O.H.: Fuzzy logic-based generalized decision theory with imperfect information. Inform. Sci., Elsevier, 189, 18–42 (2012) Sun, B. D., Tang, J. C., Yu, D. H., Song, Z. W., Wang, P. G.: Ecosystem health assessment: a PSR analysis combining AHP and FCE methods for Jiaozhou Bay, China. Ocean Coastal Manag. 168 41–50. (2019). https://doi.org/10.1016/j.ocecoaman.2018. 10.026 7. Mirzakhanov, V.E.: Value of fuzzy logic for data mining and machine learning: a case study. Expert Syst. Appl. 162 113781 (2020) https://doi.org/10.1016/j.eswa.2020.113781 https:// doi.org/10.1016/j.eswa.2020.113781

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8. Mirzakhanov, V.E., Gardashova L.A.: Modification of the Wu-Mendel approach for linguistic summarization using IF-THEN rules. J. Experiment. Theor. Artif. Intell. 31(3), 77–97 (2019). https://doi.org/10.1080/0952813X.2018.1518998 9. Xiaofeng, G.: Risk Assessment of pipeline failure based on fuzzy analytic hierarchy process. IOP Conf. Ser.: Earth Environ. Sci., 384 (1), 012010 (2019) 10. Shukri, F.A.A., Isa, Z.: Ranking fuzzy numbers with fuzzy analytical hierarchy in risk assessment. Civil Eng. Architect. 8(4), 669–705 (2020)

Healthy Weight Estimation by Using Fuzzy Concept Farida Huseynova(B) Azerbaijan State Oil and Industry University, Azadlig ave. 20, AZ1010 Baku, Azerbaijan [email protected]

Abstract. The human brain encodes the information imprecisely, as information about the normal weight. Linguistic hedges and fuzzy sets can be helpful for description of approximate knowledge of primary data and verify it by the