Fuzzy Models in Economics [1st ed.] 9783030612818, 9783030612825

Table of contents :
Front Matter ....Pages i-xvi
Fuzzy Analysis of Socioeconomic Development Using Linguistic Intuitionistic Fuzzy Numbers (Gorkhmaz Imanov)....Pages 1-26
Fuzzy Analysis of Economic Diversification Level (Gorkhmaz Imanov)....Pages 27-39
Measuring the Financial Stability (Gorkhmaz Imanov)....Pages 41-53
Fuzzy Estimation of National Green Economy Index and Investments Distribution (Gorkhmaz Imanov)....Pages 55-71
Models of Socioeconomic Security (Gorkhmaz Imanov)....Pages 73-98
Assessment of the Development of Information Economy (Gorkhmaz Imanov)....Pages 99-113

Citation preview

Studies in Fuzziness and Soft Computing

Gorkhmaz Imanov

Fuzzy Models in Economics

Studies in Fuzziness and Soft Computing Volume 402

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

The series “Studies in Fuzziness and Soft Computing” contains publications on various topics in the area of soft computing, which include fuzzy sets, rough sets, neural networks, evolutionary computation, probabilistic and evidential reasoning, multi-valued logic, and related fields. The publications within “Studies in Fuzziness and Soft Computing” are primarily monographs and edited volumes. They cover significant recent developments in the field, both of a foundational and applicable character. An important feature of the series is its short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results. Indexed by ISI, DBLP and Ulrichs, SCOPUS, Zentralblatt Math, GeoRef, Current Mathematical Publications, IngentaConnect, MetaPress and Springerlink. The books of the series are submitted for indexing to Web of Science.

More information about this series at http://www.springer.com/series/2941

Gorkhmaz Imanov

Fuzzy Models in Economics

123

Gorkhmaz Imanov Doctor of Economic Sciences Foreign member, Real Academia de Ciencias Economicas y Financieras (R.A.C.E.F) Corresponding Member of ANAS, Head, Fuzzy Economy Laboratory Control System Institute, National Academy of Sciences of Azerbaijan (NASA) Baku, Azerbaijan

ISSN 1434-9922 ISSN 1860-0808 (electronic) Studies in Fuzziness and Soft Computing ISBN 978-3-030-61281-8 ISBN 978-3-030-61282-5 (eBook) https://doi.org/10.1007/978-3-030-61282-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 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

In memory of Prof. Lotfi A. Zadeh, the founder of Fuzzy Logic Theory

Foreword

Most ideas go through our brains without leaving a trace. We learn them; We memorize them, perhaps, and replace them with others in the limited landscape of our memory, where we end up being strangers, because we always evoke them differently. But other ideas, the least, and yet the most powerful, take over our brain as soon as they reach it and change it: they modify our way of thinking and then change ourselves. My teacher Arnold Kaufmann used to describe Zadeh as one of those geniuses who with their ideas change the intelligence of Humanity. Since he listed them, none of us have thought as before. No one accepts that any way of thinking implies binary reasoning. And around us, machines, our computational reflex, have adopted Zadeh’s cool ideas in their relationship with humans. Zadeh changed my brain from the day, between 1968 and 1970, when Prof. Kaufmann warned me on the phone: “I have sent you a work by Professor Zadeh that deserves to be read.” And I received, shortly thereafter, a copy of the article “Fuzzy Sets” which, to begin with, changed the direction of my modest work and gave my research a whole new meaning. It was not long before Gorkmaz Imanov, a well-known scientist from Zadeh, an Azeri compatriot, who, fascinated by the progress of his teacher, knew how to anticipate that this logic provided conceptual tools that could be applied to the economic sphere. And it was Zadeh himself who told him about my research, which, in his wake and that of Professor Kaufmann, has long pointed in that direction as well. So Imanov contacted me then and, on the occasion of the Kaufmann Prize that we awarded Zadeh in 2004, the two came to Barcelona. Days later, the FEGI Foundation and the Rovira i Virgili University awarded Zadeh the I Kaufmann Medal in Reus. The scientist who made this meeting possible, already integrated into the Royal Academy of Economic and Financial Sciences, was also Gorkmaz Imanov, who accompanied him.

vii

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Foreword

At the airport we were waiting for Zadeh, who was flying in from Berkeley, my wife, Ana Maria, and me. We soon realized that the teacher was already part of our family, so we invited him to eat at home. Between courses, Zadeh began to speak in Russian, his mother tongue, with my son Jaume. And already in the university, prof. Zadeh demonstrated that his didactic capacity went hand in hand with his investigative power. He began by explaining how in the field of thermodynamics with the notion of entropy it is possible to study how the disorder works and evolves in a complex technological system. And also proved how the chaos theory allows interesting investigations on the evolution of a mechanistic system attacked by a disorder. We realized that the Mechanistic mathematics, with certainty and chance, are not scientifically usable in many areas of knowledge. And, mainly in the social sciences, due to the subjectivity that permeates the information necessary to obtain numerical results aimed at decision support. We already have theoretical and technical elements that are capable of adequately dealing with complexity and uncertainty that they meet under the umbrella of the “Fuzzy Sets Theory”. Zadeh never hid the most remote antecedents of the Fuzzy Sets Theory, which are already in Epicurus (341–270 BC) who is credited with rejecting the idea of rigorous binariness of the “Principle of the Excluded Middle” (a proposition or is true or is false). He stated that this principle is only valid if there is no third possibility “tertium non datur” (exclusive third). Twenty-two centuries later Lukasiewicz exposes his “Valencia Principle”, according to which there are propositions that are neither true nor false but indeterminate (each proposition has a truth value). And half a century later, in 1965, is when Lofti Zadeh published the aforementioned article “Fuzzy Sets”. With it, the way is opened for a new treatment of uncertainty. Soon after, with Kaufmann, we began the task of incorporating the basic elements of Zadeh’s work in the field of social sciences and, in particular, in the economic sciences. It was precisely our vocation as a teacher and researcher, Kaufmann in the field of engineering, and in the field of economics, that led us to consider the possibility of developing schemes and models to solve economic and social problems in a context of complexity and uncertainty. There were not a few researchers in our field who were not convinced of the effectiveness of the formal elements normally accepted at the time, impeccable in their formality, but far from the approaches that emerged day by day, in the work of companies and institutions. We wanted to give them the opportunity to read, like me, “Fuzzy Sets”, and they studied it to completely change the focus of their work, and thus give new meaning to their teaching and research tasks. It was exciting to incorporate them into our endeavor and to set Barcelona as a future objective to host the studies, research, and teaching of Economic and Management Systems in the field of uncertainty based on the Fuzzy Sets.

Foreword

ix

Lotfi Zadeh’s work allowed us to delve into the very roots of the structure of economic thought. The inability of the “exclusive third principle” to support valid reasoning for the study of complex economic phenomena led much later to state the “principle of gradual simultaneity”, which I presented in 1996, at the SIGEF Congress in Buenos Aires. This principle has been the starting point for the development of new logical operators that have allowed the development of important elements for the treatment of the subjectivity components inherent in economic and management problems. The models and algorithms developed to continue to provide important results in dealing with the real problems of today’s society, where decisions face new, highly complex challenges. The first works came to light, on the one hand, with our participation in international Congresses defending, sometimes not without some difficulty, postulates that started from the findings of Lotfi Zadeh: “How difficult it is still to remove the consciences of those who hold the” truth “of inherited science”!1

And all these years of work of our teams, in the footsteps of Master Zadeh, and thanks to the invaluable mutual collaboration with powerful researchers such as Gorkmaz Imanov, we have been recognized with 31 “Honoris Causa” doctorates, which I have received in his name, by public universities on four continents and our membership in eleven European Scientific Academies. New theories have also emerged from our research activity, while we generalized existing ones. In this sense, the theory of forgotten effects, the theory of affinities and the theory of experts are worthy of special mention. On the other hand, the creation and development of the neural graph concept constitutes an important step to “explain” the complex connections of economic and managerial relationships. Gorkmaz Imanov is a master in this field. Since then, distinguished researchers have been awarded who, working in the economic field or creating methods, models or algorithms that can be used in this field, have made contributions of high scientific and/or technical interest. Hence, after Zadeh, they have been awarded the Kaufmann medal: H. J. Zimmermann, M. M. Gupta, J. Klir, J. Gil Aluja, J. Kacprzyk, and C. Carlsson. And now we continue to work with Z numbers, defined by Zadeh in 2011, in order to formalize the remarkable human ability to make rational decisions in environments of uncertainty and imprecision. These numbers provide a fuzzy valuation and an idea of their reliability.

Gil Aluja (2013): “Lotfi A. Zadech and Economic Uncertainty” in: R. Seising et al. (Eds.): On Fuzziness: Volume I, pp. 205–209. DOI: 10.1007/978-3-642-35641-4_31, ©Springer-Verlag Berlin Heidelberg.

1

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Foreword

Because, more than half a century after the “Fuzzy Sets”,2 the message it contains is still alive and, most importantly perhaps, it is still useful to awaken sleeping consciences, and to illuminate new routes towards a better understanding of physical, biological, and social phenomena. For those who, like Gorkmaz Imanov, have dedicated a very important part of their scientific activity to trying to understand, explain, and adequately deal with economic and managerial realities, Zadeh’s work represented a decisive impulse still in force. They have known how to take advantage of the trail of Zadeh who knew how to lean, too, on the precursors of that different way of reasoning. And he was able to see that the elements of a set have a possible degree of belonging with values that range between 0 and 1, and in this interval, they can be assigned infinity of values. But in the tribute to this work by Gorkmaz Imanov, it is clear that Zadeh was coined by the term “fuzzy/diffuse” in 1965, with his article “Fuzzy Sets”. The theses that he proposes arise from the segmented contributions of thinkers from different disciplines who, like him, had a much broader and more complex vision of the world than traditional logic was capable of reflecting. Bertrand Russell’s set paradox, Werner Heisenberg’s uncertainty principle of quantum physics, and Max Black’s theory of vague sets were also decisive in getting Zadeh to publish his research. Zadeh’s intention was to create a formalism to more efficiently handle the imprecision of human reasoning. In 1971, when he published “Quantitative Fuzzy Semantics”,3 where the formal elements that give rise to the methodology of Fuzzy Logic and its applications as they are known today appear. Starting in 1973, with Zadeh’s basic theory of fuzzy controllers, other researchers began to apply fuzzy logic to various processes and fields of knowledge. And his work crosses the Pacific and several research groups on fuzzy logic are today established in some Japanese universities. Zadeh had come to the United States from Iran to study at the Massachusetts Institute of Technology and then at Columbia University. In the 1950s, he helped to establish the foundations of modern systems theory. He introduced fuzzy logic into engineering in 1965, when he was already head of the department of electrical engineering at the University of California, Berkeley. Lotfi Zadeh in his speeches often noted that I created the theory of fuzzy logic and fuzzy sets for economists as a tool for analysis and forecasting. But unfortunately, this theory was first used by specialists in technical sciences. Economists began to use these tools later in the 80’s of the last century, in recent years, scholars from various countries have referred to the tools of this theory and use them in various studies.

2

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. Zadeh, L. A. (1971). Quantitative fuzzy semantics. Information sciences, 3(2), 159–176.

3

Foreword

xi

The economy is one of the important areas that affect other areas, as well as experiencing changes. The processes taking place in the economy also have a chain relationship between themselves. Therefore, changes in one area of the economy have different effects on other areas. Since then, many have found, in Zadeh’s theory, the way to translate “in formulas” vague descriptions in relation to “poorly defined” classes, among which the principle of the excluded third party and of non-contradiction are not maintained. But few have done it like Gorkmaz Imanov. His book “Fuzzy Models in Economics” is of great interest. Professor Gorkmaz Imanov is Doctor of Economics, Corresponding Member of the National Academy of Sciences of Azerbaijan and a foreign member of the Royal Spanish Academy of Economics and Finance. It offers some models of various aspects of economic processes. It is worth mentioning that not all economic and other book indicators can be expressed with exact values. Therefore, in this book, when constructing and analyzing economic models, various fuzzy methods are used, with the help of which uncertainties can be avoided and a concrete result will be obtained in the future. The book consists of six chapters. Chapter 1 of this book provides a fuzzy analysis and assessment of socioeconomic development based on their respective indicators. The process of evaluation and analysis is carried out using linguistic intuitive fuzzy numbers. Chapter 2 of the book provides a fuzzy analysis of the level of diversification of the economy. The composite index is calculated by fuzzy entropy. The Input-Output model of the analysis of economic diversification is considered. In the final paragraph, an analysis of intersectoral relationships is carried out using the fuzzy DEMATEL method. The financial sector is one of the main areas of the economy. To maintain a longer level of the economy, financial stability is required. Chapter 3 of the book examines the measurement of the financial stability of the economy. In the initial paragraphs, the stability index of the financial system is built, and a standard approach to the measurement of the aggregate index of financial stability is presented. The final paragraph suggests a fuzzy approach to the measurement of the financial stability index. Recently, global climate changes have been observed, which in turn, have had a negative impact on public health. One of the big influences is exerted by some economic processes taking place in the world. In order to maintain and improve sustainable development, it is necessary to switch to a Green Economy. This term has been approved by the UNEP program. In Chap. 4 of the book, indicators of the Green Economy are considered, a model for assessing the environmental quality index and a model of the Green Economy is proposed. The last paragraph proposes a fuzzy entropy of estimating the distribution of investments between different factors.

xii

Foreword

With socioeconomic development, the safety of this factor must also be observed. Chapter 5 of the book provides a fuzzy analysis of macroeconomic stability. The following are fuzzy estimates of the country’s level of social security and aggregated indices of financial and environmental security. Recently, scientific and technological progress is developing at a faster pace. Its main factor is information. STP has also affected the economics of countries. The information has also become one of the main factors of the economy. Chapter 6 of this book examines the assessment of the development of the information economy. In the initial paragraph of this chapter, the formalization and development of the information economy is presented. In the following paragraphs, a fuzzy model for assessing the development of the information economy and analyzing the cause-effect relationships is proposed. After reviewing the material of the book, we can confirm that the models and tasks proposed and considered by the author widely cover the problems of the modern economy of the countries of the world. Zadeh’s great achievement was to give this fuzzy field of logic a new name, a new location, and an entirely new mathematical framework. The great merit of Gorkmaz Imanov and some of our school has been to properly transform the roots of economic science, after many years of deep sleep. Zadeh is no longer with us, but his method has forever changed our brains and the way we think. What will never change in those who knew him is the memory of his undying goodness, his love of science, and his generous dedication to human progress. Thanks, Lofti; Thanks, Gorkmaz. Prof. Jaime Gil Aluja President of Royal Spanish Academy of Economics and Finance Barcelona, Spain

Preface

The founder of the theory of fuzzy logic, Lotfi. A. Zadeh, in his work “Concept of a linguistic variable and its application to approximate reasoning”, published by American Elsevier Publishing Company, New York, in 1973, classified economics as a fuzzy system noting that “… weather common quantitative methods of system analysis are able to be indeed effective when analyzing humanistic systems, that is, systems in which human judgment and knowledge play an important role… Economic, political, legal, education systems, etc., may be an example of a humanistic system.” Further, he noted that “… big difficulty of humanistic system demands an approach that is fundamentally different from universally accepted quantitative methods of system analysis”. In particular, the idea is that “… for realistic behavior modeling of such systems, it may be necessary to somewhat reduce the use of quantitative methods, and instead apply the linguistic approach, according to which as values of variables are allowed not only numbers but also words and sentences of a natural or artificial language. Such variables form the basis of fuzzy logic and approximate way of reasoning that can be more attuned to the complexity and inaccuracy of the humanistic system, rather than common quantitative methods of analysis.” The proposed book is devoted to the use of fuzzy logic tools in subsystems of socioeconomic systems such as economics, finance, social, and environmental sciences. The book consists of six chapters. Chapter 1 is devoted to fuzzy analysis of socioeconomic development, taking into account elements of a linguistic intuitionistic fuzzy number. At this purpose, linguistic intuitionistic fuzzy data and the possibilities of using these elements in the analysis of aggregated indexing are analyzed. Using the statistical information on Azerbaijan, specific calculations and analysis of the relevant indicators of the socioeconomic system are described. Chapter 2 is devoted to fuzzy analysis of the level of economic diversification using the fuzzy entropy and the fuzzy DEMATEL method to define intersectoral relations.

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Preface

Chapter 3 is devoted to issues related to define the financial stability level, based on a fuzzy index. In this chapter, a standard approach to this problem is comprehensibly described. Chapter 4 discusses issues of assessing the level of development of a green economy, taking into account fuzzy tools. To this end, on the basis of 11 elements that determine the level of development of a green economy, a fuzzy model is developed. To calculate the index, it is recommended to use the method of fuzzy reasoning taking into account weighting factors. Chapter 5 analyzes fuzzy models of macroeconomic, social, environmental, and financial security. In order to define the aggregated indices, the concepts of a linguistic intuitionistic fuzzy number and weights are used. The suggested approach is demonstrated on the basis of data on Azerbaijan. In Chapter 6, a methodology of fuzzy assessment of the development of information economy is given. As the basis of development of the human capital, the level of knowledge and technology in the country is investigated. The method, based on the tools and techniques of the theory of intuitionistic fuzzy sets and logic, and the DEMATEL method, is used to determine the quality of development of information economy. Further, elements of resources of the economy are analyzed in a more detailed way. In the process of writing this work my students have helped me a lot: H. S. Alieva. (in the 3rd chapter), R. A. Yusifzade (in the 3rd and 4th chapters), M. M. Murtuzaeva (in the 5th and 6th chapters), S. M. Pur Riza (in the 5th chapter), which I greatly appreciated. I am also grateful to A. R. Dostalieva and A. S. Muslimzade for preparing the manuscript for publishing. Baku, Azerbaijan

Prof. Gorkhmaz Imanov

Contents

1 Fuzzy Analysis of Socioeconomic Development Using Linguistic Intuitionistic Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Indicators and Sub-indices for the Analysis of Socio-economic Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Linguistic Intuitionistic Fuzzy Set . . . . . . . . . . . . . . . . . . . . . . 1.3 Fuzzy Analysis of National Innovation Development . . . . . . . . 1.4 Fuzzy Models for the Evaluation of Quality Indices of Social and Economic Systems . . . . . . . . . . . . . . . . . . . . . . . 1.5 Algorithm with the Weighted Rules . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Fuzzy Analysis of Economic Diversification Level . . . . . . . . . 2.1 Fuzzy Entropy Composite Index . . . . . . . . . . . . . . . . . . . 2.2 Input–Output Model Analysis of Economic Diversification 2.3 Using the Fuzzy DEMATEL Method for the Analysis of Intersectoral Relations . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 4 12

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18 21 26

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27 27 28

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31 39

3 Measuring the Financial Stability . . . . . . . . . . . . . . . . . . . . . . 3.1 Construction of a Stability Index of a Financial System . . . 3.2 Standard Approach to Measuring an Aggregated Financial Stability Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Fuzzy Approach to Measuring the Financial Stability Index References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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41 42

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44 45 52

4 Fuzzy Estimation of National Green Economy Index and Investments Distribution . . . . . . . . . . . . . . . . . . . 4.1 Indicators of the Green Economy . . . . . . . . . . . . . 4.2 Model Estimation for the Ecological Quality Index . 4.3 Model of the Green Economy . . . . . . . . . . . . . . . .

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55 56 59 64

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Contents

4.4 Fuzzy Entropy Based Estimation of the Distribution of Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Models of Socioeconomic Security . . . . . . . . . . . . . . . . . . . . . 5.1 Fuzzy Analysis of Macroeconomic Stability . . . . . . . . . . . . 5.2 Fuzzy Estimation of the Country’s Social Security Level . . 5.3 Evaluation of the Aggregated Index of Financial Security . . 5.4 Evaluation of the Aggregate Index of Ecological Security . . 5.5 Evaluation of the Fuzzy Aggregate Index of the Ecological Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Assessment of the Development of Information Economy . . . . 6.1 Formation and Development of Information Economy . . . . 6.2 Fuzzy Model of the Estimation of Quality of Development of Information Economy . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Analysis of the Cause-Effect Relationship . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65 70

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73 73 78 83 90

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93 97

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99 99

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Chapter 1

Fuzzy Analysis of Socioeconomic Development Using Linguistic Intuitionistic Fuzzy Numbers

The influence of global factors on the state of the national economy is becoming increasingly significant. The world economic system today is a complex mechanism in which each national economy has its own role. And, therefore, the analysis of the influence of global factors on the state of the national economy is of great importance. In economic research, for the analysis of socio-economic development various indicators and instruments are used. The approach depends mainly on the aims of analysis, the levels of development and specialization of the analyzed country, and its place in the world economy. This chapter analyzes the degree of influence of external factors on the state of the economy, social indicators and the government’s response to these changes. In order to do this, we define the concepts of “external factor—economic state—social consequences—government response”. The socio-economic indicators of Azerbaijan are considered as an object of analysis, and the linguistic intuitionistic fuzzy sets are used as an instrument. The choice of the analytics instrument is primarily due to the fact that the linguistic intuitionistic fuzzy set makes it possible to take into account statistical information errors and to devise a quality level of development.

1.1 Indicators and Sub-indices for the Analysis of Socio-economic Development Following subchapter has been reproduced from “Analysis of Socioeconomic development by intuitionistic linguistic fuzzy numbers”, Gorkhmaz Imanov, Emin Garibli, Rovshan Akbarov, with permissions from Elsevier. Copyright@, 2017 Elsevier. In the context of globalization, the analysis of the economic development of the oilproducing country should be based on the concept of “External factors—economic condition—social consequences of the economy—government response”. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 G. Imanov, Fuzzy Models in Economics, Studies in Fuzziness and Soft Computing 402, https://doi.org/10.1007/978-3-030-61282-5_1

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2

1 Fuzzy Analysis of Socioeconomic Development …

The main external factors—EFI, for oil-producing countries, affecting the state of the economy are: – Oil price on the world market—WOP; – Exchange rates—USD; – Foreign investments—FIN. The economic state—ESI is described by the following indicators: Oil and gas revenues (mln. US dollars)—OIN; – Volume of investments (mln. AZ. manats ( ))—INV; – Fixed assets (mln. )—MPF; – Financial Stability Index—AFS, (calculation of this index is given by Imanov et al. 2017). The social consequences (SCI) of economy are described as: – – – – – – – – – – – – – – – – – –

Households income (per capita, AZ. manats ( )—INC; Employment (thsd. people)—EMP; Average monthly wages—WAG; Unemployment (%)—UNE; Water supply (%)—WAT; Sewerage (%)—CAN; Central heating system (%)—HES; Gas supply (%)—GAS; Hot water supply (%)—HWA; Providing bathroom, shower (%)—BAT; Ecological Security Index—ESE; more details about this index are given by Imanov et al. (2016); Natural increase of population (for every 1000 people)—GPO; Growth + (decrease-) of migration (thsd. people)—MIG; Expenditure on education (mln. )—EDU; Expenditure on science (mln. )—SCI; Expenditure on health care (mln. )—HEA; The average monthly value of pensions ( )—PEN; The average monthly allowance and compensation per capita ( )—COM. The government’s response (GRI) is described as:

– – – – – –

New work places (number)—NWP; Social investments (mln. )—SIN; Wages growth ( )—GWA; Growth in pensions ( )—GPE; Personnel retraining (number)—TRA; Improvement in housing conditions (number of families)—IHO.

Statistical information on the development of Azerbaijan, corresponding to the problem statement, is presented in Table 1.1

1.1 Indicators and Sub-indices for the Analysis of Socio-economic Development

3

Table 1.1 Values of socio-economic indicators of Azerbaijan during 2010–2015 Indicators EFI

ESI

SCI

GRI

Sub-indices

Years 2010

2011

2012

2013

2014

2015

WOP

79.50

111.26

111.67

108.66

98.95

52.39

USD

0.8026

0.7897

0.7856

0.7845

0.7844

1.0261

FIN

8247.8

8673.9

10314

10540.9

11697.7

11697.7

OIN

35097.36

43355.78

43013.83

45342.2

38015.7

22483.45

INV

17591.4

21588.9

25777.8

27340

27907.5

27907.5

PRF

83054.5

93942.5

107258.7

121671.3

141098.8

150000 −0.169

AFS

0.008

−0.336

−0.214

0.099

0.322

INC

144.2

166.0

190.9

214.7

230.0

240.5

EMP

4329.1

4375.2

4445.3

4521.2

4602.9

4671.6

WAG

331.5

364.2

398.4

425.1

444.5

466.9

UNE

5.6

5.4

5.2

5

5.2

5

WAT

86.8

87.2

87.3

87.3

87.1

86.8

CAN

84.3

84.6

84.9

84.9

85.1

85.0

HES

66.6

64.6

64.6

64.6

64.8

64.6

GAS

86.1

85.0

85.9

85.9

92.1

91.9

HWA

7.2

4.7

5.2

5.2

8.8

6.7

BAT

72.5

71.9

72.0

72.0

72.8

75.0

ESE

−0.48

−0.58

2.012

2.9

2.17

1.39

GPO

12.5

13.5

13.0

12.8

12.2

11.7

MIG

1.4

1.7

2.0

2.3

1.1

1.1

EDU

1180.8

1268.5

1453.2

1437.7

1553.9

1605.1

SCI

92.8

106.1

116.7

117.0

124.2

113.2

HEA

429.2

493.4

609.4

618.9

665.3

708.2

PEN

100.4

112.9

145.1

152.0

170.5

173.4

COM

34.5

39.7

44.3

44.4

49.6

50.6

NWP

73009

94111

120355

190900

127315

115869

SIN

2901.4

3447.2

4072.9

4081.8

4484.4

4442.9

GWA

33.5

32.7

34.2

26.7

19.4

22.4

GPE

4.6

12.5

32.2

6.9

18.5

2.9

TRA

2143

1503

2530

1877

2610

2687

IHO

743

788

413

661

547

501

Reproduced from “Analysis of Socioeconomic development by intuitionistic linguistic fuzzy numbers”, Gorkhmaz Imanov, Emin Garibli, Rovshan Akbarov, with permissions from Elsevier. Copyright@, 2017 Elsevier

4

1 Fuzzy Analysis of Socioeconomic Development …

For the analysis of economic development of Azerbaijan, the linguistic intuitionistic fuzzy set is used as an instrument.

1.2 Linguistic Intuitionistic Fuzzy Set Following subchapter has been reproduced from “Analysis of Socioeconomic development by intuitionistic linguistic fuzzy numbers”, Gorkhmaz Imanov, Emin Garibli, Rovshan Akbarov, with permissions from Elsevier. Copyright@, 2017 Elsevier. The intuitionistic fuzzy set (IFS), introduced by Atanassov [1], is a generalization of the concept of Zadeh’s fuzzy set [2]. In 2009, Wang and Li proposed a linguistic intuitionistic fuzzy set [3] defined as:     A = x, Sθ(x) , μA (x), νA (x) |x ∈ X

(1.1)

where Sθ(x) ∈ S, μA : X → [0, 1] and νA : X → [0, 1], that satisfies the condition μA (x) + νA (x) ≤ 1, μA (x) and νA (x), represent the membership and non-membership degrees, respectively, of elements x to the linguistic value Sθ(x) . For each linguistic intuitionistic fuzzy set     A = x, Sθ(x) , μA (x), νA (x) |x ∈ X , there is associated πA (x) = 1 − μA (x) − νA (x), which is called an intuitionistic fuzzy index of the element x of the linguistic variable Sθ(x) . For the linguistic intuitionistic fuzzy set     A = x, Sθ(x) , μA (x), νA (x) |x ∈ X , the triple (Sθ(x) , (μA (x), νA (x))) is called a linguistic intuitionistic fuzzy number. Data Processing In order to solve the problem by applying the appropriate model, we used data on the State Statistical Committee of Azerbaijan (https://stat.gov.az) and BP Statistical Review of World Energy [June 2015] for 2010–2015. At the first stage of problem solution, where the selected indicators have a different nature, and therefore, are measured in different units and their values are quantities of different orders, the primary information is normalized by the following formulas: min it = X it − X i , X X imax − X imin

(1.2)

1.2 Linguistic Intuitionistic Fuzzy Set max it = X i − X i X X imax − X imin

5

(1.3)

it —is normalized value of the primary information, Ximax —is the maximum where: X value of the primary information in row i, Ximin —minimum value of the primary information in row i. Formula (1.2) is used for the indicators, the great importance of which positively affects the growth of indices. Formula (1.3) is applied to those indicators, a great value, which adversely affects the economic process. For normalization of the Exchange Rate, Migration Growth and Unemployment indicators is used the formula (1.3) and for the rest, formula (1.2). The normalized values of statistical data of Azerbaijan in 2010–2015 years are presented in Table 1.2. After normalization of the primary information, the indicators from Table 1.2 are divided into the following terms: – Low (L)—(−0.03, 0.17, 0.36); – Medium (M)—(0.30, 0.50, 0.69); – High (H)—(0.63, 0.83, 1.03) In the “External factor” sub-index, the term low (L) shows a positive effect, high (H)—the negative impact of the index on the economic state and social consequences. The accuracy and completeness of the primary information largely determines the choice of the types of applied models. The cognition of the quantitative relations of economic processes and phenomena is based on economic dimensions. At the same time measurement accuracy is largely predetermines the accuracy of the final results of the quantitative analysis by means of modeling. In his classic book “On the Accuracy of Economic Observation”, Oskar Morgenstern [4] considers the general but widely ignored problem faced by researchers related to the quality of economic data. For the researcher, the quality of economic data is of paramount importance. This book gives some sources of errors that affect the accuracy of economic information. In this work we use the tools and techniques of the theory of intuitionistic fuzzy sets which makes possible to take into account inaccuracies in economic statistics with the help of the reliability coefficient. This is done with the membership function—μ A(x) and non-membership—ν A(x) . In this way when formulating model parameters, the following kinds of membership and non-membership functions are used: ⎧ x−a ⎪ ⎨  b−a ∗ d; a < x ≤ b c−x μ A(x) = ∗ d; b ≤ x < c c−b ⎪ ⎩ 0; in other ⎧  x−a ⎪ ⎨ 1 −  b−a ; a < x ≤ b ν A(x) = 1 − c−x ; b≤x |x ∈ X }

(1.9)

where μ A : X → [0, 1]ν A : X → [0, 1] and 0 ≤ μ A (x) + ν A (x) ≤ 1 ∀x ∈ X wher e: μ A (x), ν A (x) ∈ [0, 1] numbers denote the membership or non-membership degree of x to A, respectively. For each element of X, there is associated an intuitionistic fuzzy index x in A defined as π A (x) = 1 − μ A (x) − ν A (x) The sub-index indicators of the Global Innovation Index of Azerbaijan in 2011– 2015, corresponding to the indicators expressed as the intuitionistic fuzzy sets, are given in Table 1.6.

1.3 Fuzzy Analysis of National Innovation Development

15

Table 1.6 Values of the indicators expressed by the intuitionistic fuzzy sets 2011

2012

μA

νA

μA

2013 νA

2014

2015

μA

νA

μA

νA

μA

νA

Resources and conditions for innovation 1. INS

0.83

0.17

0.04

0.96

0.22

0.78

0.28

0.72

0.50

0.50

2. HC

0.64

0.36

0.41

0.59

0.05

0.95

0.34

0.66

0.26

0.74

3. INF

0.25

0.75

0.10

0.90

0.02

0.98

0.60

0.40

0.97

0.03

4. MS

0.47

0.53

0.41

0.59

0.13

0.87

0.80

0.20

0.17

0.83

5. BS

0.54

0.46

0.69

0.31

0.11

0.89

0.41

0.59

0.36

0.64

1. KTO

0.05

0.95

0.38

0.62

0.94

0.06

0.49

0.51

0.49

0.51

2. CRO

0.59

0.41

0.21

0.79

0.57

0.43

0.03

0.97

0.10

0.90

Practical results of innovation

In this work we use a generalized entropy measure for the intuitionistic fuzzy set F, composed of n elements, proposed by Szmidt and Kacprzyk [6], in order to define the weights of sub-indices of the Global Innovation Index (GII):  max Count Ai ∩ Aic , (i = 1, . . . , n )  E(Ai ) = max Count Ai ∪ Aic

(1.10)

The results of calculations of the entropy for indicators of the sub-index of disposable resources and innovation conditions (Input) for 2011 are given below: E( A1 ) =

0.17 (0.83, 0.17, 0) ∩ (0.17, 0.83, 0) = = 0.21 (0.83, 0.17, 0) ∪ (0.17, 0.83, 0) 0.83

E(A2 ) =

0.36 (0.64, 0.36, 0) ∩ (0.36, 0.64, 0) = = 0.56 (0.64, 0.36, 0) ∪ (0.36, 0.64, 0) 0.64

E( A3 ) =

0.25 (0.25, 0.75, 0) ∩ (0.75, 0.25, 0) = = 0.33 (0.25, 0.75, 0) ∪ (0.75, 0.25, 0) 0.75

E(A4 ) =

0.47 (0.47, 0.53, 0) ∩ (0.53, 0.47, 0) = = 0.89 (0.47, 0.53, 0) ∪ (0.53, 0.47, 0) 0.53

E(A5 ) =

0.46 (0.54, 0.46, 0) ∩ (0.46, 0.54, 0) = = 0.85 (0.54, 0.46, 0) ∪ (0.46, 0.54, 0) 0.54

Then the weights of individual indicators of the Input sub-index are defined on the basis of the following formula: wi =

1 − E(Ai )

n n − i=1 E(Ai )

(1.11)

16

1 Fuzzy Analysis of Socioeconomic Development …

The weights of individual indicators of Input sub-index for 2011 are computed as follows: w1 (2011) =

1 − 0.21 0.79 = = 0.37 5 − 2.83 2.17

w2 (2011) =

1 − 0.56 0.44 = = 0.20 5 − 2.83 2.17

w3 (2011) =

0.67 1 − 0.33 = = 0.31 5 − 2.83 2.17

w4 (2011) =

0.11 1 − 0.89 = = 0.05 5 − 2.83 2.17

w5 (2011) =

0.15 1 − 0.85 = = 0.07 5 − 2.83 2.17

The calculation of entropy for the indicators of obtained practical results of innovation (Output) sub-index for 2011 is shown below: E( A10 ) =

0.05 (0.05, 0.95, 0) ∩ (0.95, 0.05, 0) = = 0.05 (0.05, 0.95, 0) ∪ (0.95, 0.05, 0) 0.95

E(A20 ) =

0.41 (0.59, 0.41, 0) ∩ (0.41, 0.59, 0) = = 0.70 (0.59, 0.41, 0) ∪ (0.41, 0.59, 0) 0.59

The weights of individual indicators of Output sub-index for 2011 are calculated as: w10 (2011) =

0.95 1 − 0.05 = = 0.76 2 − 0.75 1.25

w20 (2011) =

0.3 1 − 0.7 = = 0.24 2 − 0.75 1.25

In the next stage the value of fuzzy sub-indices of the Global Innovation Index (GII) and the Innovation Efficiency Ratio (IER) for 2011 are defined via the estimated weights of the Input and Output indicators: I nput =0.37(L M) + 0.2(U M) + 0.31(L) + 0.05(L M) + 0.07(L M) =0.37(24.9, 37.45, 50) + 0.2(49.9, 62.45, 75) + 0.31(1, 13, 25) + 0.05(24.9, 37.45, 50) + 0.07(24.9, 37.45, 50) = =(22.51, 34.87, 47.25) == L − L M Out put =0.76(L) + 0.24(L) = 0.76(1, 13, 25) + 0.24(1, 13, 25)

1.3 Fuzzy Analysis of National Innovation Development

17

=(0.76, 9.88, 19) + (0.24, 3.12, 6) = (1, 13, 25) = L M GI I =

(22.51, 47.87, 72.25) (22.51, 34.87, 47.25) + (1, 13, 25) = = 2 2 = (11.26, 23.94, 36.13) = L − L M

IER =

(22.51, 34.87, 47.25) = (0.9, 2.68, 47.25) = L − L M (1, 13, 25)

The value of the sub-indices’ weights, of the global index of financial stability, and of the innovation efficiency ratio for Azerbaijan in 2011–2015 are presented in Table 1.7. As a general conclusion, the results obtained give us an opportunity to define the weights of sub-indices, on the basis of which the quality and efficiency of innovation activity of country are defined and this, in turn, facilitates decision-makers working in this field. Table 1.7 The results of calculations of sub-indices’ weights and global innovation index for 2011–2015 Indicators

Years 2011

2012

2013

2014

2015

w1

0.37

0.32

0.16

0.25

0.01

w2

0.20

0.1

0.22

0.99

0.23

w3

0.31

0.3

0.22

0.13

0.33

w4

0.05

0.1

0.02

0.31

0.28

w5

0.07

0.18

0.2

0.12

0.15

w10

0.76

0.35

0.79

0.04

0.04

w20

0.24

0.65

0.21

0.96

0.96

Input

(21.5, 34.9, 47.3) = L − LM

(24.9, 37.5, 50) = LM

(24.1, 36.6, 49) = LM

(31.5, 44, 56.3) = LM − UM

(27.6, 41, 54.5) = LM − UM

Output

(1, 13, 25) = LM

(16.5, 28.9, 41.3) = L − LM

(6, 18, 30.3) = (1, 13, 25) = L L − LM

(24.3, 36.5, 49) = LM

GII

(11.3, 24, 30.6) = L − LM

(20.7, 33.2, 43.9) = L + LM

(15, 27.4, 40) = L − LM

(16.3, 28.4, (25.9, 38.8, 40.6) = L − LM 51.8) = LM − UM

IER

(1, 2.7, 47.3) = L − LM

(0.6, 1.3, 3) =L

(1, 2, 8) = L

(1.3, 3.4, 56.3) = L − UM

(1, 1.2, 2.2) = L

18

1 Fuzzy Analysis of Socioeconomic Development …

1.4 Fuzzy Models for the Evaluation of Quality Indices of Social and Economic Systems Following subchapter has been reproduced from “Decision Making Systems in Business Administration”, Gorkhmaz Imanov, with permissions from World Scientific. Copyright@, 2012 World Scientific. The economic, social and political events occurring in the world, demand revision model of evolution of problems of social and economic system. As it is known when evaluating the indicators of social and economic system are used based on the theories of Keynes and Friedman are used. At the same time, such an approach does not always correspond to today’s requirements and there was a necessity of revision of existing approaches to modeling of social and economic system. The socioeconomic system is a basis of each society and it consists of the economic and social systems. The concept of a social system is of a broader economic nature since its focal point is the human being. The economic system basically describes processes of production, distribution, an exchange and consumption of products and services. Basic indicator of the economic system is the Gross Domestic Product (GDP) the components of which characterize acts of market processes. The functioning of the economic system is narrowly connected with the processes occurring in social system. There are many approaches to the investigation of social systems, however in the most complete and finished form it has been presented in Parson’s [7, 8] and Luhmann’s works [9, 10] in which the authors have made an attempt to create logicdeductive theoretical models of society covering a human reality in all its integrity and variety. Supposedly, it is accepted to understand the ordered, hierarchical set of individuals, social groups as social system, community of the organizations united by stable connections and relations, interact with environment as a unit. Each social system should satisfy certain material, social and spiritual needs of the members of the society. The macro-level of the social system is societal system which include economic, social, political, cultural, etc. subsystems. The social system constantly reproduces a social quality of the structures and, accordingly, a social quality of individuals and groups. The theory of social quality has been proposed by Beck, Maesen, Thomese and Walker [11, 12]. The social quality represents degree of participation of citizens in the social and economic life of a society at which their well-being and individual potential raises. In the above mentioned articles an attempt has been made to construct fuzzy models of the quality indices of social qualities (SSQI—social system quality index) and of economic system (ESQI—economic system quality index). Problem Statement Today, to define the level of development of a society (country), various indices, such as:

1.4 Fuzzy Models for the Evaluation of Quality Indices of Social and Economic Systems

19

– the human development index (HDI), – the life quality index (LQI), – the sustainable development index (SDI) etc. are used. However, each of them has a number of disadvantages so that they cannot be regarded as comprehensive and universal indexes. The main problem is that the data obtained upon using them needs a deeper and detailed elaboration on the basis of additional statistical information concerning that particular country, including its characteristic features, specific problems faced in that particular country, and its current situation. Moreover, the use of these indices is based on a number of assumptions which, certainly, not always represent the facts. For the modeling of societal systems, we have investigated the following environments in which people operate: – – – – –

economic (EE), social (SE), political (PE), spiritual (SPE), and natural (NE).

These environments are interconnected and their functioning result defines the quality of social development of a society (SSQ). The components of a social system act as follows: 1. The economic environment (EE) is characterized by: • • • • • • •

rates of increase of gross national product (GDP), gross national product per capita (GDP/P), rate of inflation (CPI), share of import products in consumption (FIM), share of hi-tech production in export (TEX), financial stability (FIS), business environment index (BEN,.

and the output parameter of this subsystem is the Economic Environment Quality Index (EEQI). 2. The social environment (SE) includes such indicators as: • life expectancy of the population (LEP), • decile (a parity between the income of 10% of the richest population and the income of 10% of the poorest population) (DEC), • rate of unemployment (UNE), • relation of the number of persons deceased to the number born (RDB), • expenditures for education (EXE), • public health services (EXH), • culture (EXC), • science (EXS).

20

1 Fuzzy Analysis of Socioeconomic Development …

• monthly average salary (WAG), • state pension expenses (PEN), and the output of this subsystem is Social Environment Quality Index (SEQI). 3. Components of the political environment (PE) are: • • • • • • • • • • • • •

risk of military conflict (RAC), risk of social explosion (RSE), constitutional mechanisms of delegation of power (CMP), relation between the state and opposition (GSO), threat of politically motivated violence (TPV), international disputes and tensions (IDT), government policy towards business (GPB), effectiveness of political system in policy formulation and execution (EPS), quality of bureaucracy (QUB), transparency and fairness of legal system (TLS), efficiency of legal system (ELS), corruption (COR), impact of crime (CRI),

and the output of this subsystem is the Political Environment Quality Index (PEQI). 4. The spiritual environment (SE) includes: • • • • • • •

level of religiousness of society (LOR), tolerance level (LOT), level of impact of religion on society development (LOI), quality of cultural development of society (QCS), level of information support (LIS), quality of a science (QIS), quality of health care (QHC),

and the output of this subsystem is the Spiritual Environment Quality Index (Sp EQI). 5. The natural environment (NE) is characterized by: • • • • • •

quality of air (AQI), quality of water (WQI), quality of land (LQI), biodiversity (EBI), environmental protection investments (EPI), environmental damage (NED),

and the output of this subsystem is the Natural Environment Quality Index (NEQI). The system of indicators of various environments are heterogeneous, i.e. the majority of its indicators have not only quantitative measurement but also qualitative.

1.4 Fuzzy Models for the Evaluation of Quality Indices of Social and Economic Systems

21

At an initial stage, the necessary information on subsystem indicators were gathered from thereports of the United Nations Organization, the World Bank [13], the International Monetary Fund [14] and other international organizations [15]. The opinions of experts were also taken into account. The indicators of the political environment have been taken from [16]. The collected information has given the chance to define linguistic variables and their corresponding intervals. In the algorithms the weighted rules has been used. The application of this algorithm is motivated by the fact that for the solution of the problem with linguistic variables a definition of scales of input and output characteristics is required. This allows to reduce the number of possible rules, giving the chance to improve the accuracy of the results. On the basis of the indices EEQI, SERI, PEQI, Sp EQI, NEQI, the composite social system quality index, SSQI, was calculated.

1.5 Algorithm with the Weighted Rules The algorithm of weighted rules is employed in our approach, the idea of Mamdani’s fuzzy inference and the algorithm of the batch least square of groups are used [17]. To demonstrate the steps of the algorithm we used information on the model of economic environment, the parameters of which are listed in Table 1.8. In Table 1.8 the following indicators are employed as the input: • GDP/P—GDP per capita in thousand USD, Table 1.8 Parameters of the model of economic environment Indicators

Terms and supports

1. GDP/P

Very low 0.320–17

Low 16.5–33

Moderate 32.5–50

High 49.5–67

Very high 66.5–84

Azerbaijan Very low 4.0

2.  GDP

Very low -∞–1

Low 0.8–3

Moderate 2.8–5

High 4.5–8

Very high 7.5–∞

Moderate 5

3. CPI

Very low 0.1–3

Low 2.5–5.0

Moderate 4.5–8

High 7.5–10

Very high 9–∞

Moderate 5.8

4. FIM

Very high 0–4

High 6–12

Moderate 10–20

Low 18–30

Very low 25–100

Low 30

5. TEX

Very high 10–7.5

High 8–5.5

Moderate 6–3.5

Low 4–1.5

Very low 2–0

Very low 2

6. FIS

Crises 100–79

Nearly crises 80–59

Weak stability 60–39

Stability 40–19

Very stability 20–1

Stability 40

7. BEN

Very bad 0–2

Bad 1.9–4

Moderate 3.9–6

Good 5.9–8

Very good 7.9–10

Moderate 5.3

8. EEQI

Very bad 0–2

Bad 1.5–4

Moderate 3.5–6

Good 5.5–8

Very good 7.5–10

Moderate 4.7

22

• • • • • •

1 Fuzzy Analysis of Socioeconomic Development …

 GDP—GDP rate of gross in percent, CPI—level of inflation, FIM—portion of imported food in consumption, TEX—portion of advanced technology products in export, FIS—financial stability index, BEN—business environment score,

and EEQI, the Economic Environment Quality Index, is the output variable. In the first step, the fuzzification is carried out using the Gaussian functions. Further, on the basis of the set of terms (in our case we have 5 terms), the initial fuzzy rules are determined. By using the n-factorial base on the inputs and output, and considering the terms, all possible rules are generated. Further, the peak point, cij , of each fuzzy number’s membership function of the terms are defined. On the basis of cij , a matrix C = (cij ) is constructed. The initial rules are expressed via cij . For our example the matrix C may be the following: ⎛

C1 ⎜ 8.66 ⎜ ⎜ ⎜ 24.75 C =⎜ ⎜ 41.25 ⎜ ⎝ 58.25 75.25

C2 −1.50 1.90 3.90 6.25 10.25

C3 1.55 3.75 6.25 8.75 14.50

C4 2.00 9.00 15.00 24.00 62.50

C5 8.75 6.75 4.75 2.75 1.00

C6 89.50 69.50 49.50 29.50 10.50

⎞ Cy 1.00 ⎟ ⎟ ⎟ 2.75 ⎟ ⎟ 4.75 ⎟ ⎟ 6.75 ⎠ 8.75

After that by means of the formula mentioned below a degree of membership of each point of support of the fuzzy number corresponding to the linguistic variables are defined: μi (x) =

n 

   i i 2 1 x j −c j exp − 2 σ i

(1.12)

j

j=1

where: n—the number of input variables; x ij —support points of the fuzzy number of the terms; i—an index of a term; cij —a peak point of a corresponding terms i; σ ji average square deviation of an interval of the corresponding term. For our example the values of σ ji are obtained as follows: Very low

Low

Moderate

High

Very high

GDP/P

4.8208

4.8499

5.0517

5.0517

5.0808

GDR

0.3317

0.6364

0.6708

1.0400

0.7517

CPI

0.8367

0.7517

1.0400

0.7517

0.9000

FIM

2.3402

1.7635

2.8870

3.4643

21.6797

TEX

0.7517

0.7517

0.7517

0.7211

0.5788 (continued)

1.5 Algorithm with the Weighted Rules

23

(continued) Very low

Low

Moderate

High

FIS

6.0918

6.0918

6.0623

6.0623

Very high 5.4850

BEN

0.5788

0.6055

0.6364

0.6364

0.6519

By using the values of σ ji given above, the values of μi (x) for each term are obtained as: Very low

Low

Moderate

High

Very high

GDP/P

0.0000000000

0.0000000000

0.0000000000

0.0000000000

0.0000000000

GDP

0.0040867714

0.0000167017

0.0000101301

0.0000000152

0.0000022603

CPI

0.0000005043

0.0000022603

0.0000000152

0.0000022603

0.0000001855

FIM

0.0000000000

0.0000000000

0.0000000000

0.0000000000

0.0000000000

TEX

0.0000022603

0.0000022603

0.0000022603

0.0000037267

0.0000453999

FIS

0.0000000000

0.0000000000

0.0000000000

0.0000000000

0.0000000000

BEN

0.0000453999

0.0000275364

0.0000167017

0.0000167017

0.0000167017

Then, the weights of the antecedent of the initial rules are: wia = n 

μ (x)

R i i=1 μi (x)

(1.13)

wi = 1

i=1

where: wi —the weight of the antecedent of the initial rules, μi (x)—the value of the membership degree of fuzzy variables in the antecedent part of the rules. By substituting the value obtained in formula (1.12) into formula (1.13), we obtain:    i i 2 1 x j −c j j=1 exp − 2 σ ji    wia = i i 2

R n 1 x j −c j exp − i=1 j=1 2 σi n

(1.14)

j

with wia , the weights of terms of the antecedent parts, as given below: Very low

Low

Moderate

High

Very high

GDP/P

0.0000

0.0000

0.0000

0.0000

0.0000

GDP

0.9884

0.3425

0.3480

0.0007

0.0350

CPI

0.0001

0.0464

0.0005

0.0996

0.0029 (continued)

24

1 Fuzzy Analysis of Socioeconomic Development …

(continued) Very low

Low

Moderate

High

Very high

FIM

0.0000

0.0000

0.0000

0.0000

0.0000

TEX

0.0005

0.0464

0.0777

0.1641

0.7034

FIS

0.0000

0.0000

0.0000

0.0000

0.0000

BEN

0.0110

0.5647

0.5738

0.7356

0.2588

n

1.00

1.00

1.00

1.00

1.00

wi

i=1

Using the below formula we obtain the values of weights, wic , of the consequence part of the rules as:    i i 2 1 x j −c j exp − j=1 2 σ ji    wic = i i 2

R n 1 x j −c j exp − i=1 j=1 2 σi

R

i=1 bi

n

(1.15)

j

where: bi is a peak value of the membership function of the corresponding terms of the consequence part of the rules. Then, using the maximum values wic , wia we define the new set of rules as: R1: If GDP/P = Moderate—41.3 (w1a = 0.000) and GDP = Very Low—0.5 (w2a = 0.9884) and CPI = High—8.8 (w3a = 0.0996) and FIM = Very Low— 4 (w4a = 0.000) and TEX = Very High—1 (w5a = 0.7034) and FIS = Very High—10.5 (w6a = 0.000) and BEN = Moderate 5 (w7a = 0.5738) then EEQI = Moderate—4.8 R2: If GDP/P = Very Low—4.0 (w1a = 0.000) and GDP = Moderate—5 (w2a = 0.9884) and CPI = Moderate—5.8 (w3a = 0.0001) and FIM = Low—30 (w4a = 0.0005) and TEX = Very Low—2.0 (w5a = 0.7034) and FIS = Stable—40 (w6a = 0.000) and BEN = Moderate—5.3 (w7a = 0.0110) then EEQI = ? In the new set of rules, R1 is the rule found and R2 is the rule corresponding to a fixed meaning of input variables (the last column of Table 1.8). Using the composition operation the corresponding fuzzy numbers are then determined. In the last stage, by using the centroid method, the defuzzification of fuzzy numbers is performed. As result, we find the crisp value of EEQI which is “moderate”, equal to 4.763. By using this algorithm we obtain: • • • •

SEQI = (moderate—0.5); PEQI = (moderate—2.95); Sp EQI = (moderate—4.75); NEQI = (bad—2.95).

1.5 Algorithm with the Weighted Rules

25

Results of the Solution of the Problems of Assessment of the Social System Quality Index On the basis of the indices defined such as EEQI, SEQI, PEQI, Sp EQI and NEQI, the Social System Quality Index (SSQI) is obtained equal to a moderate value of 4.25. In the case of Azerbaijan, the SSQI is basically affected by moderate qualities of economic, political, social, spiritual environments and a bad level of natural environment. More specifically the quality of the economic environment has been affected by: – average percent of inflation (5.8%), – high share of import products (30) in consumption, – low share of high technological products (2) in export the quality of the social environment has been affected by: • • • • •

very low level of the monthly average salary (USD 401), low level of expenses on public health services (3.7), low level of pension expenses (3.7), expenses for education (1.9) and very low level on development of a science (0.241);

the quality of the political environment has been affected by: • • • •

bad mutual relations between the government and opposition, low degree of transparency and justice of political system, low efficiency of legal system and high level of corruption;

the quality of the spiritual environment has been affected by: • very low level of influence of religious organizations on the increase of standard of living of the population, • low degree of quality of public health services and education; the quality of the natural environment has been affected by: • • • •

very bad quality of air, bad quality of water, bad index of a natural biodiversity and very low level of capital investments for environmental protection.

26

1 Fuzzy Analysis of Socioeconomic Development …

References 1. Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. 2. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. 3. Wang, J. Q., & Li, J. J. (2009). The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Science and Technology Information, 33, 8–9. 4. Oskar, M. (1963). On the accuracy of economic observations, (2nd ed., 340 pp.). Princeton, NJ: Princeton University Press. 5. Li, L. (2016). A new entropy-based intuitionistic fuzzy multi-attribute decision making method. American Journal of Applied Mathematics, 4(6), 277–282. 6. Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118, 467–477. 7. Parsons, T. (1966). Societies evolutionary and comparative perspectives. Prentice Hall. 8. Parsons, T. (1971). System of modern societies. Prentice Hall. 9. Luhmann, N. (1995). Social systems, writing science. , Stanford, CA: Stanford University Press. 10. Luhmann, N. (1990). The autopoiesis of social systems. In N. Luhmann (Ed.), Essays on self-reference. New York: Columbia University Press. 11. Beck, W., van der Maesen, L., & Walker, A. (1997). Social quality: from issue to concept. In W. Beck, L. van der Maesen, & A. Walker (Eds.), The social quality of Europe. The Hague, Netherlands: Kluwer Law International. 12. W. Beck, L. van der Maesen, G. Thomese, & A. Walker. (2001). Introduction: Who and what is the European Union for?. In W. Beck, L. van der Maesen, G. Thomese, & A. Walker (Eds.), Social quality: A vision for Europe. The Hague, Netherlands: Kluwer Law. 13. World Bank. (2009, November). World development report 2010: Development and climate change (300 pp). 14. International Financial Statistics, International Monetary Fund (2008, June). 15. Transparency International the global coalition against corruption. Annual Report (2009) (68 pp.). 16. World investment prospects to 2011. Foreign direct investment and the challenge of political risk. Written with the Columbia Program on International Investment (250 pp.) 17. Mamdani, E. H. (1974). Application of fuzzy algorithms for control of simple dynamic plant. Proceedings of the Institution of Electrical Engineers, 121(12), 1585–1588.

Chapter 2

Fuzzy Analysis of Economic Diversification Level

The diversification of the economic structure is the main state in attaining sustainable development. Normally diversified economy provides an optimal growth and relation among industries of the national economy. There are various methods for determining the level of economic diversification. In literature, the following methods are particularly emphasized: Ogive Index [1], Entropy Index [2], and Herfindahl–Hirschman Index [3]. Simultaneously, the level of diversification is determined by means of V. Leontiev’s input–output model [4–6]. In this chapter, fuzzy entropy composite index and a fuzzy version of the input– output model were used for the estimation of diversification level,. The calculation is carried out using thee data for the Republic of Azerbaijan [https://stat.gov.az].

2.1 Fuzzy Entropy Composite Index In order to calculate the Fuzzy Entropy Composite Index of diversification level of the Azerbaijan economy, we use the structural indicators of GDP for 2013. Using the formula of equiproportional distribution (1/N = 1/13 = 0.077, where N is the number of sectors), the intervals and their corresponding terms are determined as: Lowest norm Below norm Norm Above norm

(VLN)—(0.010, 0.030, 0.050) (LON)—(0.040, 0.053, 0.065) (NOR)—(0.060, 0.080, 0.100) (HAN)—(0.090, 0.295, 0.500)

Further, the membership degree of structural parameters to the corresponding terms µ A (x) is defined. Based on this information and the fuzzy entropy of economic sectors, E i ( Ai ), parameters of the model are computed. The obtained results of the parameter calculations are shown in Table 2.1. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 G. Imanov, Fuzzy Models in Economics, Studies in Fuzziness and Soft Computing 402, https://doi.org/10.1007/978-3-030-61282-5_2

27

28

2 Fuzzy Analysis of Economic Diversification Level

Table 2.1 Parameters of the entropy models Economic sectors

2013

µ A (x)

Terms

E i (Ai )

Agriculture

0.057

0.667

LON

0.7395

Mining industry

0.420

0.39

HAN

0.4535

Manufacturing

0.045

0.25

VLN

0.2698

Construction

0.124

0.166

HAN

0.1756

Trade

0.076

0.8

NOR

0.8627

Transport and communication

0.066

0.3

NOR

0.3208

Tourism

0.020

0.5

VLN

0.5833

Real estate

0.022

0.6

VLN

0.6964

State governance and social insurance

0.027

0.85

VLN

0.8779

Education

0.050

0.769

LON

0.8188

Health care

0.019

0.45

VLN

0.5094

Finance, insurance

0.062

0.25

LON

0.2679

Other services

0.012

0.1

VLN

0.0995

On the basis of the following formula the Fuzzy Entropy Composite Index of diversification, written E(A), is defined: E( A) =

n  i=1

  n   Ai ∩ AiC  1.9 + 4.226 + 5.1 + 2.988  = E i (Ai )i =  Ai ∪ AC  19.1 + 15.774 + 15.9 + 17.012 i i=1 =0.209689, i = 1, . . . , 13

The obtained results of calculations of the Fuzzy Entropy Composite Index demonstrate a low level of diversification of the Azerbaijani economy in 2013. The results of investigations [5, 6] of the economic diversification level by using the methods of equiproportional distribution do not provide a complete evaluation of the economic diversification. In order to get a full view the use of input–output balance model is recomended.

2.2 Input–Output Model Analysis of Economic Diversification Siegel [7], and Wagner and Deller [5] suggest the analysis of regional economic diversification based on Leontiev’s input–output model. Following this idea, we propose a fuzzy approach to analyze the input–output balance. For this purpose, the input–output balance of 2006 of Azerbaijan is fuzzified in the following manner. The minimum and maximum values for the coefficients are

2.2 Input–Output Model Analysis of Economic Diversification

29

identified in a direct relation matrix. The interval of minimum and maximum values is divided into appropriate linguistic terms shown in Table 2.2. The linguistic matrix formulated on the basis of the linguistic terms shown in Table 2.3 is described in Table 2.4. As it can be seen from Table 2.3, the number of all intersectoral relations is 225 of which 170 (75.5%) are very weak, 20 (9%)—weak, 9 (4%)—average, 15 (6.7%)—below average, 10 (4.4%)—strong and 1 (0.4%)—very strong. Table 2.2 Direct relation matrix of the input–output balance in 2006 1

2

3

4

5

6

7

0.204269

0.003035

0.000001

0.084648

0.000001

0.002291

0.000763

1

Agriculture

2

Fishing

0.000000

0.189500

0.000000

0.000054

0.000000

0.000000

0.000000

3

Mining industry

0.001415

0.004435

0.014485

0.221853

0.526327

0.060578

0.000215

4

Manufacturing

0.038532

0.058219

0.032094

0.291153

0.099320

0.134819

0.169255

5

Electricity, gas and water

0.018128

0.057058

0.005949

0.030128

0.090972

0.004440

0.004781

6

Construction

0.019910

0.000000

0.009124

0.026276

0.037204

0.303251

0.063960

7

Trade

0.072712

0.000103

0.007313

0.033896

0.016781

0.000193

0.042780

8

Tourism

0.000301

0.001419

0.000279

0.000522

0.000558

0.002499

0.009662

9

Transport, storage and communication

0.018382

0.053113

0.018334

0.026855

0.015597

0.028151

0.021167

10

Finance, insurance

0.000550

0.001830

0.000258

0.003223

0.001666

0.001988

0.001692

11

Real estate

0.001841

0.000582

0.005590

0.016417

0.002520

0.027050

0.017117

12

Education services

0.000000

0.000000

0.000006

0.000301

0.000027

0.000690

0.000046

13

Health care and social services

0.000027

0.001364

0.000073

0.000358

0.000072

0.000081

0.000004

14

Public administration and social insurance

0.000000

0.000000

0.001883

0.000086

0.001571

0.018739

0.026356

15

Public utilities

0.000418

0.000261

0.000567

0.004718

0.000778

0.002041

0.001347

8

9

10

11

12

13

14

15

0.000506

0.000003

0.000000

0.000246

0.001681

0.000000

0.000357

0.000764

1

Agriculture

2

Fishing

0.000786

0.000000

0.000000

0.000000

0.000000

0.000000

0.000008

0.000000

3

Mining industry

0.000067

0.002764

0.000000

0.001746

0.000095

0.000024

0.000026

0.001358

4

Manufacturing

0.040592

0.088213

0.049674

0.070987

0.095654

0.256503

0.064769

0.129991

5

Electricity, gas and water

0.012823

0.007426

0.002043

0.017129

0.012629

0.014314

0.017298

0.007215

6

Construction

0.077207

0.015718

0.002830

0.067204

0.038156

0.014581

0.224881

0.088182

7

Trade

0.002240

0.004837

0.015993

0.008761

0.000678

0.003900

0.002501

0.000892

8

Tourism

0.141207

0.002847

0.002758

0.007699

0.004848

0.000506

0.006517

0.007620

9

Transport, storage and communication

0.035524

0.263558

0.055142

0.083494

0.015965

0.014565

0.029849

0.033603

10

Finance, insurance

0.003063

0.006351

0.043175

0.002439

0.002679

0.000847

0.006385

0.003528

11

Real estate

0.014041

0.029639

0.105612

0.152905

0.008587

0.005131

0.018405

0.009638

12

Education services

0.000000

0.000573

0.000935

0.001445

0.019255

0.000000

0.000662

0.000031 (continued)

30

2 Fuzzy Analysis of Economic Diversification Level

Table 2.2 (continued) 8

9

10

11

12

13

14

15

13

Health care and social services

0.000106

0.000097

0.000003

0.000332

0.008220

0.001914

0.000657

0.000255

14

Public administration and social insurance

0.004295

0.022167

0.001177

0.018313

0.001859

0.000487

0.017934

0.000185

15

Public utilities

0.004169

0.004531

0.001701

0.002610

0.012704

0.004135

0.005157

0.103799

Table 2.3 Interval terms Term code

Terms

A

C

B

R1

Very weak

0

0.01

0.02

R2

Weak

0.015

0.03

0.045

R3

Average

0.04

0.055

0.07

R4

Below average

0.065

0.1075

0.15

R5

Strong

0.1

0.25

0.4

R6

Very strong

0.35

0.5

0.65

Table 2.4 Linguistic matrix of intersectoral relations 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1

R5

R1

R1

R4

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

2

R1

R5

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

3

R1

R1

R1

R5

R6

R3

R1

R1

R1

R1

R1

R1

R1

R1

R1

4

R2

R3

R2

R5

R4

R4

R5

R2

R4

R3

R4

R4

R5

R3

R4

5

R1

R3

R1

R2

R4

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

6

R1

R1

R1

R2

R2

R5

R3

R4

R1

R1

R3

R2

R1

R5

R4

7

R4

R1

R1

R2

R1

R1

R2

R1

R1

R1

R1

R1

R1

R1

R1

8

R1

R1

R1

R1

R1

R1

R1

R4

R1

R1

R1

R1

R1

R1

R1

9

R1

R3

R1

R2

R1

R2

R2

R2

R5

R3

R4

R1

R1

R2

R2

10

R1

R1

R1

R1

R1

R1

R1

R1

R1

R2

R1

R1

R1

R1

R1

11

R1

R1

R1

R1

R1

R2

R1

R1

R2

R4

R5

R1

R1

R1

R1

12

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

13

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

14

R1

R1

R1

R1

R1

R1

R2

R1

R2

R1

R1

R1

R1

R1

R1

15

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R1

R4

2.3 Using the Fuzzy DEMATEL Method for the Analysis of Intersectoral Relations

31

2.3 Using the Fuzzy DEMATEL Method for the Analysis of Intersectoral Relations In order to analyze intersectoral relations and identify the leading industries affecting the overall development of the economy, we use the fuzzy DEMATEL method proposed by Lin and Wu [8]. For this purpose we construct a matrix of triangular fuzzy numbers (Table 2.5) corresponding to a linguistic matrix (Table 2.4). Table 2.5 The matrix of Fuzzy numbers of intersectoral relations 1

2

3

4

5

6

7

1

(0.1, 0.25, 0.4)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.065, 0.108, 0.15)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

2

(0, 0.01, 0.02)

(0.1, 0.25, 0.4) (0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

3

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.1, 0.25, 0.4) (0.35, 0.5, 0.65)

(0.04, 0.055, 0.07)

(0, 0.01, 0.02)

4

(0.015, 0.03, 0.045)

(0.04, 0.055, 0.07)

(0.015, 0.03, 0.045)

(0.1, 0.25, 0.4) (0.065, 0.108, 0.15)

(0.065, 0.108, 0.15)

(0.1, 0.25, 0.4)

5

(0, 0.01, 0.02)

(0.04, 0.055, 0.07)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0.065, 0.108, 0.15)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

6

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0.015, 0.03, 0.045)

(0.1, 0.25, 0.4) (0.04, 0.055, 0.07)

7

(0.065, 0.108, 0.15)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

8

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

9

(0, 0.01, 0.02)

(0.04, 0.055, 0.07

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0.015, 0.03, 0.045)

10

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

11

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0, 0.01, 0.02)

12

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

13

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

14

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

15

(0, 0.01, 0.02) 8

9

10

11

12

13

14

15

1

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

2

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

3

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

4

(0.015, 0.03, 0.045)

(0.065, 0.108, 0.15)

(0.04, 0.055, 0.07

(0.065, 0.108, 0.15)

(0.065, 0.108, 0.15)

(0.1, 0.25, 0.4)

(0.04, 0.055, 0.07

(0.065, 0.108, 0.15)

5

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

6

(0.065, 0.108, 0.15)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.04, 0.055, 0.07

(0.015, 0.03, 0.045)

(0, 0.01, 0.02)

(0.1, 0.25, 0.4)

(0.065, 0.108, 0.15) (continued)

32

2 Fuzzy Analysis of Economic Diversification Level

Table 2.5 (continued) 8

9

10

11

12

13

14

15

7

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

8

(0.065, 0.108, 0.15)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

9

(0.015, 0.03, 0.045)

(0.1, 0.25, 0.4)

(0.04, 0.055, 0.07

(0.065, 0.108, 0.15)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0.015, 0.03, 0.045)

10

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

11

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0.065, 0.108, 0.15)

(0.1, 0.25, 0.4)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

12

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

13

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

14

(0, 0.01, 0.02)

(0.015, 0.03, 0.045)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

15

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0, 0.01, 0.02)

(0.065, 0.108, 0.15)

Then, a fuzzy number S is calculated on the basis of elements shown in the Table 2.5 and the following formula: S=

max 1 ≤ i ≤ n

1 n

j=1 (li j , m i j , u i j )

=

1 (0.76, 1.40, 2.04)

= (0.49, 0.71, 1.32)

(2.1)

Here, li j , m i j , u i j are the left, middle and right elements of a triangular fuzzy number, respectively. Further, the normalized matrix T (Table 2.6) is determined on the basis of the following formula: T =S∗A

(2.2)

As the next stage in calculations, the total intersectoral relations matrix F (Table 2.7) is defined by means of the following formula: F = T (I − T )−1 ,

(2.3)

where I is the identity matrix. In the last stage, the sum of elements of the rows and columns shown Table 2.8 is determined by using the following formulas: Ri =

n  j=1

(li j , m i j , u i j ), (i = 1, 2, . . . , n)

(2.4)

2.3 Using the Fuzzy DEMATEL Method for the Analysis of Intersectoral Relations

33

Table 2.6 The normalized matrix of the intersectoral relations—T 1

2

3

4

5

6

7

1

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.07, 0.11, 0.15

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

2

0.00, 0.01, 0.02

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

3

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.00, 0.00

0.10, 0.25, 0.40

0.35, 0.50, 0.65

0.04, 0.06, 0.07

0.00, 0.01, 0.02

4

0.01, 0.03, 0.04

0.04, 0.06, 0.07

0.01, 0.03, 0.04

0.00, 0.00, 0.00

0.07, 0.11, 0.15

0.07, 0.11, 0.15

0.10, 0.25, 0.40

5

0.00, 0.01, 0.02

0.04, 0.06, 0.07

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

6

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.01, 0.03, 0.04

0.00, 0.00, 0.00

0.04, 0.06, 0.07

7

0.07, 0.11, 0.15

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.00, 0.00

8

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

9

0.00, 0.01, 0.02

0.04, 0.06, 0.07

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.01, 0.03, 0.04

10

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

11

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.00, 0.01, 0.02

12

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

13

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

14

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.01, 0.03, 0.04

15

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

8

9

10

11

12

13

14

15

1

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

2

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

3

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

4

0.01, 0.03, 0.04

0.07, 0.11, 0.15

0.04, 0.06, 0.07

0.07, 0.11, 0.15

0.07, 0.11, 0.15

0.10, 0.25, 0.40

0.04, 0.06, 0.07

0.07, 0.11, 0.15

5

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

6

0.07, 0.11, 0.15

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.04, 0.06, 0.07

0.01, 0.03, 0.04

0.00, 0.01, 0.02

0.10, 0.25, 0.40

0.07, 0.11, 0.15

7

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

8

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

9

0.01, 0.03, 0.04

0.00, 0.00, 0.00

0.04, 0.06, 0.07

0.07, 0.11, 0.15

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.01, 0.03, 0.04

10

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02 (continued)

34

2 Fuzzy Analysis of Economic Diversification Level

Table 2.6 (continued) 8

9

10

11

12

13

14

15

11

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.07, 0.11, 0.15

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

12

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

13

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.00, 0.00

0.00, 0.01, 0.02

0.00, 0.01, 0.02

14

0.00, 0.01, 0.02

0.01, 0.03, 0.04

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.00, 0.00

0.00, 0.01, 0.02

12

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.01, 0.02

0.00, 0.00, 0.00

Table 2.7 Total intersectoral relations matrix—F 1

2

3

4

5

6

7

1

0.00, 0.00, 0.01

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.02, 0.04, 0.11

0.00, 0.01, 0.04

0.00, 0.01, 0.03

0.00, 0.01, 0.05

2

0.00, 0.00, 0.02

0.00, 0.00, 0.01

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

3

0.00, 0.01, 0.05

0.00, 0.01, 0.06

0.00, 0.00, 0.03

0.02, 0.09, 0.30

0.08, 0.18, 0.47

0.01, 0.02, 0.09

0.00, 0.01, 0.11

4

0.00, 0.02, 0.08

0.01, 0.02, 0.08

0.00, 0.01, 0.05

0.00, 0.00, 0.06

0.02, 0.04, 0.15

0.02, 0.04, 0.13

0.02, 0.09, 0.30

5

0.00, 0.00, 0.02

0.01, 0.02, 0.05

0.00, 0.00, 0.02

0.00, 0.01, 0.04

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

6

0.00, 0.01, 0.03

0.00, 0.00, 0.03

0.00, 0.00, 0.03

0.00, 0.01, 0.05

0.00, 0.01, 0.06

0.00, 0.00, 0.02

0.01, 0.02, 0.08

7

0.02, 0.04, 0.10

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.01, 0.05

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

8

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

9

0.00, 0.00, 0.03

0.01, 0.02, 0.06

0.00, 0.00, 0.02

0.00, 0.01, 0.05

0.00, 0.01, 0.03

0.00, 0.01, 0.04

0.00, 0.01, 0.05

10

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

11

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.03

0.00, 0.01, 0.04

0.00, 0.00, 0.03

12

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

13

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

14

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.01, 0.04

15

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

8

9

10

11

12

13

14

15

1

0.00, 0.00, 0.02

0.00, 0.01, 0.03

0.00, 0.00, 0.03

0.00, 0.01, 0.03

0.00, 0.01, 0.03

0.00, 0.01, 0.05

0.00, 0.00, 0.03

0.00, 0.01, 0.03

2

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02 (continued)

2.3 Using the Fuzzy DEMATEL Method for the Analysis of Intersectoral Relations

35

Table 2.7 (continued) 8

9

10

11

12

13

14

15

3

0.00, 0.01, 0.05

0.00, 0.01, 0.06

0.00, 0.01, 0.05

0.00, 0.01, 0.07

0.00, 0.01, 0.06

0.00, 0.01, 0.11

0.00, 0.01, 0.07

0.00, 0.01, 0.07

4

0.00, 0.01, 0.07

0.02, 0.04, 0.13

0.01, 0.02, 0.09

0.02, 0.04, 0.14

0.02, 0.04, 0.13

0.02, 0.09, 0.29

0.01, 0.02, 0.11

0.02, 0.04, 0.14

5

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.02

6

0.02, 0.04, 0.11

0.00, 0.01, 0.04

0.00, 0.01, 0.03

0.01, 0.02, 0.07

0.00, 0.01, 0.05

0.00, 0.01, 0.04

0.02, 0.09, 0.28

0.02, 0.04, 0.12

7

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.03

0.00, 0.00, 0.03

8

0.00, 0.00, 0.01

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

9

0.00, 0.01, 0.04

0.00, 0.00, 0.02

0.01, 0.02, 0.06

0.02, 0.04, 0.11

0.00, 0.00, 0.03

0.00, 0.01, 0.03

0.00, 0.01, 0.05

0.00, 0.01, 0.05

10

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.01

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

11

0.00, 0.00, 0.02

0.00, 0.01, 0.04

0.02, 0.04, 0.10

0.00, 0.00, 0.01

0.00, 0.00, 0.02

0.00, 0.00, 0.03

0.00, 0.00, 0.03

0.00, 0.00, 0.02

12

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.01

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

13

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.01

0.00, 0.00, 0.02

0.00, 0.00, 0.02

14

0.00, 0.00, 0.02

0.00, 0.01, 0.04

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.01

0.00, 0.00, 0.02

15

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.02

0.00, 0.00, 0.01

Table 2.8 The results of the solution I-O matrix for 2006 Number of Dl economic sectors

Dm

Du

Rl

Rm

Ru

Dl + Rl

Dm + Rm

Du + Ru

Dl − Rl

Dm − Rm

Du − Ru

1

0.019

0.108

0.541

0.020

0.105

0.480

0.039

0.213

1.021

−0.461

0.003

0.521

2

0.000

0.056

0.297

0.031

0.113

0.469

0.031

0.169

0.766

−0.469

−0.057

0.266

3

0.124

0.388

1.633

0.004

0.065

0.327

0.128

0.453

1.960

−0.203

0.323

1.629

4

0.185

0.539

1.941

0.055

0.215

0.852

0.240

0.754

2.793

−0.667

0.324

1.886

5

0.014

0.083

0.386

0.105

0.286

1.010

0.119

0.369

1.396

−0.996

−0.203

0.281

6

0.087

0.277

1.023

0.034

0.130

0.543

0.121

0.407

1.566

−0.456

0.147

0.989

7

0.020

0.104

0.472

0.043

0.191

0.848

0.063

0.295

1.320

−0.828

−0.087

0.429

8

0.000

0.056

0.297

0.024

0.111

0.479

0.024

0.167

0.776

−0.479

−0.055

0.273

9

0.058

0.176

0.667

0.024

0.113

0.505

0.082

0.289

1.172

−0.447

0.063

0.643

10

0.000

0.056

0.297

0.036

0.131

0.539

0.036

0.187

0.836

−0.539

−0.075

0.261

11

0.023

0.109

0.464

0.042

0.153

0.625

0.065

0.262

1.089

−0.602

−0.044

0.422

12

0.000

0.056

0.297

0.020

0.105

0.476

0.020

0.161

0.773

−0.476

−0.049

0.277

13

0.000

0.056

0.297

0.025

0.157

0.747

0.025

0.213

1.044

−0.747

−0.101

0.272

14

0.007

0.072

0.347

0.039

0.177

0.755

0.046

0.249

1.102

−0.748

−0.105

0.308

15

0.000

0.056

0.297

0.036

0.143

0.603

0.036

0.199

0.900

−0.603

−0.087

0.261

36

2 Fuzzy Analysis of Economic Diversification Level

Fig. 2.1 Diagram results of the solution I-O matrix for 2006

Dj =

n 

(li j , m i j , u i j ), (j = 1, 2, . . . , n)

(2.5)

j=1

The results of the analysis of development of the Azerbaijan economy carried out by the International Economic Organizations such as UNDP [9], The World Bank in 2005 [10], and Chemonics International in 2009 [11] show a high potential for the development of agriculture, agro-industry and service sectors (Fig. 2.1). The results of investigation show that the diversification of the Azerbaijan economy does not claim to be fully covered. For a complete investigation of this problem there is a need to study other subsystems of the economy, such as those related to employment, investments, exports and imports, etc.. The results should be integrated into one indicator of the diversification level of the national economy. The process of diversification of the national economy should be done regularly (Table 2.9).

Real estate

Professional activities

Administration

Public administration and social security

Education

Health care

14

15

16

17

Transport

8

13

Trade

7

12

Construction

6

Finance and insurance

Water supply

5

11

Energy

4

Tourism

Manufacturing industry

3

Information technology

Mining industry

2

10

Agriculture

1

9

Economic sectors

Code

0

0

0

0

0.073

0.024

0.05

0

0.012

0.051

0

0.106

0

0.023

0.278

0.093

0.027

Dl

0.194

0.194

0.194

0.194

0.316

0.234

0.277

0.194

0.213

0.28

0.194

0.368

0.194

0.232

0.654

0.354

0.24

Dm

0.989

0.989

0.989

0.989

1.308

1.093

1.209

0.989

1.038

1.223

0.989

1.434

0.989

1.087

2.187

1.432

1.117

Du

Table 2.9 The results of the solution I-O matrix for 2011

0.05

0

0.062

0.025

0.049

0.062

0.025

0.025

0.025

0.025

0.025

0.062

0.087

0.071

0.059

0

0.024

Rl

0.277

0.194

0.298

0.235

0.275

0.287

0.236

0.235

0.236

0.236

0.235

0.298

0.341

0.311

0.292

0.194

0.235

Rm

1.211

0.989

1.264

1.099

1.2

1.211

1.099

1.098

1.1

1.1

1.099

1.264

1.38

1.289

1.24

0.989

1.096

Ru

Dl + Rl

0.05

0

0.062

0.025

0.122

0.086

0.075

0.025

0.037

0.076

0.025

0.168

0.087

0.094

0.337

0.093

0.051

Dm + Rm

0.471

0.388

0.492

0.429

0.591

0.521

0.513

0.429

0.449

0.516

0.429

0.666

0.535

0.543

0.946

0.548

0.475

2.2

1.978

2.253

2.088

2.508

2.304

2.308

2.087

2.138

2.323

2.088

2.698

2.369

2.376

3.427

2.421

2.213

Du + Ru

Dm − Rm 0.005 0.16 0.362 −0.079 −0.147 0.07 −0.041 0.044 −0.023 −0.041 0.041 −0.053 0.041 −0.041 −0.104

0 −0.083

Dl − Rl −1.069 −0.896 −0.962 −1.266 −1.38 −1.158 −1.099 −1.049 −1.088 −1.098 −1.049 −1.187 −1.127 −1.099 −1.264

−0.989 −1.211

(continued)

0.939

0.989

0.927

0.964

1.259

1.031

1.184

0.964

1.013

1.198

0.964

1.372

0.902

1.016

2.128

1.432

1.093

Du − Ru

2.3 Using the Fuzzy DEMATEL Method for the Analysis of Intersectoral Relations 37

Economic sectors

Recreation

Other services

Code

18

19

Table 2.9 (continued)

0.183

4.903

0.737

0.194

Dm

0

0

Dl

21.977

0.937

0.989

Du

0.737

0.037

0.024

Rl

4.906

0.257

0.234

Rm

21.977

1.156

1.093

Ru

Dl + Rl

1.474

0.037

0.024 9.809

0.44

0.428

Dm + Rm

43.954

2.093

2.082

Du + Ru

Dm − Rm −0.04 −0.074 −0.003

Dl − Rl −1.093 −1.156 −21.24

21.24

0.9

0.965

Du − Ru

38 2 Fuzzy Analysis of Economic Diversification Level

References

39

References 1. Tress R. C. (1938). Unemployment and the diversification of industry. The Manchester School, 9, 140–152. 2. Jacquemin, A., & Berry, C. (1979). Entropy measure of diversification and corporate growth. The Journal of Industrial Economics, 27, 359–369. 3. Hirschman, A. O. (1964, September). The paternity of an index. American Economic Review 761–762. 4. Smith, S. M., & Gibson, C. S. (1988). Industrial diversification in nonmetropolitan counties and its effect on economic stability. Western Journal of Agricultural Economics, 13, 193–201. 5. Wagner, J. E., & Deller, S. C. (1993, September). A Measure of Economic Diversity: An InputOutput Approach, Staff Paper 93.3, USDA Forest Service and the University of WisconsinExtension. 6. Wagner, J. E. (2000). Regional economic diversity: Action, concept, or state of confusion. The Journal of Regional Analysis and Policy, 30, 2. 7. Siegel, P. B., Johnson, T. G., & Alwang, J. (1995). Regional economic diversity and diversification. Growth and Change., 26(2), 261–284. 8. Lin, C. L., & Wu, W. W. (2004). A fuzzy extension of the DEMATEL methods for group decision making. European Journal Operation Research, 156, 445–455. 9. Study of Azerbaijan’s current and potential comparative advantage, Center of Economic Reforms Ministry of Economic Development and UNDP (2004). 10. Realizing Azerbaijan’s Comparative Advantages in Agriculture, Azerbaijan Agricultural Markets Study. The World Bank (2005). 11. Stryker, J. D., Ahmadov, V., Rashidova, T., & Pala D. C. (2009). Domestic Resource Cost Analysis of Azerbaijan. Presented by Chemonics International (USAID).

Chapter 3

Measuring the Financial Stability

Financial stability is a broad concept that includes various aspects of a financial system, such as institutions, infrastructure, markets, just to name a few. This is an important phenomenon in terms of the real economic growth. The financial system is stable only when it is able to promote the productivity of the economy and to prevent financial imbalances, which arise endogenously or as a result of adverse and unforeseen events, cf. Shinasi [1]. The consequences of the financial and economic crises of the late twentieth and the early twenty first centuries have made it clear to experts and officials at central banks, financial institutions and to independent experts, that there is an acute need for research in the field of financial stability at the national and international level. The purpose of these research efforts should be to develop appropriate approaches and evaluation methods for a timely identification of sources of the financial instability and to design a correct appropriate response to them. The major objective of analysis of the financial stability is to examine different relationships, detecting negative trends, as well as economic, regulatory and institutional determinants to assess the state of the financial system and its vulnerabilities. For the consideration of the financial stability of the system as a phenomenon within a particular state or region a set of indicators is commonly employed that reflect the state of not only the financial sector institutions, infrastructure and the market in general but also real, public and external sectors of the economy so that it takes into account changes in the macroeconomic environment which have a significant impact on the financial system. From the analyses of international comparability of indicators there have been developed guidelines for the compilation of financial soundness indicators, by the IMF and the monetary authorities of particular countries. Furthermore, the European Central Bank has developed a list of indicators for macro prudential monitoring of the financial stability of the European Union banking system.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 G. Imanov, Fuzzy Models in Economics, Studies in Fuzziness and Soft Computing 402, https://doi.org/10.1007/978-3-030-61282-5_3

41

42

3 Measuring the Financial Stability

In order to assess and monitor the financial stability for an individual country, independent experts and the monetary authorities of the European Union have developed indicators taking into consideration the features of national economies [2–5]. The purpose of research reported in this book is to add a new input to the literature on the financial stability by examining the case of an emerging country like Azerbaijan. More specifically, the main objective of this work is to provide a new approach for the weighting procedure to estimate an aggregate financial stability index. To the best of our knowledge, very little, if at all, has been done in the field of studying the financial stability in the case of Azerbaijan. Moreover, this is the first attempt to develop a fuzzy estimation of this index. In this work, for the first time on the basis of annual data for the period 2005– 2015 a standard method has been used to estimate an aggregate index (AFSI) and its corresponding composite indices, with the weights of the sub-indices equal to 0.25. Then, to compute the weights, the tools and techniques of Atanassov’s intuitionistic fuzzy sets theory have been applied. The fuzzy approach developed in this work make it possible to obtain the following advantages: • In standard procedures for the calculation of the financial stability index, the value “0” indicates instability and “1” stands for stability of the financial system. The fuzzy approach is convenient here because it allows to express some in-between situations exemplified by “very low stability”, “low stability”, etc. Which parallels the way the human experts and decision or policy makers tend to describe a real situation, that is, using natural language. • Diversified terms are obtained not only for the aggregate stability index but also for the composite indices. This allows to individually establish a stability level for the particular sub-indices. • In the rich empirical literature the weights for the individual indicators and for the aggregate stability index are assigned to be equal but some of them have been defined in a different way depending on the author’s individual judgments. As mentioned in Albulescu [6] the latter requires complete data and it is difficult to justify and demonstrate the choice of the statistical weight. In our case we assume an impact of individual indicators on the financial stability index to be equal but the composite indexes have weights represented by the intuitionistic fuzzy sets which are specified for the years in question. For a deeper analysis we deal with an extention of the list of individual indicators and then we apply a fuzzy approach to all indicators in order to obtain different weights for the individual indicators.

3.1 Construction of a Stability Index of a Financial System Selection of indicators. In order to measure an aggregated financial stability index, the sub-groups’ indicators are used. The indicators of sub-indices of the financial stability index consist of the following ones:

3.1 Construction of a Stability Index of a Financial System

43

1. The indicators of the Financial Market Index—FMI Total credit to GDP ratio (DC)—provides information about the ability of credit institutions in performing their intermediation functions. A high value of this indicator increases the value of a sub-index. • Interest Spread (IS)—defined as the difference between the credit rates and deposits rates. The high spreads interpreted as an incompetence of intermediation and allocation of resources, and low spreads are an indicator of the effectiveness of the banking system. High interest spreads have a negative impact on the financial stability. • Herfindahl–Hirschman Index (HHI) in assets—demonstrates the concentration level of the financial market. The US Department of Justice considers markets with the value of HHI equal or less than 1,000 to be unconcentrated, beyween 1000 and 800 to be moderately concentratee, and above 1000 to be highly concentrated. The market capitalization data has not been available for the analyzed period so that we have been satisfied with the data represented above. 2. The indicators of the Financial Vulnerability Index—FVI • Fiscal deficit to GDP ratio (FD) is taken as an indicator of financial system stress. A high value of this indicator has a negative impact on the economic development. • Current account (CA)—the indicators of the balance of payments allow to track up the coming external shocks. A significant deficit in the current account may indicate an increasing possibility of a currency crisis and reduction of the liquidity of the national financial system. • Inflation rate (IN). A rising inflation distorts price proportions and profitability indicators of economic processes which can lead to an inefficient use of financial resources; it deters the inflow of foreign investment; it also devalues national currency savings. • Real Effective Exchange Rate (REER). This indicator reflects the exports competitiveness. An increase in this indicator expresses the competitiveness of a sector. A high volatility negatively affects the financial system. • Public Debt to GDP ratio (PD)—a high level of this indicator negatively affects the financial stability. • International Reserves to Import ratio (IR)—a sufficient level of international reserves makes it possible for the monetary authorities to conduct an independent and flexible monetary and currency policy by adjusting the level and volatility of the exchange rate of a national currency and provide liquidity to economic agents at financial markets in a stressful and crisis periods. A high value of this indicator positively affects the financial system. • Non-government Credit to Total Credit ratio (NGC)—a reduction in the value of this indicator has a negative impact. • Ratio of M2 to International Reserves (MIR)—an increase adversely affects the adequacy of reserves.

44

3 Measuring the Financial Stability

• M2 multiplier (MM)—a high value has a negative influence to financial stability. 3. Indicators of the Financial Soundness Index—FSI • Return on Assets (ROA)—a high value refers to the effectiveness of the banking system. • Bank Capital to Assets Ratio (BCA)—an increase in this indicator has a positive effect on the performance of the banking system. • Liquid Assets to Total Assets ratio (LAA)—its growth indicates an increasing liquidity, while a decrease shows a decline in the liquidity of the banking sector. • Bank regulatory capital to risk weighted assets (RCRA)—the growth in the value of this indicator negatively affects the banking system. 4. Indicators of World Economic Climate Index (WEI) [7] • World Economic Growth (WEG)—Azerbaijan has a newly formulated financial system and growth in the global economy has a positive impact on the financial system of the country • Oil Price in the world market (OPR) [8]—due to the fact that Azerbaijan is a resource rich country and its economy is supported to a high extent by oil revenues, a rise in oil prices has a positive effect on in the economy as a whole. All financial systems are interconnected and a decrease of values of the indicators such as, the world economic growth, the world inflation and oil prices, etc. has a negative impact at the national level for the economic and financial stability, C. Albulescu [9].

3.2 Standard Approach to Measuring an Aggregated Financial Stability Index A standard procedure of calculation an aggregate index of financial stability includes the normalization of the individual indicators. For this purpose has been used the formula as follows: −

X tn

Xt − Xt = σt

(3.1)

where, X tn is the normalized value of indicator X in year t, X t —the average value of the indicator X, σt —is the standard deviation of indicator X during year t. After the normalization the individual indicators have been grouped into the respective four sub-indices by the using the following formulas:

3.2 Standard Approach to Measuring an Aggregated Financial Stability Index

3 FMI =

j=1

3 9

FV I =

j=1

j=1

Xsj

4 3

FW I =

Xvj

9 4

FSI =

Xmj

j=1

X wj

3

45

(3.2)

(3.3)

(3.4)

(3.5)

The aggregate index of the financial stability is computed as follows: AFSI = w1 ∗ FMI + w2 ∗ FVI + w3 ∗ FSI + w4 ∗ FWI

(3.6)

where, wi (i = 1, .., 4)—are weights of the corresponding sub-indices. According to the standard method of calculation of the aggregate financial stability index, the individual indicators have been normalized in the first step. Table 3.1 shows the normalized values of indicators for the 2005–2015 years. The results of calculation of the sub-indices and the aggregate index of Azerbaijan during 2005–2015 are given in Table 3.2 and Fig. 3.1. We have assumed that the weights of each of the sub-indices are equal to 0.25. According to the standard method the outcome shows that AFSI has not received the value “1” during the 2005–2015 period which means that the financial system of Azerbaijan has not been stable during this time. This result is somehow unexpected because after 2006 the country experiences an oil boom period in which the banking sector performance has been satisfactory according to data.

3.3 Fuzzy Approach to Measuring the Financial Stability Index The measuring of the financial stability index has two distinct purposes. One is to help ensure the accountability of the authorities responsible for performing the task. The other is to support the implementation of the chosen strategy to attain the goal in real time. The former calls for an ex post measurement of the financial instability, i.e. for the assessments of whether the financial instability prevailed or not at some point in the past. The latter relies on an ex ante measurement, i.e. on the assessment of whether the financial system is fragile or not today. While both ex ante and ex post measurements are “fuzzy”, the challenges in supporting the strategy implementation are tougher [10].

−6.69

1.81

−6.69

HHI

−1.29 −0.24 −0.73

−1.45

−2.18

NGC

MFR

−1.20

−0.52

0.76

−1.69

−1.4

−1.57

REE

IR

0.17

0.37

IN

PD

−1.10

−0.11

−1.68

CA

−0.50

0.28

−0.50

1.46

0.75

1.031

−1.12

−0.2

0.24

0.20

−0.6

2007

FD

Financial vulnerability indicators

0.79

−1.3

−1.08

2006

IS

2005

DC

Financial market indicators—FMI

Years

−0.78

−0.32

−0.15

−1.72

0.24

2.09

1.36

0.49

1.23

1.08

−0.72

2008

0.42

−1.31

−0.19

0.14

−0.08

0.95

−0.94

0.221

−0.15

0.53

0.86 −0.23

0.40

−1.48

0.81

−0.9

0.071

2010

−0.88

−1.12

1.36

0.20

0.01

2009

Table 3.1 Normalized values of the indicators of financial stability in Azerbaijan during 2005–2015

−0.25

−0.07

0.43

−0.56

0.86

0.105

0.64

1.21

−0.98

−1.12

−0.37

2011

0.48

0.26

0.67

0.06

0.66

−0.94

0.21

0.672

−0.75

−1.27

0.27

2012

0.39

1.28

1.32

0.96

0.72

−0.74

−0.15

1.21

−1.04

−1.05

0.36

2013

0.96

1.57

1.59

1.83

1.48

−0.90

−0.5

−0.76

−1.12

−0.02

1.33

2014

(continued)

1.21

0.93

−0.40

0.39

−0.35

−0.50

−1.76

0.08

0.24

0.29

2.04

2015

46 3 Measuring the Financial Stability

0.9

1.96

1.53

BCA

LAA

RCRA

0.02

0.73

ECI

1.14

1.02 −0.76

0.67

−1.28

OPR

0.49

1.86

WEG

World economic index

0.32

ROA

−0.09

−0.35

−1.62

MM

Financial soundness indicators

2006

2005

Years

Table 3.1 (continued) 2009

0.96 0.73

−0.40 0.02

−2.35

−2.54 −0.88

0.77

−0.27

0.03

−0.02

1.12

0.90 −0.85

0.46 −0.33

0.86

−0.35

0.24

0.45

−0.35

2008

−0.20

0.99

0.92

2007

2010

0.58

−0.07

0.90

−0.44

−0.10

0.24

−1.16

−0.35

2011

2012

−0.95

1.10

0.14

−1.58

−0.67

1.14

−0.27

−0.44

0.08

−0.35

−0.57 −0.18

−1.43

−0.35

−1.03

−0.35

0.58

1.10

−0.21

0.18

−0.85

0.46

−0.49

0.92

2013

0.30

0.73

−0.15

0.75

−0.53

0.39

−0.22

2.20

2014

2015

−0.11

−1.40

−0.27

−1.63

−0.89

−2.69

1.80

−0.35

3.3 Fuzzy Approach to Measuring the Financial Stability Index 47

48

3 Measuring the Financial Stability

Table 3.2 Sub-indices and the aggregate index of financial stability of Azerbaijan during 2005– 2015 2005

2006

2007

2008

2009

2010

FMI

−2.06 −2.33 −0.05

0.53

FVI

−1.13 −0.38 −0.01

0.10 −0.33 −0.06

FSI

1.18

0.57

WEI

0.04

0.47

AFSI −0.49 −0.42

0.54

0.14

2012

2013

2014 2015

0.53 −0.01 −0.82 −0.58 −0.58 0.06

0.85

0.66 0.83

−0.08

0.23 −0.36 −0.84 −0.53 −0.17 0.10

−0.85

0.41 −0.62 −1.13 0.22

2011

0.04 −0.18

0.22

0.19 0.07

0.49 0.29

−0.59

0.01 −0.34 −0.21

0.10 0.32

−0.17

0.47

0.10

2.5 1.5 0.5 -0.5

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

-1.5 -2.5

FMI

FVI

FSI

WEI

AFSI

Fig. 3.1 Sub-indices and the aggregated index of financial stability of Azerbaijan

The literature mentions several methods for determining the weights of the variables in the Financial Stability Index (FSI). These are econometric estimations with a macroeconomic model, a reduced form aggregate demand function (backwardlooking IS curve), or a Vector Autoregression Model (VAR). The weights can also be determined by the way of economic argument, such as a variable’s importance for the financial system. Alternatively, each variable in the index can be given an equal weights. In some studies, the above methods are combined [3]. In determining the weights of sub-indices expert assessments are mainly used. However, it should be noted that the values of these weights depend not only on time but also on situation existing in the various financial markets and the global economy. In order to define the weights of individual sub-indices of the aggregated index, we have used the tools and techniques of Atanassov’s intuitionistic fuzzy set theory [11]. In this study, in order to define weights of the financial stability sub-indices, we use the generalized entropy measure of intuitionistic fuzzy set F, composed ofn elements, proposed by Szmidt and Kacprzyk [12] E(F) =

n 1  maxCount (Fi ∩ Fic ) ) ( n i=1 maxCount (Fi ∪ Fic )

(3.7)

3.3 Fuzzy Approach to Measuring the Financial Stability Index

49

Table 3.3 Linguistic values of the sub-indices in the period 2005–2015 Sub-indices

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

FMI

VS

VL

LS

ST

ST

LS

LS

LS

LS

ST

HS

FVI

LS

LS

LS

ST

LS

LS

ST

ST

HS

HS

LS

FSI

HS

ST

ST

ST

ST

LS

LS

LS

LS

ST

LS

WEI

ST

ST

ST

LS

LS

ST

ST

ST

ST

ST

LS

where     Fi ∩ Fic = min μ Fi , μcFi , max ν Fi , ν Fc i 

(3.8)

    Fi ∪ Fic = min μ Fi , μcFi , max ν Fi , ν Fc i 

(3.9)

The weights of each individual index are defined by using the following formula: wi =

1 − E(Ai ) n n − i=1 E(Ai )

(3.10)

Given the same weight, we are not able to examine the changes in the economy each year. A fuzzy approach can well close this gap. In the fuzzy approach to aggregate the index of the financial stability the obtained values of the sub-indices for 2005–2015 years are classified into the following terms: – – – –

very low stability—VLS = (−2.43, −2.43, −1.20); low stability—LS = (−1.23, 0.00, 0.00); stable—S = (0.00, 0.00, 0.65); high stability—HS = (0.63; 1.28; 1.28).

The matrix of linguistic variables for the years of 2005–2015 is given in Table 3.3. The indicators of the financial stability sub-indices of Azerbaijan for 2005–2015, corresponding to the indicators expressed by the intuitionistic fuzzy sets, are given in Table 3.4. The calculation of entropy for each individual sub-indices during the year of 2005 is given below: E(A1 ) =

0.35 (0.35, 0.65, 0) ∩ (0.65, 0.35, 0) = = 0.54 (0.35, 0.65, 0) ∪ (0.65, 0.35, 0) 0.65

E( A2 ) =

0.07 (0.93, 0.07, 0) ∩ (0.07, 0.93, 0) = = 0.08 (0.93, 0.07, 0) ∪ (0.07, 0.93, 0) 0.93

E(A3 ) =

0.3 (0.3, 0.7, 0) ∩ (0.7, 0.3, 0) = = 0.43 (0.3, 0.7, 0) ∪ (0.7, 0.3, 0) 0.7

50

3 Measuring the Financial Stability

Table 3.4 Indicators expresses by the intuitionistic fuzzy sets Years

Sub-indices FMI

FVI

FSI

WEI

μ1 t

ν1 t

π1 t

μ2 t

ν2 t

π2 t

μ3 t

ν3 t

π3 t

μ4 t

ν4 t

π4 t

2005

0.70

0.30

0

0.08

0.92

0

0.85

0.15

0

0.94

0.06

0

2006

0.92

0.08

0

0.69

0.31

0

0.12

0.88

0

0.28

0.72

0

2007

0.96

0.04

0

0.99

0.01

0

0.16

0.84

0

0.36

0.64

0

2008

0.18

0.82

0

0.85

0.15

0

0.78

0.22

0

0.50

0.50

0

2009

0.20

0.80

0

0.73

0.27

0

0.64

0.36

0

0.08

0.92

0

2010

0.99

0.01

0

0.95

0.05

0

0.70

0.30

0

0.27

0.73

0

2011

0.33

0.67

0

0.66

0.34

0

0.32

0.68

0

0.85

0.15

0

2012

0.53

0.47

0

0.70

0.30

0

0.57

0.43

0

0.89

0.11

0

2013

0.53

0.47

0

0.04

0.96

0

0.86

0.14

0

0.24

0.76

0

2014

0.89

0.11

0

0.31

0.69

0

0.85

0.15

0

0.54

0.46

0

2015

0.35

0.65

0

0.93

0.07

0

0.30

0.70

0

0.52

0.48

0

E( A4 ) =

(0.52, 0.48, 0) ∩ (0.48, 0.52, 0) 0.48 = = 0.92 (0.52, 0.48, 0) ∪ (0.48, 0.52, 0) 0.52

The entropy for each individual sub-index in 2005–2014 is as given below: 2005—E( A1 ) = 0.43; E( A2 ) = 0.09; E( A3 ) = 0.18; E( A4 ) = 0.06 2006—E( A1 ) = 0.09; E( A2 ) = 0.45; E( A3 ) = 0.14; E( A4 ) = 0.39 2007—E( A1 ) = 0.04; E( A2 ) = 0.01; E( A3 ) = 0.19; E( A4 ) = 0.56 2008—E( A1 ) = 0.22; E( A2 ) = 0.18; E( A3 ) = 0.28; E( A4 ) = 1 2009—E( A1 ) = 0.25; E( A2 ) = 0.37; E( A3 ) = 0.56; E( A4 ) = 0.09 2010—E( A1 ) = 0.01; E( A2 ) = 0.05; E( A3 ) = 0.43; E( A4 ) = 0.37 2011—E( A1 ) = 0.49; E( A2 ) = 0.52; E( A3 ) = 0.47; E( A4 ) = 0.18 2012—E( A1 ) = 0.89; E( A2 ) = 0.43; E( A3 ) = 0.75; E( A4 ) = 0.12 2013—E( A1 ) = 0.89; E( A2 ) = 0.04; E( A3 ) = 0.16; E( A4 ) = 0.32 2014—E( A1 ) = 0.12; E( A2 ) = 0.45; E( A3 ) = 0.18; E( A4 ) = 0.85 The weights of the individual sub-indices for 2015 are calculated as follows: w1 (2015) =

0.46 1 − 0.54 = = 0.23 4 − 1.97 2.03

w2 (2015) =

0.92 1 − 0.08 = = 0.45 4 − 1.97 2.03

w3 (2015) =

0.57 1 − 0.43 = = 0.28 4 − 1.97 2.03

w4 (2015) =

0.08 1 − 0.92 = = 0.04 4 − 1.97 2.03

3.3 Fuzzy Approach to Measuring the Financial Stability Index

51

Using the weights of the individual sub-indices and their linguistic values (Table 3.3), the aggregated index of financial stability is calculated for 2015 as follows: AF S I (2015) =0.23 ∗ H S + 0.45 ∗ L S + 0.28 ∗ L S + 0.04 ∗ L S = 0.23 ∗ (0.63, 1.28, 1.28) + 0.45 ∗ (−1.23, 0, 0) + 0.28 ∗ (−1.23, 0, 0) + 0.04 ∗ (−1.23, 0, 0) = (0.15, 0.29, 0.29) + (−0.55, 0, 0) + (−0.34, 0, 0) + (−0.05, 0, 0) = (−0.79, 0.29, 0.29) = L S − ST The weights of the sub-indices and the aggregated index of financial stability for the period 2005–2015 are given in Table 3.5. Comparing two approaches with respect to the derivation of the AFSI, the fuzzy approach is more satisfactory than the standard method because it has been in a position to capture changes in the economy. Considering the fact that Azerbaijan is a country in transition with a new financial system, the results obtained show a low stability during the periods of 2005–2007 and 2009–2013. Table 3.5 Weights of the sub-indices and the aggregated indices Years

Indicators w1

w2

w3

w4

AFSI

2005

0.18

0.25

0.28

0.29

(−0.57, −0.08, 0.33) LS–ST

2006

0.31

0.19

0.29

0.21

(−0.98, −0.75, −0.04) LS

2007

0.3

0.31

0.25

0.14

(−0.75, 0, 0.0251) LS–ST

2008

0.34

0.35

0.31

0

(0, 0, 0.65) ST

2009

0.28

0.23

0.16

0.33

(−0.69, 0, 0.228) LS–ST

2010

0.32

0.3

0.18

0.2

(−1, 0, 0.13) LS–ST

2011

0.22

0.21

0.23

0.35

(−0.55, 0, 0.37) LS–ST

2012

0.06

0.32

0.14

0.49

(−0.24, 0, 0.53) LS–ST

2013

0.04

0.37

0.32

0.26

(−0.2, 0.47, 0.64) LS–ST

2014

0.37

0.23

0.34

0.06

(0.15, 0.29, 0.79) ST–HS

2015

0.23

0.45

0.28

0.04

(−0.79, 0.29, 0.29) LS–ST

52

3 Measuring the Financial Stability

The aggregate index is higher in 2008 and 2014 which reflects a higher stability of the financial system. The reason for this has been the economic growth supported by oil which has stimulated the banking sector. With respect to the “Contract of the Century, 1994” the economy has profited from oil revenues and 2007 was an oil boom period for the country when the oil revenues have contributed to the economy and financial system. As a result of the global economic crisis since 2009, the stability has decreased to a low stable level. Then, since 2010 the economy has been in a recovery stage and an increase of oil prices has contributed to a higher stability attained in 2014. However, an oil price decline at the end of 2014 and a devaluation of the exchange rate in 2015 have affected the banking sector activity and performance. It has resulted in a low stable level of financial stability. The methods developed for the calculation of weights of the composite indices and the quality level of the financial stability in Azerbaijan has been defined for the period of 2005–2015. The main contribution has been the determination of weights for the respective weights. It is worth noting that the implementation of equal weights to the aggregate index makes it not possible to reflect the economic changes in the period of 2005– 2015. The fuzzy approach, on the other hand, makes it possible to obtain weights for the particular years. Moreover the fuzzy approach has also made it possible to avoid the disjunction of such a phenomena like “stability” and “unstability” by allowing for the use of terms like “very low stability”, “low stability” and etc. The results obtaned by using the fuzzy approach are also more acceptable than those obtained by standard methods because they are able to capture key periods of financial stability during the sample period. In the future, to improve the outcomes and for a deeper research our main goal will be to extend the list of individual indicators and then apply a fuzzy approach to obtain different weights for all individual indicators.

References 1. Shinasi, G. J. (2004). Defining financial stability. International Monetary Fund WP/187 2. Illing, M., & Liu, Y. (2003). An index of financial stress for Canada (63 pp.). National Bank of Canada Working Paper/14. 3. Van den End, J. W. (2006). Indicator and boundaries of financial stability (24 pp.). De Nederlandsche Bank Working Paper/97. 4. Jordan, A., & Smith, L. (2014). Measuring the level of financial stability in the Bahamas. In 46th Annual Monetary Studies Conference: Macro-Prudential Supervision, Financial Stability And Monetary Policy, Central Bank of Trinidad and Tobago. 5. Karanovic, G., & Karanovic, B. (2015). Developing an aggregate index for measuring financial stability in the Balkans. In 7th International Conference, The Economies of Balkan and Eastern Europe Countries in the Changed World, EBEEC (pp. 3–17). 6. Albulescu, C. T. (2008). Assessing Romanian financial sector stability by means of an aggregate index. Oeconomica, 17(2), 67–87. 7. CESifo Group Munich. www.ifo.de/w/4LsApn939.

References

53

8. Commodity Markets Outlook, World Bank Group, April 2016, 78 pp. 9. Albulescu, C. T. (2010). Forecasting the Romanian financial system stability using a stochastic simulation model. Romanian Journal of Economic Forecasting, 1, 81–98. 10. Borio, C., & Drehmann, M. (2009). Towards an operational framework for financial stability: “Fuzzy” measurement and its consequences (50 pp.). BIS Working Papers/284. 11. Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. 12. Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118, 467–477.

Chapter 4

Fuzzy Estimation of National Green Economy Index and Investments Distribution

Green Economy is one of the most important concepts of the sustainable development of a country. UNEP defines the green economy as “one that results in improved human well-being and social equity, while significantly reducing environmental risks and ecological scarcities. It is—low carbon, resource, efficient, and socially inclusive” [1]. The concept of a green economy has to replace the brown economy as the world economic development progresses. Decades of creating new wealth through the ‘brown economy’ model based on fossil fuels have not substantiality addressed the social marginalization and environmental degradation as well as the resource depletion. In addition, the world is still far from delivering the Millennium Development Goals by 2015 [1]. The United Nation Department of Economic and Social Affairs [2], after having analyzed over 80 publications on the green economy and green growth concepts, offers economic, social and ecological indicators to measure the level of green economy development. Also, it is suggested to use the Global Green Economy Index [2]—GGEI, and the NASDAQ OMX Green Economy Benchmark Index (QGREEN), in order to estimate the level of the Green Economy. The GGEI is estimated by using the following indicators: • clean energy technology, • sustainable forms of tourism and • improved domestic environmental quality. The QGREEN includes the following indicators: • • • • •

energy efficiency, clean fuels, renewable energy generation, natural resources, water,

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 G. Imanov, Fuzzy Models in Economics, Studies in Fuzziness and Soft Computing 402, https://doi.org/10.1007/978-3-030-61282-5_4

55

56

4 Fuzzy Estimation of National Green Economy Index …

• pollution mitigation and • advanced materials. The green economy will emerge in different forms in different regions, depending on local economic strengths and weaknesses. This paper proposes the National Green Economy Index (NGEI) to define the level of development and methods for the estimation of the investments distribution to sectors of the green economy in Azerbaijan. To meet this objective we use following eleven indicators: • • • • • • • • • • •

Ecological quality—ECQ, Renewable energy—REE, Protection land—PRL, Green tourism—TOR, Quality of life—QOL, Green GDP—EPP, Energy intensity—ENI, Organic agriculture—ORA, Worldwide governance index—WGI, International Innovation Index—III, Transport greenhouse gas emissions per capita—GHG.

In order to achieve this, we have primarily applied the data available on Azerbaijan and international organizations (UNEP, OECD). In order to solve the problem of the National Green Economy Index (NGEI) we have used fuzzy set and fuzzy logic theories. The structure of the green economy quality, and its related National Green Economy Index (NGEI), and its indicators, is shown in Fig. 4.1.

4.1 Indicators of the Green Economy 1.

2.

3.

Natural Environment can be described as combination of living and nonliving things occurring naturally in any specific region [3]. The quality of the natural environment of any state can be characterized by a synthesis of the quality of air, water and land, biodiversity, pollution, noise, etc. At the country level it is also important to take into consideration such aspects influencing the natural environment like the environmental protection investments versus the environmental damage [4]. Ecological Quality Index involves the main indicators which describe the level of development of the national green economy and is characterized by the quality of air, water, land, biodiversity, environmental protection investments, and environmental damage. Renewable energy can be broadly defined as the energy coming from replenishable sources. In its various forms, it is derived directly or indirectly from the sun, transferring of kinetic energy of the moving water or air, or from heat generated

4.1 Indicators of the Green Economy

Protection land

57

Green economy development index

Renewable energy

Green tourism

Quality of life

Organic

Energy security

agriculture

Natural environment quality index

World Governance Index

Green GDP

Transport Greenhouse Gas Emissions Per Capita

International Innovation Index

Air quality

Water quality

Land quality

Biodiversi-

ty

Fig. 4.1 Structure of elements of the green economy quality

Economic damage

Environmental protection funds

58

4.

5.

6.

4 Fuzzy Estimation of National Green Economy Index …

deep within the earth. In the definition there is included the energy generated from solar, wind, biomass, geothermal, hydropower and ocean resources, and biofuels and hydrogen derived from renewable resources [5]. IEA estimates that about 11% of world marketed energy consumption is from the renewable energy sources, with a projection for 15% by 2040 (International Energy Outlook 2013). Protected land is a protected area which is a clearly defined geographical space, recognized, dedicated and managed, through legal or other effective means, to attain the long term conservation of nature with associated ecosystem services and cultural values.” [6]. There are over 161,000 protected areas in the world (as of October 2010) with more added daily, representing between 10 and 15% of the world’s land surface area. By contrast, only 1.17% of the world’s oceans is included in the world’s ca. 6,800 Marine Protected Areas (https://mdgs.un. org/unsd/mdg/Host.aspx?Content=Products/ProgressReports.htm/). Green tourism refers to tourism activities that can be maintained or sustained, indefinitely in their social, economic, cultural, and environmental contexts of “sustainable tourism”. The sustainable tourism is not a special form of tourism; rather, all forms of tourism may strive to be more sustainable [7]. A clear distraction should be made between the concepts of ecotourism and sustainable tourism: “the term ecotourism itself refers to a segment within the tourism sector with focus on environmental sustainability, while the sustainable principles should apply to all types of tourism activities, operations, establishments and projects, including conventional and alternative forms” (International Year of Ecotourism 2002, http//unep.fr/scp/tourism/events/iye/pdf/iye _leaflet_text.pdf). Quality of life index (https://nationranking.wordpress.com/2011/03/06/2011-qli/) includes the following sub-indices related to: • • • • • •

7.

8.

health, education, wealth, democracy, peace, and environment [8].

Green GDP index = (GDP – RME – EPE) / GDP, where GDP—gross domestic product, RME—volume of export of raw materials, EPE—environmental protection expenditure. The green gross domestic product is an index describing the economic growth with environmental impacts, positive or negative, of that gross, factored into the country’s conventional GDP index. This index reflects the resource depletion, environmental degradation, and the funding of the environmental protection initiatives is subtracted from the GDP value. Energy security represents a combination of the national security level and the availability of natural resources and energy for consumption, either from

4.1 Indicators of the Green Economy

59

internal resources or from reliable external supplies [9]. In the present paper we propose to apply the index based on the fossil fuel resources available within the country, i.e. how many years the country can continue its current rate of fuel consumption on its own resources. 9. Organic agriculture is “an ecological production management system that promotes and enhances biodiversity, biological cycles, and soil biological activity. It is based on minimal of off-farm inputs and on management practices that restore, maintain, or enhance ecological harmony. The primary goal of organic agriculture is to optimize the health and productivity of interdependent communities of soil life, plants animals, and people [10]”. 10. World Governance Index (WGI) includes the following indices [11]: • • • • •

Peace and Security, Rule of Law, Human Rights and Participation, Sustainable Development. And Human Development.

11. International innovation index is proposed by Boston Consulting Group and “takes into account two types of innovation output; tangible outcomes, new products, knowledge, formulas, designs, and expertise that are easily quantified and can be legally protected through patents or other intellectual-property vehicles, intangible outcomes, new processes or ways of doing business that lead to a competitive advantage, such as a new company wide production process that results in higher quality and greater productivity. Intangible outcomes are not themselves easily quantified but can have a major impact on quantifiable results, such as overall business performance. They generally cannot be legally protected” [12]. 12. Transport greenhouse gas emissions per capita (GHG). The transport sector CO2 emissions represent 23% (globally) and 30% (OECD) of overall CO2 emissions from the fossil fuel combustion. The sector accounts for approximately 15% of overall greenhouse gas emissions. The global CO2 emissions from transport have grown by 45% from 1990 to 2007, led by emissions from the road sector in terms of volume and by shipping and aviation in terms of the highest growth rates [13].

4.2 Model Estimation for the Ecological Quality Index In order to build a fuzzy model for the assessment of the ecological quality index we have used ecological data from various international organizations and data available on Azerbaijan. Table 4.1 shows details of this fuzzy model. In order to solve the stated problem, which corresponds to the model of interest, the algorithm of the weighted rules has been used, and is given in Sect. 1.4. The consecutive steps of the algoritm are as given below.

60

4 Fuzzy Estimation of National Green Economy Index …

Table 4.1 Fuzzy model of the ecological quality index Parameter

Definition

Terms and its values

Azerbaijan

I Air Quality Index (AQI)

Moderate 39–60

Good 59–80

Very good 79–100

1. Annual μgr/m3 Average SO2 (SO2 )

Moderate 20–35

Low 10–25

Very low 0–15

Low 15

2. Annual μgr/m3 Average NO2 (NO2 )

Moderate 40–50

Low 30–45

Very low 20–35

High 50

3. Annual μgr/m3 Average TSP (TSP)

Moderate 30–40

Low 15–30

Very low 10–20

Very high 300

II Water Quality Index (WQI)

Moderate 40–60

Good 60–80

Very good 80–100

Bad 21.8

4. Dissolved (ml/l) oxygen concentrations (milliliters of dissolved oxygen per liter of water) (DOC)

Moderate 9–12

Good 7–10

Very good 69.5

High 58

8. Annual average forest area (AAF)

Moderate 19–30

Good 29–40

Very good 39–50

Bad 11.3

Moderate 39 60

Good 59–80

Very good 79–100

Bad 29.5

IV Environmental Biodiversity Index (EBI)

% of land area

(continued)

4.2 Model Estimation for the Ecological Quality Index

61

Table 4.1 (continued) Parameter

Definition

9. Territories under protection (TUP) 10. Percentage of the country territory in the threatened ecoregions (TTER)

%

11. National 0–1 Biodiversity Index (NBI)

Terms and its values

Azerbaijan

Moderate 14–22

Good 21–30

Very good >29

Bad 10.1

Moderate 20–30

Good 10–20

Very good 0–10

40

Moderate 0.30–0.50

Good 0.45–0.65

Very good 0.6–1

Good 0.534

V 12. CO2 and particulate emissions damage

MT per capita Moderate 2.3–3.6

Low 1.1–2.4

Very low 0–1.2

High 4.4 (2009)

VI 13. Capital investments for environmental protection programs

% of GDP

High 3.4–5

Very high > 4.9

Very low 0.5 (2009)

59–80

70–100

QNE Parameter

Moderate 2.2–3.5

39–60 Definition

I Air Quality Index (AQI)

Terms and its values

Azerbaijan

Very bad 0–20

Bad 19 40

μgr/m3

Very high >40

High 30–45

Low 15

2. Annual Average NO2 μgr/m3 (NO2 )

Very high >60

High 50–60

High 50

Very high > 50

High 35–50

Very high 300

Very bad 0–20

Bad 20–40

Bad 21.8

Very bad >14

Bad 11–14

Good 8.27

Very bad 79

Low 80–59

Very low 150

Very bad 0–20

Bad 19.5–40

Moderate 49.5

% of land area

Very low 0–15

Low 14.5–25

High 58

8. Annual average forest % of land area area (AAF)

Very bad 0–10

Bad 9–20

Bad 11.3

IV Environmental Biodiversity Index (EBI)

Very bad 0–20

Bad 19–40

Bad 29.5

9. Territories under protection (TUP)

Very bad 40

Bad 0–40

40

11. National Biodiversity Index (NBI)

0–1

Very bad 4.5

High 3.5–5

H igh 4.4 (2009)

VI 13. Capital investments for environmental protection programs

% of GDP

Very low 0–1.2

Low 1.1–2.3

Very low 0.5 (2009)

0–20

19–40

QNE

Fuzzification is carried out in the first step, and a Gaussian function is applied. Further, on the basis of the quantity of terms, initial fuzzy rules are defined (for example, if the quantity of terms is 3, the number of initial rules is equal to 3). In the following step, other possible rules are defined by the Cartesian product of terms in the initial rules. Then, the peak  of each corresponding interval ci j is defined   on the basis of  point the matrix C = ci j where the i-index is corrected due to C = ci j , and the j is the index of terms defined as ci j . The initial rules are expressed via ci j . After that, by means of the formula shown below, degrees of membership of each point of the support of the fuzzy number corresponding to linguistic variables are defined as:

4.2 Model Estimation for the Ecological Quality Index

μ(x) =

n 

 − 21

exp

63

 x i −ci 2 

j=1

j

σ ji

(4.1)

where: n—number of input variables; x i —terms; i—index of term; cij —peak point of corresponding terms i; and σ ji —average square deviation of interval of a corresponding term. After that, the weighted antecedent of the initial rules is defined with the weights: nμi (x) i=1 μi (x)

wia = n

(4.2)

wia = 1

i=1

where: wia —weighted antecedent of the initialed rules, μi (x)—degree of membership of fuzzy variables involved in the antecedent part of the rules. By substituting the value of formula (4.1) in formula (4.2), we obtain: 2 ⎤  i 1 x j −c j ⎦ ⎣ j=1 exp − 2 σ ji ⎡ 2 ⎤  i R n 1 x j −c j ⎦ ⎣ exp − i=1 j=1 2 σ ji ⎡

n

wia =

(4.3)

In the next step, the weights of the consequence part of the rules are calculated due to the formula: R

wic =

i=1

bi

j=1

R n i=1

j=1

1 x j −c j 2 exp[− ( ) ] 2 σ ji i

n

i

1 x j −c j 2 exp[− ( ) ] 2 σ ji i

i

(4.4)

where: bi —peak point of the corresponding terms of the consequence part of the rules. Further, using the maximum values of wic , wia , we define new system of rules. In the new system of rule, we have: R1 is the rule which we find, and R2 is the rule which corresponds to a fixed meaning of the input variables. By using the composition operation we define the corresponding fuzzy numbers. Finally, the defuzzification of fuzzy numbers is carried out using the well-known centroid method. By using the algorithm outlined above, the meaning (linguistic value) of the ecological quality index, which is equal to Bad, is obtained. A very bad quality of air, a bad quality of water, a bad value of the index of biodiversity and a very low level of investments for environmental protection have contributed to the bad value of the ecological quality index.

64

4 Fuzzy Estimation of National Green Economy Index …

4.3 Model of the Green Economy In order to model the quality of the Green Economy the following terms have been used: Very Low (VL), Low (L), Medium (M), High (H) and Very High (VH), which have been scaled in the interval [0, 1]. In the process of modeling we have also used the terms—very bad (VB), Bad (B), Moderate (M), Good (G), and Very Good (VG). In order to estimate the indices of the level of development of the Green Economy we have proposed a method that is based on Zadeh’s compositional rule of inference [14] which consists of the following steps: 1. Development of a table describing parameters of the model on the basis of information obtained from international organizations and experts. In the first column of the table the input parameters of the model are shown, and in the following columns the terms and their corresponding intervals are given. The last column specifies the crisp meaning of the input parameters for a fixed period; 2. Definition of the membership degrees of the crisp meaning of the input parameters of the relevant terms. For this purpose we have used the Gaussian membership function: μ A (x, ci , σi ) = e−(x−ci )

2

/2σi2

(4.5)

where ci is the center of the i-th fuzzy set and σi is the width of one of the i-th fuzzy sets. 3. Determination of the minimum degree of membership to the corresponding term of the input parameters, i.e. min μi j ; j

4. Determination of the maximum of the minimum  values  of the degrees of membership to the corresponding term, i.e. max min μi j . The obtained value will i

j

reflect the quality of the National Green Economy. The proposed methodology has been tested on the basis of information on quality parameters of the model of the Green Economy (Table 4.2). The source materials are obtained from international organizations and data for Azerbaijan Republic [15, 16]. Information on the Green Economy indicators of Azerbaijan is given in the last column of Table 4.2. At a second stage we have determined the degree of membership of national indicators of the Green Economy to the appropriate term. Specifically, the membership degrees of 11 indicators of the terms is as follows: Very low (VL)

Low (L)

Medium (M)

High (H)

μ R E E = 0.03

μ EC Q = 0.55

μ Q O L = 0.29

μ E N I = 0.05

μP RL = 1

μ I I I = 0.38

Very high (H)

μG H G = 0.08

μT O R = 0.03

μ O R A = 0.96

μ E E P = 0.02

μW G I = 0.06

0 (continued)

4.3 Model of the Green Economy

65

(continued) Very low (VL)

Low (L)

Medium (M)

High (H)

Very high (H)

min:0.02

min:038

min:0.06

min:0.05

min:0

The maximum value, which is equal to 0.38, is determined among the minimum values. This value corresponds to the term “low” which is hence the defining index of the level of development of the Green Economy. Research that has been undertaken, using fuzzy logic methods, on the National Green Economy Development Index for Azerbaijan, shows that a very low value of this index is primarily influenced by a very low level of renewable energy use, low levels of protected land, green tourism and ecological quality in Azerbaijan. The problem of distribution between sectors of the Green Economy has to be studied in order to improve this situation in the future.

4.4 Fuzzy Entropy Based Estimation of the Distribution of Investments A successful development of the Green Economy depends on the distribution of investments. The estimation of the index of the national Green Economy requires the definition of an optimal distribution of investment over sectors of the economy. In the present report, we investigate the distribution of investments using a fuzzy model based on the fuzzy entropy and fuzzy weight. The fuzzy entropy of the input parameters is determined based on the actual values and their fuzzified values. Further, the fuzzy entropy related to the input parameters determines their weights. The investment distribution problem, corresponding to the model is solved on the basis of information on Azerbaijan. In order to estimate a weight of a fuzzy number we will use the fuzzy entropy. Different authors have defined the fuzzy entropy is different ways. In this work we use the concept and definition of the fuzzy entropy proposed by Kosko [17]: (A) =

|A ∩ Ac | |A ∪ Ac |

(4.6)

where: |A ∩ Ac | and |A ∪ Ac | denote the cardinalities of the sets A ∩ Ac and A ∪ Ac , and Ac stands for the compliment of the set A which is defined as μ AC (x) = 1 − μ A (x), ∀x

(4.7)

The entropy weight of the i-th indicator is defined as follows wi =

1 − E(Ai ) m m − i=1 E(Ai )

(4.8)

66

4 Fuzzy Estimation of National Green Economy Index …

Table 4.2 Model of green economy Categories

Source indicators

Development level World Indicators Very low

Low

Medium

Azerbaijan

2010

0–0.2

0.18–0.4

0.38–0.6

L-0.25

0–0.2

0.18–0.4

0.38–0.6

VL-0.013

0–0.2

0.18–0.4

0.38–0.6

VL- 0.102

0–0.2

0.18–0.4

0.38–0.6

VL-0.012

0–0.2

0.18–0.4

0.38–0.6

M-0.548

0–0.2

0.18–0.4

0.38–0.6

VL-0.008

VB 0.56–0.45

B 0.44–0.33

M 0.32–0.21

G-0.1

0–0.2

0.18–0.4

0.38–0.6

M-0.5

0–0.2

0.18–0.4

0.38–0.6

M-0.578

1

Ecological quality—ECQ

2

Renewable energy—REE

3

Protection land—PRL

4

Green tourism—TOR

5

Quality of life—QOL

6

Green GDP

7

Energy intensityENI

8

Organic agriculture—ORA

9

Worldwide governance index—WGI

10

International Innovation Index—III

VB (-2)–(-1.1)

B (-1.2)–(-0.3)

M (-0.4)–0.5

B-0.54

11

Transport greenhouse gas emissions per capita -GHG

20–10

9.5–3

2.9–1

H-0.55

Categories

2012

2011

2010

2008

Source indicators

Development level World indicators High

1

Ecological quality—ECQ

2

Renewable energy—REE

3

Protection land—PRL

4

Green tourism—TOR

5

Quality of life—QOL

6

Green GDP

2010

2012

2011

Very high

Azerbaijan

0.58–0.8

0.78–1

L-0.25

0.58–0.8

0.78–1

VL-0.013

0.58–0.8

0.78–1

VL- 0.102

0.58–0.8

0.78–1

VL-0.012

0.58–0.8

0.78–1

M-0.548

0.58–0.8

0.78–1

VL-0.008 (continued)

4.4 Fuzzy Entropy Based Estimation of the Distribution of Investments

67

Table 4.2 (continued) Categories

Source indicators

Development level World indicators

7

Energy intensity-ENI

8

Organic agriculture—ORA

9

Worldwide governance index—WGI

10

International Innovation Index—III

11

Transport greenhouse gas emissions per capita—GHG

2010

2008

High

Very high

Azerbaijan

G 0.2–0.09

VG 0.08 → 0

G-0.1

0.58–0.8

0.78–1

M-0.5

0.58–08

0.78–1

M 0578

VG 1.2–2

B-0.54

0.4–0

H 0.55

G 0.4–1.3

0.9–05

In oder to estimate fuzzy weight parameters of the Green Economy Index, we have used as an as example μα of the ecological quality which is equal to 0.55. The fuzzy number, which correspond to μα = 0.55, is shown in Fig. 4.2. In the first step, the interval [0.19;0.4] is divided into 35 parts, the length’s of which equals 0.21. This lengths is divided into 35 parts, e.g. d = 0.21/35 = 0.006. In the interval [0.19;0.25] the number of parts eis qual to 10, in [0.25;0.34] is equal to 15, and in [0.34;0.4] is equal to 10. For the obtained points to estimate the degree of membership we have used the trapezoidal membership function, e.g.: ⎧ ⎪ 0 x < a, ⎪ ⎪ x−a ⎪ ⎪ · μ a ≤x ≤b α ⎨ b−a μ(x) = μα b≤x ≤c ⎪ d−x ⎪ ⎪ · μ c ≤ x ≤ d, α ⎪ d−c ⎪ ⎩ 0, x > d.x > d. Fig. 4.2 Fuzzy number representing the ecological quality

(4.9)

μ 1 μα= 0.55 0.19

0.25

0.34

0.4

X

68

4 Fuzzy Estimation of National Green Economy Index …

For example, in point 0.55 the membership degrees is estimated as follows: μ(0.196) =

0.196 − 0.19 ∗ 0.55 = 0.0550 0.25 − 0.19

μ(0.202) =

0.202 − 0.19 ∗ 0.55 = 0.1100 0.25 − 0.19

μ(0.208) =

0.208 − 0.19 ∗ 0.55 = 0.1650 0.25 − 0.19

μ(0.214) =

0.214 − 0.19 ∗ 0.55 = 0.2200 0.25 − 0.19

μ(0.220) =

0.220 − 0.19 ∗ 0.55 = 0.2750 0.25 − 0.19

μ(0.226) =

0.226 − 0.19 ∗ 0.55 = 0.3300 0.25 − 0.19

μ(0.232) =

0.232 − 0.19 ∗ 0.55 = 0.3850 0.25 − 0.19

μ(0.238) =

0.238 − 0.19 ∗ 0.55 = 0.4400 0.25 − 0.19

μ(0.244) =

0.244 − 0.19 ∗ 0.55 = 0.4950 0.25 − 0.19

μ(0.25) =

0.25 − 0.19 ∗ 0.55 = 0.5500 0.25 − 0.19

The degree of membership of points of the interval of the support of the trapezoidal fuzzy number, i.e., [0.25;0.34] do not change and are equal to 0.55(μ∝ ). In the interval [0.34,0.4], the membership degree is correspondingly equal to. 0.5500;0.4950;0.4400;0;3850;0.3300;0.2750;0.2200;0.1650;0.1100;0.0550 The fuzzy expression set of A is as follows: A = [{(0.1900;0.0000), (0.1960;0.0550), (0.2020;0.1100), (0.2080;0.11650), (0.2140;0.2200), (0.2200;0.2750), (0.2260;0.3300), (0.2320;0.3850), (0.2380;0.4400), (0.2440;0.4950)}. {(0.25;0.55), (0.256;0.55), (0.262;0.55), (0.268;0.55), (0.274;0.55), (0.28;0.55), (0.286;0.55), (0.292;0.55), (0.298;0.55), (0.304;0.55), (0.31;0.55), (0.316;0.55), (0.322;0.55), (0.328;0.55), (0.334;0.55)} {(0.34;0.55), (0.346;0.4950), (0.352;0.44), (0.358;0.3850), (0.364;0.33), (0.37;0.275), (0.376;0.2200), (0.382;0.1165), (0.388;0.11), (0.400;0.00)}]

4.4 Fuzzy Entropy Based Estimation of the Distribution of Investments

69

Table 4.3 Entropy of the indicators Abbreviation of variables

Meaning of variables

Number of intervals

|A ∩ Ac |

ECQ

Ecological quality

35

13.103

20.297

0.6456

REE

Renewable energy

100

2.94

97.06

0.0303

PRL

Protection land

50

25.00

25.00

1.0000

TOR

Green tourism

100

2.94

97.06

0.0303

QOL

Quality of life

35

8.70

27.30

0.3187

GGP

Green GDP

200

3.96

197.04

0.0201

ENI

Energy Intensity

50

2.45

48.55

0.0505

ORA

Organic Agriculture

35

17.28

17.72

0.9752

WGI

Worldwide 35 governance index

2.04

33.96

0.0601

III

International 50 Innovation Index

15.20

34.80

0.4368

GHG

Transport greenhouse gas emissions per capital

7.68

93.32

0.0823

100

|A ∪ Ac |

Entropy E(A)

The compliment Ac set of A is as follows: Ac = [{(0.1900;1), (0.1960;0.0450), (0.2020;0.8900), (0.2080;0.8835), (0.2140;0.8800), (0.2200;0.7250), (0.2260;0.6700), (0.2320;0.6150), (0.2380;0.5600), (0.2440;0.5050)}. {(0.25;0.45), (0.256;0.45), (0.262;0.45), (0.268;0.45), (0.274;0.45), (0.28;0.45), (0.286;0.45), (0.292;0.45), (0.298;0.45), (0.304;0.45), (0.31;0.45), (0.316;0.45), (0.322;0.45), (0.328;0.45), (0.334;0.45)} {(0.34;0.45), (0.346;0.5050), (0.352;0.56), (0.358;0.6150), (0.364;0.67), (0.37;0.725), (0.376;0.8800), (0.382;0.8835), (0.388;0.89), (0.400;1)}] and 2∗(0.055+0.11+0.1165+0.22+0.275+0.3300+0.3850+0.4400+0.4950)+15∗0.55 = E(A) = 2∗(1+0.0450+0.89+0.8835+0.88+0.7250+0.6700+0.6150+0.5600+0.5050)+15∗0.45 13.03 = 0.6456 20.297 Therefore, the calculated entropy of the variables are shown in Table 4.3. At the last stage on the base of the we have defined the meanings of fuzzy weights which are shown in Table 4.4. The estimated fuzzy weights give a possibility to define a direction and priority of investments for the particular sectors of the Green Economy.

70

4 Fuzzy Estimation of National Green Economy Index …

Table 4.4 Fuzzy weights of sectors of the Green Economy Abbreviation of variables

Meaning of variables

Fuzzy weights

Terms

ECQ

Ecological quality

0.0480

L

REE

Renewable energy

0.1320

VL

PRL

Protection land

0.0000

VL

TOR

Green tourism

0.1320

VL

QOL

Quality of life

0.0927

M

GGP

Green GDP

0.1333

VL

ENI

Energy Intensity

0.1292

H

ORA

Organic Agriculture

0.0034

M

WGI

Worldwide governance index

0.1279

M

III

International Innovation Index

0.0766

L

GHG

Transport greenhouse gas emissions per capita

0.1249

H

References 1. United Nations Environment Programme (UNEP). (2011). Towards a green economy. Pathways to sustainable development and poverty eradication. 2. United Nations Department of Economic and Social Affairs (UN-DESA). (2012). A guidebook to the green economy, Issue 1. 3. Johnson, D. L., Ambrose, S. H., Bassett, T. J., Bowen, M. L., Crummey, D. E., Isaacson, J. S., et al. (1997). Meanings of environmental terms. Journal of Environmental Quality, 26(3), 581–589. 4. Anderson, T. L. (2008). Environmental quality. In: D. R. Henderson (Ed.), Concise Encyclopedia of economics (2nd ed.). Indianapolis: Library of Economics and Liberty. ISBN 9780865976658. 5. IEA. (2008). Renewable information (2008th ed.). International Energy Agency: OECD Publishing, Paris. 6. Dudley, N. (Ed.). (2008). Guidelines for appling protected areas management categories (pp. 8– 9). Gland, Switzerland: IUCN. 7. Making Tourism More Sustainable. A Guide for Policy Makers. United Nations Enviroment Programme. World Tourism Organization, 2005, 210 p. 8. Quality of Life Index 2011, National Ranking, Quantifying the World of Sovereign States. https://nationranking.wordpress.com/2011/03/06/2011-qli/. 9. Energy Technology Perspectives 2012, Pathways to a Clean Energy System, International Energy Agency (2012) (2nd ed.), France, p. 690. 10. The World of Organic Agriculture, Statistics and Emerging Trends, 2014. https://www.organicworld.net/yearbook-2014.html. 11. World Governance Index, version 2.0, 2011 Report, 26 p. 12. Andrew, J. P., DeRocco E. S., & Taylor, A. (2009, March). The innovation Imperative in Manufacturing. How the United States Can Restore Its Edge, 32 p. 13. Reducing Transport Greenhouse Gas Emissions: Trends & Data 2010—© OECD/ITF 2010, 94 p. 14. Zadeh, L. A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernet. SMC, 3, 28–44. 15. Report of Ministry of Ecology and Natural Resources of Azerbaijan Republic, Part I, Baku2013, 96 p.

References

71

16. Report of Ministry of Ecology and Natural Resources of Azerbaijan Republic, Part II, Baku2013, 235 p. 17. Kosko, B. (1990). Fuzziness vs probability. International Journal of General Systems, 17(2–3), 211–240.

Chapter 5

Models of Socioeconomic Security

5.1 Fuzzy Analysis of Macroeconomic Stability World Bank describes macroeconomic stability as follows: when the inflation rate is low and predictable, the real interest rates are appropriate, the real exchange rate is competitive and predictable, the public sector saving rates are compatible with the resource mobilization requirements of the program, and the balance of payments situation is perceived as variable [1]. According to the Maastricht Treaty [2] the macroeconomic stability is measured through five variables: – Low and stable inflation (the Maastricht criteria capped at 3%); – Low long-term interest rate (the Maastricht criteria restricted to the range of 9%); – Low debt to Gross Domestic Product ratio (the Maastricht criteria capped at 60% of GDP); – Low deficit (the Maastricht criteria capped at 3% of GDP); – Monetary stability (the Maastricht criteria permitted fluctuations of at most 2.5%). In order to calculate the level of macroeconomic stability, econometric models are mainly used. By means of a linguistic intuitionistic fuzzy number, we calculate the aggregate index of macroeconomic stability of Azerbaijan for the period of 2010– 2016 years [3]. For this purpose, we use the following macroeconomic indicators: – – – – – – – –

Growth Rate of Gross Domestic Product—GGD; Inflation %—INF; Interest rate %—INR; National Debt Relative to GDP %—NAD; Budget Deficit (% of GDP)—DEF; Exchange Rate—EXR; Current Account Balance (% of GDP)—CAB; Unemployment Rate %—UNE;

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 G. Imanov, Fuzzy Models in Economics, Studies in Fuzziness and Soft Computing 402, https://doi.org/10.1007/978-3-030-61282-5_5

73

74

5 Models of Socioeconomic Security

– Growth rate of Foreign Investment—FEI Calculation of Parameters of the Linguistic Intuitionistic Fuzzy Set On the basis of the intuitionistic fuzzy set (IFS) and the linguistic intuitionistic fuzzy number (IFN), by using thresholds recommended by the Maastricht Treaty and the Alert Mechanism European Commission [4] for the indicators of macroeconomic stability, linguistic variable Sθ(x) is defined a shown in Table 5.1. In order to define the membership and non-membership degrees, Attanassov’s function [5] is used, that is: ⎧   ⎪ ⎪ u x˜ x−t_ ⎪ ⎪ ift ≤ x < t ⎪ t−t ⎪ _ _ ⎨ ifx = t μx˜ (x) = u x˜ ⎪ u x˜ (t−x ) ⎪ ⎪ ift < x ≤ t ⎪ t−t ⎪ ⎪ ⎩0 i f x < t or x > t

(5.1)

_

and Table 5.1 Linguistic variables of macroeconomic stability indicators Indicators

Unstable-S0

Low stable-S1

GGD

−∞

−1.05

0.1

0

1.25

2.5

INF

9

9.5

+∞

3

6.25

9.5

NAD

55

65

+∞

25

42.5

60

INR

9

9.5

+∞

3.5

6.5

9.5

DEF

9

9.5

+∞

3.5

6.75

10

EXR

−∞

−50

−32

−11

−10

CAB

−∞

2

2.5

−3

−2.5

−2

UNE

11

11.5

+∞

7.5

9.75

12

FDI

−∞

−3

−2.5

−3

−2.25

−1.5

Indicators

Stable-S2

High stable-S3

GGD

2

2.5

3

2.5

4.25

7

INF

2

3.25

4

0

1.5

3

NAD

1

20

30

0

7.5

15

INR

1

2.5

4

−3

0

3

DEF

1

2.75

4

−1.5

0.25

2

EXR

−

0

11

−

−

−30

CAB

−

1

6

5

17.5

30

UNE

5

6.75

8

4

5

6

FDI

−

0.65

3.3

3

10

+∞

5.1 Fuzzy Analysis of Macroeconomic Stability

75

  ⎧ t−x+wx˜ x−t ⎪ ⎪ _ ⎪ ⎪ ift ≤ x < t ⎪ t−t ⎪ _ _ ⎨ i f x = t w x˜ νx˜ (x) = ⎪ [x−t+w x˜ (t−x )] ⎪ ⎪ ift < x ≤ t ⎪ t−t ⎪ ⎪ ⎩1 i f x < t or x > t

(5.2)

_

For calculating the membership and non-membership function the reduction coefficients (u x˜ , wx˜ ) are employed which take into account the accuracy of statistical information. The results of the calculation of the membership degree and the non-membership degree and the linguistic indices are presented in Table 5.2. Then, the weights of k-th macroeconomic indicators in t-years are obtained by using Boran, Genc, Kurt and Akay’s [6] TOPSIS based method and are shown in Table 5.3. Table 5.2 Intuitionistic fuzzy numbers representing the values of the macroeconomic stability indicators Indicators

2010

2011

Sθ

μ

ν

GGD

S3

0.8

INF

S1

0.67

NAD

S1

INR DEF

2012

Sθ

μ

ν

Sθ

μ

ν

0.16

S1

0.07

0.92

S2

0.36

0.62

0.25

S1

0.39

0.56

S3

0.53

0.4

0.78

0.18

S3

0.024

0.97

S0

0.9

0.05

S3

0.74

0.22

S3

0.56

0.41

S3

0.66

0.3

S3

0.53

0.43

S3

0.68

0.28

S3

0.83

0.13

EXR

S2

0.83

0.08

S2

0.73

0.19

S2

0.81

0.09

CAB

S2

0.13

0.86

S3

0.22

0.75

S3

0.64

0.28

UNE

S2

0.34

0.62

S3

0.51

0.43

S3

0.24

0.68

FDI

S2

0.51

0.42

S2

0.66

0.25

S2

0.62

0.31

Indicators

2013

2014

2015

2016

Sθ

μ

ν

Sθ

μ

ν

Sθ

μ

ν

Sθ

μ

ν

GGD

S3

0.48

0.49

S2

0.36

0.62

S1

0.79

0.16

S0

0.9

0.05

INF

S3

0.32

0.64

S3

0.75

0.04

S1

0.25

0.72

S0

0.8

0.1

NAD

S0

0.9

0.05

S0

0.9

0.05

S0

0.9

0.05

S3

0.44

0.54

INR

S3

0.53

0.44

S3

0.26

0.72

S2

0.33

0.45

S1

0.78

0.17

DEF

S3

0.68

0.28

S3

0.49

0.49

S3

0.15

0.85

S3

0.53

0.43

EXR

S2

0.84

0.06

S2

0.85

0.05

S1

0.17

0.81

S0

0.85

0.05

CAB

S3

0.71

0.2

S3

0.53

0.40

S2

0.58

0.35

S2

0.13

0.86

UNE

S3

0.85

0.05

S3

0.76

0.15

S3

0.85

0.05

S3

0.76

0.15

FDI

S2

0.67

0.24

S2

0.65

0.28

S2

0.71

0.2

S2

0.7

0.21

76

5 Models of Socioeconomic Security

Table 5.3 Weights of the macroeconomic indicators Indicators

2010

2011

2012

2013

2014

2015

2016

GGD

0.15

0.02

0.06

0.08

0.06

0.16

0.15

INF

0.13

0.10

0.10

0.05

0.16

0.05

0.14

NAD

0.14

0.01

0.16

0.15

0.16

0.18

0.07

INR

0.14

0.14

0.12

0.09

0.04

0.08

0.13

DEF

0.10

0.17

0.15

0.11

0.08

0.03

0.09

EXR

0.16

0.19

0.15

0.15

0.16

0.03

0.15

CAB

0.02

0.06

0.12

0.12

0.09

0.12

0.02

UNE

0.06

0.13

0.04

0.15

0.14

0.18

0.13

FDI

0.10

0.17

0.11

0.11

0.12

0.15

0.12

1

1

1

1

1

1

1

In order to calculate the Aggregate Index of Macroeconomic Stability (AIMS) for each year, the Linguistic Intuitionistic fuzzy Weighted Average (ILWA) formula is used [6] and the results obtained are as follows: AIMS (2010) = S2.1 (0.71, 0.22) AIMS (2011) = S2.4 (0.60, 0.33) AIMS (2012) = S2.2 (0.74, 0.19) AIMS (2013) = S2.3 (0.76, 0.14) AIMS (2014) = S2.2 (0.74, 0.13) AIMS (2015) = S1.6 (0.75, 0.15) AIMS (2016) = S1.3 (0.78, 0.13) As it can be seen from the result of calculation, the macroeconomic stability was satisfying in 2010–2014, but in 2015–2016 the level of macroeconomic stability decreased and became low. As shown in Table 5.2, the fluctuation and decrease of the Growth Rate of Gross Domestic Product (GGD) from a high stability (S3) in 2010 to an instability level (S0) in 2016 in the dynamics of the GGD trio can mainly be associated with price changes in the oil sector due to a global financial crisis. The change of oil price on the world market has had its impact on the growth of GDP, as the oil sector has a large share in the Gross Domestic Product (GDP) of Azerbaijan. Thus, a sharp decline in oil prices since the end of 2014 has led to a decline of the oil volume in the GDP. The fact that devaluation has not been observed with a noticeable increase in the non-oil sector in a short time, has led to the instability in the GDP. Since large oil revenues in the country have led to an increase in the volume of currency reserves, the fluctuations in inflation can be mainly related to monetary policy governed by the Central Bank. In order to ensure and diversify the economic stability of the country, the monetary policy regulating the inflation rate has been implemented. In 2013–2014, as a consequence of the implemented policy, a high stability of the rate of inflation has been attained. In the subsequent years, the financial

5.1 Fuzzy Analysis of Macroeconomic Stability

77

crisis which has occurred in the world has resulted in a decline of the exchange rate of the national currency of the country. As a result, since the long-term economic stability could not be achieved with a regulated monetary policy, the transition to a floating exchange rate was started, which had implied a change of the inflation rate. Thus, fluctuations toward the inflation instability started. The main factor of the economic growth of the country during the oil boom, which lasted until 2015, was due to oil revenues. Loans were mainly directed to households (44% of loans in 2014), trade (15%), mostly related to non-commercial sectors that depend heavily on oil revenues, and construction (14%). The total share of the industrial sector in the credit portfolio of banks was 10%. Thus, the role of the interest rate (INR) in the economic growth during that period was low and it is wrong to link the high economic growth to the interest rate. The fall of the interest rate from S3 to S1 in 2015–2016 is associated with a reduction of the role of the oil factor in this period. The main reason of transition of the national debt to the GDP ratio (NAD) from a low stability level (S1) in 2010 to a high stability level in 2011 is an increase in the oil production, the foreign currency (in)flow to the country and a relative increase of the national currency exchange rate (EXR). However, a fall to the instability level (S0) that started from 2012 and continued up to 2016 was linked to a decline in the oil production on a regular basis. A high level of stability in 2016 can be associated with a downturn in indebtedness and an increase in gas production. The main reason of a high level stability (S3) in the budget deficit (DEF) was at the expense of transfers to the State Budget by the Oil Fund. The macroeconomic stability level (S2) of the exchange rate (EXR) in 2010– 2014 became the main factor for keeping the exchange rate of the national currency (Manat) stable during that period. The transition to a low stability level (S1) and the instability level (S0) can be explained by a sharp decline of the oil price on the world market and a decrease in the exchange rate of the national currency. The rise of the current account balance (CAB) from the medium stability level (S2) in 2010 to the high stability level (S3) in 2011 was related to an increase in the positive saldo of the CAB: from 15.0 billion US dollars to 17.1 billion US dollars. Due to the substitution of the positive saldo with the negative one in 2015–2016 (0.2 billion US dollars and 1.4 billion US dollars, respectively), related with a decline in the crude oil price on the world market for more than two times, its stability level decreased from the high stability (S3) in 2014 to the medium stability (S2) in 2015. The unemployment rate (UNE) was almost 5% and remained in the high stability level (S3) during 2010–2016. State programs focused on ensuring the socialeconomic development of regions, creating new workplaces, developing non-oil sectors, etc. had a certain role in maintaining the high stability level observed in the unemployment rate. The stability level of the foreign investment growth rate (FDI) remained stable (medium stability level-S2) during 2010–2016s. It was associated with a high level and a dynamic growth of the foreign direct investments. It was: – 3.5 billion US dollars in 2010,

78

– – – – – –

5 Models of Socioeconomic Security

4.4 billion US dollars in 2011, 5.3 billion US dollars in 2012, 6.3 billion US dollars in 2013, 7.5 billion US dollars in 2014, 7.5 billion US dollars in 2015, and 7.4 billion US dollars in 2016.

The proposed approach to the analysis of macroeconomic stability gives us a possibility to define weak and strong sides of the macroeconomic processes which occur in the country. It enables the optimal control over the macroeconomic processes. By using the results obtained, in the future we can forecast directions of the macroeconomic development of country.

5.2 Fuzzy Estimation of the Country’s Social Security Level Social security is one of the most important aspect of economic security. According to Huber et al. [7] economic security consists of the following components: • ensuring deserving conditions for living and developing the identity; • the political, military capability of the society and the country; and • the socio-economic stability in order to eliminate internal and external threats [7]. Econometric models have been used to define the level of social security of a country. In this work a method based on the use of tools and techniques of the linguistic intuitionistic fuzzy numbers has been used to define level of the country’s social security. In order to estimate the level of country’s social security the following indicators have been analyzed: – Unemployment rate (% of total labor force)—UNE: Unused resources and the economy’s spare capacity imply the unemployment. As it is known, the unemployment tends to be cyclical and decreases when the economy expands as companies hire more workers to meet a growing demand, and increases when the economic activity slows down. The increase of the level of unemployment is already a first state, connected with the imperfection of the mechanisms of regulation and selfregulation of the economic system. The high level of unemployment is one of big acute problems of the global and national proportion [8]. – Life expectancy at birth (years)—LEB: The average number of years that a newborn is expected to live if the current mortality rates do not change. A high life expectancy and its quality indicate a stable level of social security. A low one is may indicate a dangerous state of social tension. Social tension manifests itself in a number of most significant symptoms (a significant increase in discontent among the population, mistrust of the authorities, conflict in the society, anxiety, stressfulness of relations) and is determined by the influence of the man-made, natural and social factors; [9]

5.2 Fuzzy Estimation of the Country’s Social Security Level

79

– Gini coefficient (1–100)—GIN: The Gini coefficient is a measure of economic inequality of households. The coefficient measures the variance of income or distribution of wealth among a population. At the same time, the inequality is not dangerous by itself, it is dangerous when a certain critical value is attained which may pose a threat to the country. It is for this reason that the Gini coefficient determines not only the level of social stratification, but also the level of social and political stability; [10] – Research and development expenditures (% of GDP)—R&D: this consists of the total (current and capital) expenditure on R&D carried out by resident companies, universities, research institutes, etc. It includes R&D financed from abroad but excludes the residents’ funds for R&D performed outside of the domestic economy, the R&D expenditures is measured as the percentage of GDP; [11] – Poverty level (%)—POV: The situation in which, taking into account the country’s economic and social circumstances, a person’s minimum basic needs cannot be met and will be below the monetary threshold, will be called the poverty line for the country. As countries develop, the poverty line often rises: in rich countries it is higher than in poorer countries. In order to track the level of development, the number of people living below the poverty line is monitored by the governments. The poverty line is also one of the important indicator for SDG 1, ending poverty “in all its types.” [12] – Military expenditure (% of GDP)—MIL: There are two ways to measure military expenditures: 1) spending in real terms and 2) as a percentage of GDP. The military expenditures in real terms are important as the nominal level of expenditure has an impact on the result of a possible war. The country’s military expenditures are spent no matter whether country is at war or not. If the country is not in the state of war, a part of the budget is spent on supporting the military power. All governmental expenditures include opportunity costs of priorities and objectives. Military conflicts increase the military expenditures that is a matter for concern among the population about the opportunity cost in terms of spending on human, economic and social development [13]. To define the level of social security in many investigations there are used econometric instruments. In this work we propose the use of a linguistic intuitionistic fuzzy approach. In order to assess the level of social security of the country there is employed the statistical information on Azerbaijan for two periods of 2007–2009 and 2014–2016. As the main instruments for the estimation of an aggregate index of social security the linguistic intuitionistic fuzzy numbers have been used. For the fuzzification indicators of the social security have the Gaussian membership functions (Table 5.4). Taking into account the four bands, the methodology of the Sustainable Development Goals Index and dashboards have been used to determine the threshold of linguistic indicators. The maximum (i.e., the upper limit) indicated by the green band is reached for each variable. Three colored bands from yellow to orange and red indicate a growing distance from the target. The yellow-orange thresholds for

80

5 Models of Socioeconomic Security

Table 5.4 Values of the Indicators of social security Indicators

2007

2008

2009

2014

2015

2016

UNE

6.3

5.9

5.7

4.9

5.0

5.0

LEB

73.0

73.4

73.5

74.2

75.2

75.2

GIN

31.8

31.8

33.12

25.41

28.78

28.87

R&D

1.7

1.7

0.25

0.2

0.2

0.2

POV

15.8

13.2

MIL

2.864

10.9

3.291

3.325

5.0

4.9

5.9

4.555

5.468

3.69

Table 5.5 Supports of linguistic fuzzy variables Indicators

Green

Yellow

Orange

Red

1.UNE

(0.5; 5.1)

(4.9; 7.65)

(7.35; 10.2)

(9.8; 25.9)

2.LEB

(63.7; 77)

(61.25; 66.3)

(56.8; 62.5)

(46.1; 61.2)

3.GIN

(27.5; 30)

(30; 35)

(35; 40)

(40; 63)

4.R&D

(1.47; 3.7)

(1.274; 1.53)

(0.98; 1.326)

(0; 1.02)

5.POV

(0.5; 5.33)

(5.22; 10.93)

(10.51; 16.64)

(15.98; 25)

6.MIL

(0.54; 4.53)

(4.356; 8.52)

(8.18; 12.5)

(12.01; 16.16)

all indicators have been set as the value between the red and green thresholds [14], which is demonstrated in Table 5.5. Information that has been taken into account between the green (best) and red (worst), shown in Table 5.5, has defined the linguistic index: Gr een − S G = 3; Y ellow − S Y = 2; Orange − S O = 1; Red − S R = 0 The Gaussian membership functions are a popular way for specifying fuzzy sets due to their smoothness and a brief notation. The advantage of these curves is that they are smooth and nonzero at all points. Since the Gaussian membership function are poor in response in all case, then this has proved that it is better to use the Gaussian membership functions in the data on probabilities and statistics. The Intuitionistic fuzzy Gaussian membership μ(x) and non-membership ν(x) functions are defined as [15]. μx = e− 2 ∗( 1

x−x¯ 2 σ )

−ε

ν(x) = 1 − e− 2 ∗( 1

x−x¯ 2 σ )

where x¯ is the central value and the width σ > 0. For all indicators the following parameters have been defined:

(5.3)

5.2 Fuzzy Estimation of the Country’s Social Security Level

• • • • •

81

Unemployment rate (UR)—0.05; Life expectancy at birth (LEB)—0.06; Research and development expenditure (R&D)—0.06; Poverty level (PL)—0.06; Military expenditures (ME)—0.09.

The results of computation of parameters of the membership and non-membership functions are shown in Table 5.6. Here, in order to define he weights of the indicators, Boran’s formula has been used and the results of the computations are shown in Table 5.7. By using the following formulas for the linguistic intuitionistic fuzzy weighted average, the fuzzy aggregate index of the social security (FASS) for two periods is Table 5.6 Parameters of the linguistic intuitionistic fuzzy numbers Years

2007

2008

Indicators θ

μ

ν

π

θ

UNE

2

0.95 0.01 0.05 2

LEB

3

0.78 0.16 0.06 3

GIN

2

R&D

3

POV

2009 μ

ν

π

μ

ν

π

0.91 0.05 0.05 2

0.82

0.13

0.05

0.58 0.36 0.06 3

0.53

0.41

0.06

0.63 0.31 0.06 2

0.63 0.31 0.06 2

0.67

0.27

0.06

0.76 0.18 0.06 3

0.76 0.18 0.06 0

0.44

0.50

0.06

1

0.43 0.51 0.06 1

0.85 0.09 0.06 2

0.196 0.744 0.06

MIL

3

0.88 0.04 0.09 3

0.67 0.24 0.09 3

0.65

0.26

Years

2014

μ

ν

2015 ν

π

θ

θ

0.09

2016

Indicators θ

μ

μ

ν

π

θ

π

UNE

2

0.37 0.59 0.05 2

0.91 0.05 0.05 2

0.42

0.53 0.05

LEB

3

0.26 0.68 0.06 3

0.58 0.36 0.06 3

0.05

0.89 0.06

GIN

3

0.86 0.08 0.06 2

0.63 0.31 0.06 3

0.545 0.40 0.06

R&D

0

0.42 0.52 0.06 3

0.76 0.18 0.06 0

0.42

0.52 0.06

POV

3

0.77 0.17 0.06 1

0.85 0.09 0.06 2

0.47

0.48 0.06

MIL

2

0.45 0.46 0.09 3

0.67 0.24 0.09 3

0.35

0.56 0.09

Table 5.7 Fuzzy weights of the indicators of the social security Indicators

2007

2008

2009

2014

2015

2016

UNE

0.551808

0.472997

0.436142

0.047559

0.043372

0.197729

LEB

0.062183

0.048578

0.106406

0.03133

0.003766

0.01717

GIN

0.02919

0.058958

0.186658

0.537766

0.08228

0.197027

R&D

0.054207

0.109487

0.077723

0.058185

0.042916

0.195648

POV

0.01429

0.231691

0.00564

0.256475

0.30277

0.233497

MIL

0.288323

0.078289

0.18743

0.068686

0.524896

0.15893

Sum

1

1

1

1

1

1

82

5 Models of Socioeconomic Security

calculated:  (1 k k=1 λk ∗θ ai j ,

F ASS = s 6

−

6

6

    (1 − μ aikj )λk , (ν aikj )λk 

k=1

(5.4)

k=1

F ASS(2007) = 2.39; 0.937; 0.034; 0.029 F ASS(2008) = 2.005; 0.85; 0.087; 0.06 F ASS(2009) = 2.138; 0.72; 0.21; 0.06 F ASS(2014) = 2.71; 0.78; 0.146; 0.07 F ASS(2015) = 2.172; 0.875; 0.085; 0.04 F ASS(2016) = 1.98; 0.4; 0.49; 0.1     According to [16] if α˜ j = Sθ (α˜ j ) , (u α˜ j , v α˜ j ) ( j = 1, 2, . . . n) be a collection of the intuitionistic fuzzy Linguistic Numbers (ILN), then is the mean value of these ILNs is defined as   m˜ j = Sθ (m˜ j ) , (u m˜ j , ν(m˜ j ))

(5.5)

where: ∼m 1 − the mean o f F ASS f or 2007−2009 ( f ir st period), ∼m 2 − the mean f or F ASS f or 2014−2016 second period): [17] θ (x) ˜ =

1 θ (a˜ i ) n 1

1

u(x) ˜ = 1 − ( (1 − u(a˜ j )) n ν(x) ˜ = ( ν(a˜ j )) n

On the basis of the above formulas the m˜ 1 and m˜ 2 are obtained as: m˜ 1 = 2.1778; 0.862; 0.086 m ˜ 2 = 2.287; 0.745; 0.183 Results of analysis As it can be seen from the results of calculation, the level of social security in the second period has improved and is higher than in the first period. The indicators of

5.2 Fuzzy Estimation of the Country’s Social Security Level

83

the poverty level have mainly influenced the situation which in the first period was red—Sr = 1, 3 and in the second period it has improved to yellow—S y = 3. The value of the Gini coefficients in the first period has been orange—So = 2, and in the second period has improved to yellow—S y = 3. The level of R&D expenditures have decreased from green—Sg = 3 to red—Sr = 0. The level of unemployment has not changed in both periods and is equal to yellow—Se = 2. The life expectancy at birth in both periods is equal to Sg —green. The use of tools and techniques of the linguistic intuitionistic fuzzy sets for analyzing the social development indicators makes it possible to determine not only the quantitative volume, but also the qualitative level of social security for two periods. The level of indicators that have influenced the quality of the social security is determined. The results of analyses give a possibility to the person, who makes decisions related to the socioeconomic development, to make some adjustments to the management process.

5.3 Evaluation of the Aggregated Index of Financial Security For the first time, the term “national security” was introduced by President T. Roosevelt in 1904, and until 1947 it was used in the sense of defense, and not foreign, domestic and military policy. The term “economic security” is relatively young. So, A. Arkhipov, A. Gorodetsky and B. Mikhailov [18] believe that the economic security is a combination of internal and external conditions leading to the effective, dynamic growth of the national economy, its ability to satisfy the needs of society, the state, the individual, and to ensure the competitiveness on foreign markets, guaranteeing a protection against various kinds of threats and losses. According to Abalkin [19], it is through the economic security system that the country’s most important national interests are realized: protecting and supporting domestic entrepreneurs and legal financial institutions, maintaining and developing the country’s human resources, improving living standards, and others. The economic security is defined by scientists as “a combination of conditions and factors ensuring the independence of national economy, its stability and sustainability, the ability to constantly update and improve ourselves”. According to the statement of the US Under Secretary of State for Public Relations William Blair in Congress in 1972 that “national security depends on such things as the balance of payments, the state of the economy, international assistance …”, and therefore we can safely say that the main universal characteristic of the economic security is its fulfillment of the function of material basis of the national sovereignty of the state, its national security. It should be mentioned that the most suitable name for the phenomenon under study is “security in the economic sphere”, since the economy itself cannot act as a security object as the objects are the individual, society and the state.

84

5 Models of Socioeconomic Security

The national security, and security in the economic sphere as its element, are directly related to the totality of relations on the formation, distribution and use of funds, that is, with the category of financial activity of the state (state finances). This makes it possible to single out the financial security as a component of the economic and national security. From our point of view, commonly, the financial security of the state consists in its ability to: • ensure the sustainability of the economic development of the state; • neutralize the impact of global financial crises and deliberate actions of other participants in the global economic system on the national economic system; • ensure the stability of the payment and settlement system; • prevent large-scale diversion of capital abroad; • prevent crimes and administrative offenses in the financial sector; • prevent conflicts between authorities at different levels over the distribution and use of resources of the national budget system; • attract and use foreign borrowing in the was which will be optimal for the national economy; • stimulate through taxes the development of important types of economic activity for the country, industries and regions, etc. The proposed financial security model includes the following indicators: • • • • • • • •

monetization level M2 (% to GDP), external debt (% to GDP), internal debt (% to GDP), share of budget expenditures on servicing the state debt (% of total budget expenditures), budget deficit (%), inflation level, gold and foreign currency reserves (% of GDP), and exchange rate.

In this work we propose a method, based on the linguistic intuitionistic fuzzy numbers, for the formalization of the level of the country’s financial security. In order to estimate the level of the country’s financial security the following indicators, which have an influence on this, are used: • Monetization level M2—the monetization of the economy is the ratio of the money supply (cash and cash on the accounts of enterprises and household deposits in banks) to the volume of the Gross Domestic Product (GDP). It gives an idea of the degree to which the economy is provided with the money necessary for making payments and settlements, paying salaries, benefits, scholarships, etc. • External debt—the country’s external debt, as defined by the IMF, is the amount of outstanding current, unconditional principal and interest payments made by residents of one country to non-residents, as well as commitments by residents to non-residents to be repaid at a certain time in the future.

5.3 Evaluation of the Aggregated Index of Financial Security

85

• Internal debt—Internal debt or domestic debt are the financial obligations of the state arising in connection with the attraction of funds of non-governmental organizations and population of the country for the implementation of state programs and orders. • Share of government service expenditure debt (% of total budget expenditures) SED—Budget expenditure are financial resources allocated to expenditures of debt obligations of governmental and municipal entities. Debt payments and repayment of the principal amount of the debt are funded from the state budget. Debt services are fulfilled by The Central Bank and other specialized financial institutions. • Budget deficit (Government budget deficit) is the excess of the state budget expenditures over its revenues for a certain period of time. With a certain level of net national product, the budget will be balanced. If the value of the product is lower, then there will be a budget deficit, i.e. the excess of public expenditure over public revenues for a certain period. A deficit is a state of financial health that affects a large variety of businesses, organizations, and governments. These organizations include a wide spectrum of professionals that all must monitor their budgets: accountants, business owners, financial professionals, governmental figures, and many more. One of the most famous budget shortfall is the US government deficit, but the most common is that by ordinary businesses that are mismanaged or poorly executed. If the public revenues exceed the expenditures, then there will be a budget surplus. • Inflation is a general increase in the price level of consumer and production goods, as a result of devaluation and reduction of purchasing power of the national currency. The devaluation of money is a result of imbalance between the amount of money in circulation and the amount of goods available on the market. The inflation is a social and economic phenomenon that arises as a result of a disproportionate money supply and real reproduction volumes. • Gold and foreign currency reserves (GCR’s, foreign exchange reserves) are highly liquid financial assets consisting of monetary gold, foreign currency, Special Drawing Rights (SDRs) and IMF reserve position held by the Central Bank and/or the country’s Ministry of Finance. The GCRs may also be held in banks abroad and invested in foreign securities such as the U.S. government bonds. Reserves are held in one or more reserve currencies, mostly the United States dollar and to a lesser extent the Euro. • Exchange rate, also known as the foreign exchange rate, is how much one currency is worth compared to another one. It is the rate at which one currency can be exchanged for another. The exchange rates can change for many different reasons, for example the inflation rate of the country. For much of the twentieth century the Bretton Woods system has fixed (set) the exchange rates. A Fuzzy Linguistic Approach to Evaluate the Level of Financial Security Statistical data of Azerbaijan for the period of 2010–2018 are used in order to assess the level of financial security of the country. The main instrument and tool used

86

5 Models of Socioeconomic Security

for the estimation of the aggregate index of the financial security are the linguistic intuitionistic fuzzy numbers. For the fuzzification indicators of the financial security the Gaussian membership function is employed (Table 5.8). The Sustainable Development Goals Index and dashboards are used to determine the of linguistic indicators taking into account four bounds: the maximum (i.e., the upper limit) indicated by the green band is reached for each variable, and three colored bands from yellow through orange to red indicate a growing distance from the target. The thresholds for all indicators are set as the value between the red and green thresholds as shown in Table 5.9. The Gaussian membership functions are well-known representation for specifying fuzzy sets due to their smoothness and brief notation, and that they are smooth and nonzero at all points. The intuitionistic fuzzy Gaussian membership μ(x) and non-membership ν(x) functions are defined as [15, 16]. x−x¯ 2 σ )

−ε

ν(x) = 1 − e− 2 ∗(

x−x¯ 2 σ )

μ(x) = e− 2 ∗( 1

1

(5.6)

where x—central ¯ value and width σ > 0. Then, on the base of [6], the following formulas are used to define the fuzzy weights of each indicator of the financial security (Table 5.10):   μk + πk μνkk  λk =  6 μk k=1 μk + πk νk 8 

(5.7)

λk = 1

i=1

By using the following formulas for the linguistic intuitionistic fuzzy weighted average, the fuzzy aggregate index of financial security (FAFS) for two periods is calculated as follows.  , (1 k k=1 λk ∗ϑ ai j ,

F AF S = S 6

−

6 6

  λk   k λk ,  1 − μ aikj ν ai j k=1

F AF S (2010) = S3.05 (0.751, 0.179); F AF S (2011) = S3.18 (0.649, 0.293); F AF S (2012) = S3.47 (0.349, 0.6); F AF S (2016) = S3.23 (0.723, 0.22); F AF S (2017) = S3.22 (0.736, 0.194);

k=1

(5.8)

5.7

Inflation level IL

Exchange rate ER

0.8

12.12

0.9

Budget deficit (%) BD

The volume of gold and foreign reserves (% to GDP) GFR

0.2

12.5

Internal debt (% to GDP) ID

The share of government service expenditure debt (% of total budget expenditures) SED

13.54

External debt (% to GDP) ED

2010 19.54

Monetization level M2 (% to GDP) M2

Table 5.8 Indicators of the financial security 2011

0.79

15.58

7.9

0.6

0.4

11.4

9.77

21.12

2012

0.78

16.18

1.0

0.3

0.3

13.9

14.35

25,220

2013

0.78

20.46

2.4

0.6

1

12.7

14.36

28,247

2014

0.78

21.02

1.4

0.5

0.6

14.4

16.48

29,545

2015

1.03

13.79

4.0

1.2

1.2

35

32.11

15,959

2016

1.6

2.9

12.4

0.4

5.3

2.00

20.3

19,108

2017

1.7

3.0

12.9

1.54

5.8

1.47

22.8

17,724

2018

1.7

4.4

2.3

0.27

7.8

1.7

19.0

18,351

5.3 Evaluation of the Aggregated Index of Financial Security 87

88

5 Models of Socioeconomic Security

Table 5.9 Parameters of the financial intuitionistic fuzzy model 2010

2011

Sθ

μ

2012

ν

Sθ

μ

ν

Sθ

μ

ν

1

M2

S4

0.03

0.92

S4

0.018

0.93

S4

0.00001

0.95

2

ED

S3

0.598

0.352

S3

0.426

0.524

S3

0.254

0.696

3

ID

S2

0.894

0.056

S2

0.43

0.52

S2

0.265

0.685

4

SED

S4

0.396

0.554

S4

0.518

0.432

S4

0.456

0.494

5

BD

S3

0.438

0.512

S4

0.288

0.662

S4

0.325

0.625

6

IL

S4

0.815

0.135

S3

0.797

0.153

S4

0.195

0.755

7

GFR

S3

0.48

0.47

S3

0.8

0.15

S3

0.8

0.15

8

ER

S4

0.337

0.613

S4

0.331

0.619

S4

0.331

0.619

2016

2017

2018

Sθ

μ

ν

Sθ

μ

ν

Sθ

μ

ν

1

M2

S4

0.031

0.919

S4

0.02

0.93

S4

0.026

0.924

2

ED

S2

0.24

0.71

S1

0.024

0.926

S2

0.903

0.047

3

ID

S4

0.82

0.13

S4

0.528

0.422

S4

0.666

0.284

4

SED

S2

0.818

0.132

S2

0.9

0.05

S2

0.463

0.487

5

BD

S4

0.337

0.613

S3

0.42

0.53

S4

0.317

0.633

6

IL

S3

0.629

0.321

S3

0.385

0.565

S4

0.815

0.135

7

GFR

S1

0.879

0.071

S1

0.897

0.053

S1

0.345

0.605

8

ER

S4

0.743

0.207

S4

0.839

0.111

S4

0.839

0.111

Table 5.10 Weights of the indicators of the financial security 2010

2011

2012

2016

2017

2018

1 M2

0.006294827 0.004423165 4.33742E−06 0.006875426 0.005164855 0.003007

2 ED

0.135913683 0.10881974

3 ID

0.33677044

0.112180835

0.109915122 0.117165029

0.054037613 0.006199192 0.204444 0.23882109

0.144726653 0.085924

4 SED 0.085921325 0.134775369 0.206915086

0.237235912 0.220560409 0.056007

5 BD

0.095679539 0.072232388 0.144631363

0.076667734 0.112638398 0,037,522

6 IL

0.222266585 0.246592808 0.085671.999 0.152914685 0.102700474 0,12,252

7 GFR 0.044616271 0.239819343 0.186024107

0.03941201

8 ER

0.072537329 0.083422066 0.147407243

0.194035531 0.298229024 0.133499

1

1

1

1

0.109780994 0.357078 1

1

F AF S (2018) = S3.12 (0.867, 0.065);     According to [74] if α˜ j = Sθ (α˜ j ) , (u α˜ j , v α˜ j ) ( j = 1, 2, . . . n) is a collection of the Intuitionistic Fuzzy Linguistic Numbers (ILN), then the mean of these ILNs is defined as

5.3 Evaluation of the Aggregated Index of Financial Security

89

    m˜ j = Sθ (m˜ j ) , (u m˜ j , v m˜ j )

(5.9)

where: m˜ 1 − mean o f F AF S f or 2010−2012( f ir st period), m˜ 2 − 2016−2018 years(second period): θ (x) ˜ =

  1 1 1 θ (α˜ i ) u(x) ˜ = 1 − ( (1 − u a j ) n v(x) ˜ = ( v(a j )) n n

On the base of the formulas given above, we obtain the m˜ 1 and m˜ 2 as: m˜ 1 = 3, 234; 0.615; 0.316; m˜ 2 = 3.187; 0.787; 0.141 The application of the linguistic intuitionistic fuzzy sets for the analysis of development (improvement, Increase, progress) of the financial indicators gives us the possibility (opportunity, probability) to define not only the quantitative volume but also the qualitative level of the financial security for two periods. The levels of indicators which influence the quality of financial security is yielded. The results of analyses give a possibility to a person who makes decisions related to the financial development to make some adjustments to the management process. Based on the values of the weights, we can conclude that four factors from the previously selected set have a stronger influence than the others (the corresponding maximum weights are shown in bold). These factors are: • • • •

external debt, domestic debt, inflation and the country’s foreign exchange reserves.

and recall that for all these factors, linguistic terms are defined in such a way that the favorable values of the factors are numbered in the increasing order: S1 = Red, S2 = orange, S3 = Y ellow, S4 = Gr een. Thus, we come tto the conclusion that the financial situation in the Republic of Azerbaijan has worsened over the periods under consideration which is explained by Table 5.11 which shown the linguistic values of strongly influencing factors for the years 2010–2012 and 2016–2018. This makes it possible to explain the reason for the deterioration of three of four factors with a negative dynamics except for the internal debt factor. Table 5.11 Linguistic values of strongly influencing factors for the years 2010–2012 and 2016– 2018 2010 tetta

2011

2012

2016

2017

2018

ED

3

3

3

2

1

2

ID

2

2

2

4

4

4

GFR

3

3

3

1

1

1

IL

4

3

4

3

3

3

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5 Models of Socioeconomic Security

5.4 Evaluation of the Aggregate Index of Ecological Security Analysis of various definitions of concepts of “ecological security” presented in the literature and what is used in practice show that so far there is no single definition that reflects the very meaning of this term. Some people describe the ecological security as a state of protection of the human being, the society and the environment from harmful effects of anthropogenic factors, natural disasters and catastrophes. Others define the ecological security as a component of the environment. Still others equate this concept with the protection of the natural environment. Furthermore, the concept of “ecological security” is also equated with a rational use of natural resources, their reproduction and quality improvement [20]. The ecological security is a condition when the ecology meets the needs of the inhabitants without diminishing its natural reserve. The ecological security may therefore also be meant as the state of protection of the environment and the vital human interests from possible negative effects of economic and other activities, emergency situations of a natural and technogenic character and their consequences. The ecological security is implemented at the global, regional and local levels. The global ecological security issues are studied by the UN, UNESCO, UNEP and other international organizations and institutions. International acts on the ecological protection across the biosphere, the implementation of interstate ecological programs, the establishment of inter-governmental forces for the elimination of ecological disasters with a natural or an anthropogenic character are formulated at this level. In order to assess the level of ecological security at the regional and local levels different methods are used. For the purpose of analysis used in this work, the aggregated index of ecological security, calculated by classical methods, is studied and a fuzzy approach is proposed for the formulation of this index. Problem Statement To solve the problem corresponding to the model, the concept of a pressure-stateresponse (PSR) is used. The concept of the pressure-state-response has been proposed by Frendo and Rapport [21] and has been used by the Organization for Economic Cooperation and Development (OECD) to analyze the state of natural environment [22]. The pressure-state-response (PSR) is based on the concept of causality: a human activity puts pressure (P) on the environment, and changes the quality and quantity of natural resources [state (S)]. The society responds (R) to these changes through ecological, general economic and retaliatory measures (“Social Responses”). With the above ideas in mind, we have established and placed in Table 5.12 a system of indicators which describe the concept of pressure-state-response (PSR) for Azerbaijan during the period of 2010–2015.

5.4 Evaluation of the Aggregate Index of Ecological Security

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Table 5.12 Indicators of the PSR concept for Azerbaijan Indicators

2010

2011

2012

2013

2014

2015

Population density (people per km2 of land area)

105

107

108

109

111

111

2

Population growth rate

12.5

13.5

13.0

12.8

12.2

11.7

3

Oil and gas 20198.7 production (thsd. manats)

26055.4

24,747.0

23658.0

20,977.0

14723.0

4

Cost of construction work (thsd. manats)

4531384.9 6115011.1 7716020.2 8721165.0 8591861.7 7319551.9

5

Number of cars

982553.0

6

Number of cattle 10918.9 (thsd.)

11025.0

11128.3

11254.1

11340.5

11349.0

Carbon dioxide (CO2 ) (thsd.ton)

13809.4

12471.4

15135.8

16091.9

13980.8

P 1

S 7

14399.6

1037626.0 1135936.0 1232678.0 1291008.0 1322610.0

8

Nitric oxide 11.8 (N2 O) (thsd.ton)

25.9

15.8

5.0

4.7

7.0

9

Methane (CH4 ) (thsd.ton)

18.3

298.3

385.2

248.8

95.7

34.1

10 Air polluting emissions from transportation (thsd.ton)

742

779

849

940

966

978

11 Soil erosion (ha) 3743.5

3733.05

3722.53

3712.23

3701.87

3691.53

12 Pollutants released into the atmosphere (thsd.ton)

214.8

224.0

226.5

197.3

189.3

178.0

13 Emission of polluted water through waste water (mln.man.)

6005.0

5068.0

5365.0

5154.0

5347.0

5573.0

8807.74

8807.74

8925.5

8925.5

8925.5

8925.5

15 Investment to ecological protection (thsd. manat)

260673.8

320253.5

419317.9

398187.5

283414.6

141464.8

16 Investment to science (thsd. manat)

92.8

106.1

116.7

117

124.2

131.7

R 14 National parks (km2 )

(continued)

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Table 5.12 (continued) Indicators 17 The share of energy supply from renewable energy in total amount of energy supply

2010

2011

2012

2013

2014

2015

3.1

2.4

1.8

2.0

1.8

1.9

As seen from Table 5.12, the indicators of the pressure-state-response (PSR) are of different dimensions and its is, necessary to bring them to a common measurement denominator in order to estimate an aggregate index of ecological security, For this purpose we use the following normalization formula: X tn =

X t − X¯ t σt

(5.10)

where: X tn —the normalized value of indicator X in the t-th year, X¯ t - the average value of indicator X during the analyzed period, σt —the standard deviation of indicator X during the period. The normalized values of indicators for the period of 2010–2015-th years are given in Table 5.13. Using the arithmetic means for each year subsystem, the values of the pressurestate-response (PSR) sub-indices are calculated and given in Table 5.14. Using the indicators in Table 5.14, the aggregate index of ecological security is calculated by means of the following formula: AE S I = w1 ∗ P + w2 ∗ S + w3 ∗ R

(5.11)

where: wi (i = 1, .., 3)—weights of the individual sub-indices determined by experts. In order to calculate the values of weights of the sub-indices we use the weights proposed in [23] which are, respectively: w1 = 0.37, w2 = 0.33, w3 = 0.30 The results of solution are given in a graphical form in Fig. 5.1. As it can be seen from this figure, the values of the aggregate index (Ecological Security Index, ESI) for the years of 2010 and 2011 took on the values, respectively, −0.48 and − 0.58. This shows a low level of security. In 2012 and 2013, the security increased and the values of the Ecological Security Index became 2.12 and 2.9, respectively. However, in 2014 and 2015 it again decreased taking on the values of 2.17 and 1.39, respectively.

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Table 5.13 Normalized values of the indicators for the period of 2010–2015 Indicators P 1

2010 2011 2012 2013 2014 2015

Population density (people per km2 of land 0 area)

0.333 0.5

0.667 1

1

2

Population growth rate

0.444 1

0.722 0.611 0.278 0

3

Oil and gas production (thsd. manats)

0.483 1

0.885 0.788 0.552 0

4

Cost of construction work (thsd. manats)

0

0.378 0.760 1

5

Number of cars

0

0.162 0.45

6

Number of cattle (thsd.)

0

0.247 0.487 0.779 0.98

S 7

Carbon dioxide (CO2 ) (thsd.ton)

0.533 0.370 0

8

Nitrogen Oxide (N2 O) (thsd.ton)

0.335 1

9

Methane(CH4 ) (thsd.ton)

0

0.969 0.666

0.736 0.907 1 1

0.736 1

0.417

0.524 0.014 0

0.109

0.763 1

0.628 0.211 0.043

10 Air polluting emissions from transportation 0 (thsd.ton)

0.157 0.453 0.839 0.949 1

11 Soil erosion (ha)

1

0.799 0.597 0.398 0.199 0

12 Pollutants released into the atmosphere (thsd.ton)

0.759 0.949 1

13 Emission of polluted water through waste water (mln.manat)

1

1

0.317 0.092 0.298 0.539

1

1

0

R 14 National parks (km2 ) 15 Investment to ecological protection (thsd. manat)

0.571 0.357 0

16 Investment to science(thsd. manat)

1

17 The share of energy supply from renewable 0 energy in total amount of energy supply

0.398 0.233 0

0

0

0

0.076 0.489 1

0.658 0.386 0.378 0.193 0 0.539 1

0.846 1

0.923

Table 5.14 Values of sub-indices of the ecological security index obtained by using classical method for the period of 2010–2015 P S

2010

2011

2012

−1.0762

−0.09903

0.169742

0.48421

0.183229

−0.07203

0.180529

0.267032

2013

2014 0.497342 −0.12579

R

−0.37054

−0.32514

0.301966

0.353513

0.102653

ESI

−0.48

−0.58

2.12

2.9

2.17

2015 0.023936 −0.43297 −0.06245 1.39

5.5 Evaluation of the Fuzzy Aggregate Index of the Ecological Security Generally expert opinions are used in order to determine the weights of sub-indices of the ecological security index. It should be noted that the determination of weights of the sub-indices has a particular importance for the calculation of the aggregate index. In this work for defining the objective weights of the individual sub-indices,

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5 Models of Socioeconomic Security

4 3 P

2

S

1

R

0 -1

2010

2011

2012

2013

2014

2015

ESI

-2 Fig. 5.1 Graphical presentation of yearly changes of values of the sub-indices and the Ecological Security Index (ESI)

we propose a fuzzy approach and use instruments of fuzzy sets theory and fuzzy logic for determining the fuzzy aggregate index of ecological security (FAESI). For the estimation of the aggregate index of ecological security, in the first stage information for the period of 2010–2015 is assumed to take on the following possible linguistic terms (represented by triangular fuzzy numbers the parameters of which are shown in the parantheses): – – – –

Very low security—VL = (−1.98, −1.51, −1.03); Low Security—L = (−1.13, −0.69, −0.24); High security—H = (−0.34, 0.11, 0.55); Very high security—VH = (0.45; 0.9; 1.34)

The linguistic variables for the period of 2010–2015 are given in Table 5.15. The instruments of the intuitionistic fuzzy sets theory have been used in order to define the weights of individual sub-indices of the Aggregate Index of Ecological Security. The values of the degrees of membership, non-membership and hesitation of subindices of the Ecological Security Index of Azerbaijan for the period of 2010–2015, which are now as the intuitionistic fuzzy sets, are shown in the Table 5.16. In this work, in order to define the weights of sub-indices of the Ecological Security Index, we have used the generalized entropy measure of the intuitionistic fuzzy set F, composed of n elements, proposed by Szmidt and Kacprzyk [24]: Table 5.15 Values of the linguistic variables representing the pressure-state-response (PSR) subindices of the Ecological Security Index for the period of 2010–2015 P

2010

2011

2012

2013

2014

2015

VL

H

H

VH

H

H

S

H

H

H

H

H

L

R

L

L

H

H

H

H

5.5 Evaluation of the Fuzzy Aggregate Index of the Ecological Security

95

Table 5.16 Intuitionistic fuzzy values of the sub-indices of the Ecological Security Index of Azerbaijan for the period of 2010–2015 Sub-indices Years

P μ1 t

ν1 t

π1 t

S μ2 t

ν2 t

π2 t

R μ3 t

ν3 t

π3 t

2010

0.05

0.95

0

0.84

0.16

0

0.29

0.71

0

2011

0.54

0.46

0

0.64

0.36

0

0.19

0.81

0

2012

0.86

0.14

0

0.83

0.17

0

0.56

0.44

0

2013

0.08

0.92

0

0.59

0.41

0

0.45

0.55

0

2014

0.11

0.89

0

0.48

0.52

0

0.98

0.02

0

2015

0.81

0.19

0

0.43

0.57

0

0.62

0.38

0

  max Count Ai ∩ Aic   , (i = 1, . . . , n) E(Ai ) = max Count Ai ∪ Aic

(5.12)

The calculation of the entropy of the individual sub-indices for 2014 are given below: E(A1 ) =

0.11 (0.11, 0.89, 0) ∩ (0.89, 0.11, 0) = = 0.12 (0.11, 0.89, 0) ∪ (0.89, 0.11, 0) 0.89

E(A2 ) =

0.48 (0.48, 0.52, 0) ∩ (0.52, 0.48, 0) = = 0.91 (0.48, 0.52, 0) ∪ (0.52, 0.48, 0) 0.52

E(A3 ) =

0.38 (0.38, 0.62, 0) ∩ (0.62, 0.38, 0) = = 0.61 (0.38, 0.62, 0) ∪ (0.62, 0.38, 0) 0.62

The entropy of the individual sub-indices for the years of 2010–2015 is as follows: 2010 − E(A1 ) = 0.05; E( A2 ) = 0.19; E( A3 ) = 0.36 2011 − E(A1 ) = 0.85; E( A2 ) = 0.56; E( A3 ) = 0.24 2012 − E(A1 ) = 0.17; E( A2 ) = 0.20; E( A3 ) = 0.79 2013 − E(A1 ) = 0.09; E( A2 ) = 0.68; E( A3 ) = 0.82 2014 − E(A1 ) = 0.12; E( A2 ) = 0.91; E( A3 ) = 0.61 2015 − E(A1 ) = 0.24; E( A2 ) = 0.75; E( A3 ) = 0.61 Next, on the basis of the formula:

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5 Models of Socioeconomic Security

wi =

1 − E(Ai )

n n − i=1 E(Ai )

(5.13)

the weights of individual sub-indices are defined. For 2014, the weights of the individual sub-indices are calculated as follows: w1 (2014) =

1 − 0.12 0.88 = = 0.65 3 − 1.64 1.36

w2 (2014) =

0.09 1 − 0.91 = = 0.06 3 − 1.64 1.36

w3 (2014) =

0.39 1 − 0.61 = = 0.29 3 − 1.64 1.36

Using the weights of the individual sub-indices and their linguistic values (Table 5.15), the Aggregate Index of Ecological Security (AIES) is calculated for the year of 2014 as follows: AI E S(2014) =0.65 ∗ H + 0.06 ∗ H + 0.29 ∗ H = 0.65 ∗ (−0.34, 0.11, 0.55) + 0.06 ∗ (−0.34, 0.11, 0.55) + 0.29 ∗ (−0.34, 0.11, 0.55) = = (−0.220, 0.072, 0.0.360) + (−0.020, 0.007, 0.030) + (−0.099, 0.032, 0.160) = (−0.34, 0.11, 0.55) = H The values of weights of the sub-indices and the Aggregate Indices of Ecological Security for the years of 2010–2015 are given in Table 5.17. Table 5.17 Weights of the sub-indices and the Aggregate Indices of Ecological Security for the period of 2010–2015 w1

w2

w3

AESI

2010

0.40

0.34

0.26

(−1.22,−0.94,−0.29) VL - L

2011

0.11

0.33

0.56

(−0.79,−0.34,0.1) L-H

2012

0.46

0.48

0.10

(−0.35,0.12,0.57) H - VH

2013

0.64

0.23

0.13

(0.17,0.97,1.06) H - VH

2014

0.65

0.06

0.29

(−0.34,0.11,0.55) H

2015

0.55

0.17

0.28

(−0.48,−0.03,0.41) L-H

5.5 Evaluation of the Fuzzy Aggregate Index of the Ecological Security

97

Table 5.17 shows that the weights of the individual sub-indices for each year are changing dramatically. For instance, if the value of the weight of the pressure sub-index (P) in 2011 was 0.11, in 2014 it was 0.65. The weights of state sub-index (S) in 2014 were 0.06, and 0.48 in 2012. The weights of the response sub-index (R) changed from 0.1 in 2012 to 0.56 in 2011. The results obtained can be used by decision-makers in ecological governance agencies for controlling individual indicators of the socio-eco-economic system. It should be noted that the proposed work is not intended to be a complete study of the problem. In the future, for the development of the model the maximum allowable concentration of individual elements in the environment should be considered.

References 1. World Bank. (1993). The East Asian economic miracle: Economic growth and public policy. 2. Afxentiou, P. C. (2000, Winter/Spring). Convergence, the Maastricht criteria and their benefits. The Brown Journal of World Affairs, VII(1), 245–254. 3. State Statistical Committee of Azerbaijan Republic (http:\\stat.gov.az). 4. Alert Mechanism Report 2018, To the European Parliament, the Council, the European Central bank and the European Economic and Social Committee European Commission, Brussels, 22.11.2017, 48 p. 5. Atanassov, K. (1999). Intuitionistic fuzzy sets. Heidelberg: Springer Physica-Verlag. 6. Boran, F. E., Genc, S., Kurt, M., & Akay, D. (2009). A multi-criteria intuitionistic fuzzy group decision making for supplier with TOPSIS method. Expert Systems with Applications, 36(8), 11363–11368. 7. Huber, G., Rehm, P., Schlesinger, M., & Valletta, R. (2010). Economic security at risk: Findings from the economic security index. Rockefeller Foundation: Yale University. 8. Focus Economics. https://www.focus-economics.com/economic-indicator/unemploymentrate. 9. World Health Organization. https://www.who.int/whosis/whostat2006DefinitionsAndMetad ata.pdf. 10. Corporate Finance Institute. https://corporatefinanceinstitute.com/resources/knowledge/eco nomics/gini-coefficient/. 11. OECD. (2019). Gross domestic spending on R&D (indicator). Retrieved 04 June, 2019, from https://doi.org/10.1787/d8b068b4-en. 12. Poverty and Inequality. https://datatopics.worldbank.org/world-development-indicators/the mes/poverty-and-inequality.html. 13. Military versus social expenditure: The Opportunity Cost of World Military Spending, Stockholm International Peace Research Institute (SIPRI), Media backgrounder 5 April 2016. 14. Lafortune, G., et al. (2018). SDG index and dashboards, detailed methodological paper, 56 p. 15. Sadollah, A. (2018). Which membership function is appropriate in fuzzy system? Book of Fuzzy logic based in optimization methods and control systems and its applications, Chapter 1. 16. Radhika, C., & Parvathi, R. (2016). Intuitionistic fuzzification functions. Global Journal of Pure and Applied Mathematics, 12(2), 1211–1227. 17. Liu, P. (2013). Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making. Journal of Computer and System Sciences, 79(1), 131–143. 18. Arkhipov, A., Gorodetsky, A., & Mikhailov, B. (1994). Economic security: Estimates, problems, means of support. Issues of Economics, 12, 36–44.

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19. Chernikova, E. V., & Vysotskaya, O. S. (2010). Financial security as an element of the State National Security System. Law, 7. Moscow, Russia 20. Skiter, N., Rogachev, A., & Mazaeva, T. (2015, June). Modelling ecological security of a state. Mediterranean Journal of Social Sciences, 6(3) S6, 185–192. MCSER Publishing, Roma, Italy 21. Rapport, D., & Friend, A. (1979). Towards a comprehensive framework for environment statistics: A stress-response approach. Ottawa: Statistics Canada. 22. OECD Ecological indicators. (2003). Development. Reference paper: Measurement and Use. 23. Liang, P., Liming, D., & Guijie, Y. (2010). Ecological security assessment of Beijing based on PSR model. Procedia Ecological Sciences, 2, 832–841. 24. Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118, 467–477.

Chapter 6

Assessment of the Development of Information Economy

Today, information economy is one of the most important sectors of world economy. The famous Spanish sociologist, Professor Manuel Castell [1], notes that “…A new economy emerged in the last quarter of the twentieth century on a worldwide scale. I call it informational, global, and networked to identify its fundamental distinctive features and to emphasize their intertwining. It is informational because the productivity and competitiveness of units or agents in this economy (be it firms, regions, or nations) fundamentally depend upon their capacity to generate process, and apply efficiently knowledge-based information…”.

6.1 Formation and Development of Information Economy The Organization for Economic Co-operation and Development (OECD) defined two products and services of information economy [2]: – ICT products and services: Computers and peripheral equipment, Communication equipment, Consumer electronic equipment, Miscellaneous ICT components and goods, Manufacturing services for ICT equipment, Business and productivity software and licensing services, Information technology consultancy and services, Telecommunication services, Leasing or rental services for ICT equipment, other ICT services; – Content, media products and services: Printed and other text-based content on physical media and related services, Motion picture, video, television and radio content, and related services, Music content and related services, Games software, On-line content and related services, other content and related services. It should be emphasized that the added value of the share of Global ICT in the GDP in 2015 was equal to 4.3% [3].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 G. Imanov, Fuzzy Models in Economics, Studies in Fuzziness and Soft Computing 402, https://doi.org/10.1007/978-3-030-61282-5_6

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6 Assessment of the Development of Information Economy

The main development resources of information economy are: • human capital, • knowledge and • technology. The human capital is one of the main factors which imply the development of the socio-economic system. The fundamental concept of the human capital theory was proposed by the American economists, the Nobel Prize Laureates, Shultz [4] and Becker [5]. According to the definition from experts of the Organization for Economic Co-operation and Development (OECD), the human capital is regarded as “the knowledge, skills, competencies and attributes embodied in individuals that facilitate the creation of personal, social and economic well-being” [6]. Cornell University, INSEAD, and the World Intellectual Property Organization have proposed indicators for measuring the human capital, knowledge and technology [7]. According to those studies, the human capital is expressed by the level of education, tertiary education, research and development and: 1.1 Education (ED) encompasses the following indicators: 1.1.1 Government Expenditure on Education (% of GDP)-EED; 1.1.2 Government Expenditure on Education per person, secondary (% of GDP per capita)—GEE; 1.1.3 Scholl-life expectancy, primary to tertiary education (years)—SLE; 1.1.4 Assessment in reading mathematics and science—RMS; 1.1.5 Pupil-teacher ratio, secondary—PTS; 1.2 Tertiary education (TE) includes the following indicators: 1.2.1 School enrollment, tertiary (% of GDP)—TEN; 1.2.2 Tertiary graduates in science, engineering, manufacturing and construction (% of total tertiary graduates)—GSE; 1.2.3 Tertiary inbound mobility ratio (%)—TIM; 1.3 Research and development (R&D) includes the following indicators: 1.3.1 Researches, full-time equivalence (FTE) (per Million inhabitants)— RES; 1.3.2 Gross expenditure on R&D (% of GDP)—ERD; 1.3.3 Average expenditure of the top 3 global companies on R&D, Millions $ USD—RDC; 1.3.4 Average score of the top 3 universities in the QS world university ranking—URT. Knowledge is a major resource of technological innovativeness. The standard R&D-related measures do not necessarily show successful implementation or the amount and quality of outputs. Nevertheless, these input and flow indicators form a starting point for measuring knowledge outputs and for gauging social and private

6.1 Formation and Development of Information Economy

101

rates of return to knowledge investments. Approximate indicators have been developed which translate certain knowledge inputs into knowledge outputs in order to describe and compare the economic performance of countries. These measures tend to categories industrial sectors or parts of the workforce as more or less intensive in R&D, the knowledge or information. These measures are based on the assumption that certain knowledge-intensive sectors play a key role in the long-run performance of countries by producing spill-over benefits, providing high-skill and high-wage employment and generating higher returns to capital and labor [8]. Knowledge and technology outputs are expressed by the following indicators and sub-indices; 2.1 Knowledge creation (KNC): 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5

Present application by origin—PAO; PCT international application by origin—PCT; Utility model application by origin—MAO; Scientific and technical publications STP; Citable documents H index—CDH;

2.2 Knowledge impact (KNI): 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5

Growth rate of GDP per person engaged—GRR; New business density—NBD; Total computer software spending—SOF; ISO 9001 quality certificates—ISO; High-tech and medium high-tech output—HTO;

2.3 Knowledge diffusion (KND): 2.3.1 2.3.2 2.3.3 2.3.4

Intellectual property receipts—IPR; High-tech exports—HTE; ICT services exports—ICE; Foreign direct investment net outflows—FDI;

In order to measure the production volume of information economy, Porat [9] proposes the added value calculated by means of the Leontief input–output model. Along with this, World Bank experts propose the Knowledge Economy Index [10] which is calculated on the basis of: • • • •

economic and institutional regime, education and skills, information and communication infrastructure, and innovation system.

In this chapter, by using tools and techniques of the intuitionistic fuzzy sets and logic and the DEMATEL methods, we analyze the impact level of indicators’ subindices on the development level of information economy.

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6.2 Fuzzy Model of the Estimation of Quality of Development of Information Economy In order to define the impact resources on the development of information economy, by applying the instruments of th intuitionistic fuzzy sets and logic and the DEMATEL methods, the indicators sub-indices “Human Capital” and “Knowledge And Technology” considered in the report [10] are chosen as point of departure. In that report the indicators, indices and sub-indices are developed for 127 countries of the world. In order to fuzzify these indicators, tools and techniques of the intuitionistic fuzzy logic are used. Each indicator of each country is divided into three triangular intuitionistic fuzzy numbers: • low (L), • medium (M), and • high (H). For example, for the sub-index of the “Research and Development (expenditures)” index these values will be equal to: • L = [12.29;2815.19], • M = [2704.8;5617.8], and • H = [5397.5;8255]. Taking into account the crisp meaning of “Research (expenditures) per Million of population”, which equals 1605, the membership degree is defined as the triangular piecewise linear function of vector x, depending on three scalar parameters a, b, and c, and is given by 

μ =

2815.19 − 1605 c−x = = 0.86 c−b 2815.19 − 1414.01

(6.1)

Taking into account the meaning and the degree of consistency proposed by Hersh [12], the hesitancy coefficient π is proposed. In our case, π = 0., 1. Then, the intuitionistic fuzzy membership (μ) and non-membership degree (ν) are found by using the following formulas, respectively: 

μ = μ ∗ (1 − π ) = 0.86 ∗ (1 − 0.1) = 0.77

(6.2)

ν = 1 − μ − π = 1 − 0.77 − 0.1 = 0.13

(6.3)

Thus, the intuitionistic fuzzy number which corresponds to the indicator of the sub-indices “Research per million of population” equals (0.77, 0.13, 0.1). The parameters of the intuitionistic fuzzy number of other indicators of the sub-indices are defined by the same procedure and demonstrated in Table 6.1. Then, the calculations are carried out by using the DEMATEL methods [11].

HC&R (Human capital and research)

R&D

TE

Sub-indicators

Ed

Indicators

[12.29;2815.19] [0.04;1.49] [0;2483.6] [0;33.7]

ERD RDC URT

[0.03;13.81]

RES

[2.64;18.35]

[7.25;28.9]

PTS

TIM

[336;427.9]

RMS

GSE

[5.32;10.57]

SLE

[0.8;38.0]

[5.1;27.64]

GEE

TEN

[1.1;6.76]

EED

L

Table 6.1 Intuitionistic fuzzy numbers as the values of sub-indices of the indicators M

[32.37;67.38]

[2386.2;4967.2]

[1.43;2.93]

[2704.8;5617.9]

[13.27;27.59]

[17.63;34.0]

[36.27;75.18]

[27.7;50.4]

[411.1;512.5]

[10.15;15.7]

[26.6;49.5]

[6.5;12.41]

H

[64.74;99.19]

[4772.4;7304.7]

[2.81;4.29]

[5593.5;8255.4]

[26.51;40.56]

[32.67;48.69]

[72.23;110.16]

[48.4;70.4]

[492.45;587.5]

[15.09;20.43]

[48.1;71.1]

[11.92;17.7]

Azerbaijan (IFS)

(continued)

18.63 (0.81; 0.09; 0.1)

0.00 (0; 0; 1)

0.21 (0.05; 0.15; 0.8)

1605 (0.77; 0.13; 0.1)

2.25 (0.1; 0.2; 0.7)

22.02 (0.264; 0.236; 0.5)

23.16 (0.16; 0.64; 0.2)

9 (0.03; 0.17; 0.8)

340 (0.01; 0.09; 0.9)

12.64 (0.97; 0.03; 0)

20.1 (0.47; 0.23; 0.3)

2.46 (0.03; 0.17; 0.8)

6.2 Fuzzy Model of the Estimation of Quality of Development of Information Economy 103

Knowledge and technology outputs

Know diffusion

Know impact

Sub-indicators

Know creation

Indicators

Table 6.1 (continued) L

[0.04;9.56] [0.04;3.54] [-5.91;14.15]

ICE FDI

[0.87;24.13;]

HTO HTE

[0.17;27.02]

ISO [0.0;1.07]

[0.11;0.44]

IPR

[0.03;10.66]

SOF

CDH NBD

[23;360.77]

STP [-8.08;-2.72]

[0.62;22.47]

MAO

GRR

[0.01;3.11] [0.02;16.14]

PCT

[0.02;15.08]

PAO

M

[13.59;34.32]

[3.4;7.04]

[9.8;19.07]

[1.03;2.14]

[23.19;47.38]

[25.96;53.87]

[0.42;0.77]

[10.24;21.29]

[−2.84;2.57]

[346.63;698.1]

[21.59;44.31]

[15.5;32.25]

[2.99;6.21]

[14.48;30.13]

H

[32.98;53.43]

[6.76;10.33]

[18.33;28.02]

[2.06;3.16]

[45.52;69.25]

[51.75;79.12]

[0.74;1.07]

[20.45;31.3]

[2.47;7.81]

[670.7;1015.1]

[42.57;64.85]

[30.99;47.6]

[5.97;9.13]

[28.95;44.3]

Azerbaijan (IFS)

2.64 (0.09; 0.211; 0.7)

0.49 (0.077; 0.223; 0.7)

0.13 (0; 0; 1)

0.00 (0; 0; 1)

10.36 (0.65; 0.15; 0.2)

1.47 (0.01; 0.09; 0.9)

0.06 (0; 0; 1)

0.99 (0.144; 0.656; 0.2)

1.33 (0.79; 0.11; 0.1)

58 (0.044; 0.155; 0.8)

2.63 (0.04; 0.16; 0.8)

0.14 (0; 0; 1)

0.01 (0; 0; 1)

1.24 (0.03; 0.17; 0.8)

104 6 Assessment of the Development of Information Economy

6.2 Fuzzy Model of the Estimation of Quality of Development of Information Economy

105

A matrix of factor relations is constructed by using the DEMATEL method. For this purposes the Hamming distance between two intuitionistic fuzzy sets [13] is used: di j =

     1  ∗ ( μi − μ j  + νi − ν j  + πi − π j  2

(6.4)

Then, matrix L of factor relations is constructed by using formula (6.4): ⎛

⎞ 0.000.470.900.04 ⎜ 0.470.000.200.76 ⎟ ⎟ L=⎜ ⎝ 0.900.200.000.90 ⎠ 0.040.760.900.00 For the normalization the matrix L of factor relations, the coefficient of normalization λ is defined: λ= =

max[(

1 d i i j ), ( j d ji )]



1 1 = = 0.5 max[(1.41, 1.43, 2.00, 1.70)(1.41, 1.43, 2.00, 1.70)] 2

(6.5)

By means of the value λ it is found the total influence matrix- D: ⎛

⎞ 0.0000.2350.4500.020 ⎜ 0.2350.0000.1000.380 ⎟ ⎟ D =λ∗L =⎜ ⎝ 0.4500.1000.0000.450 ⎠ 0.0200.3800.4500.000

(6.6)

On the base of matrix D, the complex influence matrix T is determined: ⎛

T = D(I − D)−1

⎞ 0.9000.9901.4301.060 ⎜ 0.9920.8271.1901.249 ⎟ ⎟ =⎜ ⎝ 1.4301.1901.4821.596 ⎠

(6.7)

1.0601.2501.5971.216 In the next stage, the sums of rows and columns of matrix T are obtained: Ri = [

n

Cj = [

j=1

n i=1

ti j ]

ti j ]

(i = 1, .., n)

(6.8)

( j = 1, .., n)

(6.9)

nx1

1xn

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6 Assessment of the Development of Information Economy

Table 6.2 Total relation indicators of research and development Ri + Cj

RES

ERD

RDC

VRT

Ri

Cj

RES

0.9

0.99

1.43*

1.06

4.38

4.382

ERD

0.992

0.827

1.19

1.249*

4.258

RDC

1.43*

1.19

1.482*

1.596*

5.698

URT

1.06

1.25*

1.597*

1.216*

5.123

Ri - Cj

8.762

−0.002

4.257

8.515

0.001

5.699

11.397

0.001

5.121

10.244

0.002

The value Ri indicates the total effects, both direct and indirect, that factor i has on other factors. The value of Cj shows the total effect, both direct and indirect effects, on all other factors j. If j = i, the value of (Ri + C j ) represent the total effects both given and received by factor i. In contrast, the value of (Ri − C j ) shows a net contribution by factor i on the system. Moreover, when (Ri − C j ) is positive, factor i is a net cause. When (Ri − C j ) is negative, factor i becomes a net receiver. The obtained results of the total relation for indicators of the sub-indices “research and development” are given in Table 6.1. For other sub-indices the results are indicated in Tables 6.2, 6.3, 6.4, 6.5 and 6.6. Table 6.3 Total relation indicators of tertiary education T EN

GSE

TIM

Ri

Cj

Ri + C j

Ri − C j

T EN

1.73*

1.61*

1.85*

5.19

5.2

10.39

−0.01

GSE

1.61*

1

1.32

3.93

3.94

7.87

−0.01

TIM

1.86*

1.33

1.31

4.5

4.48

8.98

0.02

Table 6.4 Total relation indicators of education EED

GEE

SL E

RMS

PT S

Ri

Cj

Ri + C j

Ri − C j

EED

0.23

0.34

0.56*

0.28

0.23

1.64

1.64

3.28

0

GEE

0.34

0.23

0.45*

0.39*

0.34

1.75

1.75

3.5

0

SL E

0.56*

0.45*

0.57*

0.6*

0.56*

2.74

2.75

5.49

−0.01

RMS

0.28

0.39*

0.61*

0.28

0.28

1.84

1.83

3.67

0.01

PT S

0.23

0.34

0.56*

0.28

0.23

1.64

1.64

3.28

0

Table 6.5 Total relation indicators of knowledge creation P AD

PC T

M AO

ST P

C DH

Ri

Cj

Ri + C j

P AO

1.12*

1.24*

1.14*

0.5

0.51

4.51

4.24

8.75

Ri − C j 0.27

PC T

1.19*

0.78*

0.68*

0.51

0.51

3.67

3.69

7.36

−0.02

M AO

1.19*

0.78*

0.68*

0.51

0.51

3.67

3.13

6.8

ST P

0.26

0.37

0.15

0.11

0.112

1.002

1.839

2.841

−0.837

C DH

0.48

0.52

0.48

0.209

0.207

1.896

1.849

3.745

0.047

0.54

6.2 Fuzzy Model of the Estimation of Quality of Development of Information Economy

107

Table 6.6 Total relation indicators of knowledge impact Ri

Ri − C j

N BD

SO F

I SO

HT O

0.8

1.19

0.98

1.09

0.85

N BD

1.19

1.27

1.32*

1.31*

1.17

6.26

6.26

12.52

0

SO F

0.99

1.32*

0.94

0.99

1.08

5.32

5.31

10.63

0.01

I SO

1.09

1.31*

0.99

0.98

1.06

5.43

5.43

10.86

0

HT O

0.85

1.17

1.08

1.06

0.82

10.41

10.41

20.82

0

4.91

Cj

Ri + C j

GRR GRR

4.92

9.83

−0.01

Fig. 6.1 Diagram of ED indicators

For the corresponding sub-indices, a diagram of cause and effect relationships is constructed which is shown in Figs. 6.1, 6.2, 6.3, 6.4, 6.5, and 6.6. The cause and effect diagram is constructed by mapping all coordinate sets of (R i +C j , Ri −C j ) to visualize the complex interrelationship and provide information to judge which are the most important factors and how they influence factors affected. The factors for which ti j is greater than (α) are selected in the cause and effect diagram.

6.3 Analysis of the Cause-Effect Relationship In order to define an impact level of the internal factors, a threshold value (α) is calculated. The threshold value (α) is computed by the average of the elements in matrix T, that is:

108

6 Assessment of the Development of Information Economy

Fig. 6.2 Diagram of TE indicators

Fig. 6.3 Diagram of R&D indicators

n n α=

j=1 ti j

i=1

N

(6.10)

where N is total number of the elements in matrix T. This purpose of this calculation is to eliminate some elements of a minor effect in matrix T, and we obtain:

6.3 Analysis of the Cause-Effect Relationship

Fig. 6.4 Diagram of KNC indicators

Fig. 6.5 Diagram of KNI indicators

109

110

6 Assessment of the Development of Information Economy

Fig. 6.6 Diagram of KND indicators

α (R&D) = 1.22, α(KNC) = 0.59, α (TED) = 1.51, α(KNI) = 1.29, α (EDU) = 0.38, α(KND) = 8.19, The numbers above the threshold value in tables are indicated by (*). In Table 6.2 the maximum of (R i +C j )is397 and the minimum is 8.515. Therefore, the results of priority indicators of these sub-indices are: R DC > U RT > R E S > E R D As it is seen from Fig. 6.1, the cause group criteria consist of: • • • • •

Assessment in Reading Mathematics and Science (RMS), Government Expenditure on Education (EED), Pupil-teacher ratio, Secondary (PTS), Government Expenditure on Education per people, secondary (GEE). The effect group criteria are:

• School-life expectancy, • Primary to tertiary education (SLE). The cause group criteria refer to the implication of the influencing criteria, while the effect group criteria refer to the implication of the influenced criteria. Considering the interdependence among factors, much attention should be paid to the cause group criteria related to their influence on the criteria of the group of factors. In Table 6.3, we have

6.3 Analysis of the Cause-Effect Relationship

111

TEN > TIM > GSE which means that the maximum Tertiary Enrollment (TEN)> Tertiary inbound mobility (TIM)> Graduates in science and engineer (GSE). Figure 6.2 shows, that the cause group criteria is “Tertiary inbound mobility ratio (TIM)”, and the effect group criteria consist of “Tertiary graduates in science, engineering, manufacturing and construction (GSE)” and “School enrollment, tertiary(TEN)”. From Table 6.4, it can be seen that S L E > R M S > G E E > E E D, P T S which means that the “School life expectancy (SLE)” is greater than “Assessment in reading, mathematics, and science (RMS)”, “Assessment in reading, mathematics, and science (RMS)” is greater than “Government expenditure on education per pupil, secondary (GEE)”, and “Government expenditure on education per pupil, secondary (GEE)” is greater than “Expenditure on education (EED)” and “Pupil-teacher ratio, secondary (PTS)”, respectively. Figure 6.3 demonstrates that the cause group criteria include: • Average score of the top 3 universities at the QS (URT), • Gross expenditure on R&D (ERD), • Average expenditure of the top 3 global companies by R&D (RDS), and the effect group criteria include “ Research, full-time equivalence (RES)”. From Table 6.5 it can be seen that P AO > PC T > M AO > C D H > ST P which means that “Patent applications by origin (PAO)” is more than “International applications by origin (PCT)”, “International applications by origin (PCT)” is more than “Utility model applications by origin (MAO)”, “Utility model applications by origin (MAO)”is more than “Citable documents H index (CDH)”, and “Citable documents H index (CDH)” is more than “Scientific and technical publications (STP)”, respectively. Figure 6.4 shows that the cause group criteria include: • Utility model application by origin (MAO), • Present application by origin (PAO), • Citable documents H index (CDH), while the effect group criteria are: • PCT international application by origin (PCT), • Scientific and technical publications (STP).

112

6 Assessment of the Development of Information Economy

Table 6.7 Total relation indicators of knowledge diffusion I PR

I PR

HT E

ICE

F DI

Ri

Cj

Ri + C j

7.8

7.8

8.32*

8.32*

32.24

32.2

64.44

8.32*

Ri − C j 0.04

HT E

7.8

7.8

8.32*

32.24

32.2

64.44

0.04

ICE

8.3*

8.3*

8.31*

8.36*

33.27

33.31

66.58

−0.04

F DI

8.3*

8.3*

8.36*

8.31*

33.27

33.31

66.58

−0.04

From Table 6.6 it can be seen that HT O > N BD > I SO > SO F > G RR which means that: “High-tech and medium–high-tech output (HTO)” is more than “New business density (NBD)”, “New business density (NBD)” is more than “ISO 9001 quality certification (ISO)”, “ISO 9001 quality certification (ISO)” is more than “Total computer software spending (SOF)”, “Total computer software spending (SOF)” is more than “Growth rate of GDP per person engaged (GRR)”, respectively. Figure 6.5 indicates that the cause group criteria contain: • • • •

Total computer Software spending (SOF), ISO 9001 quality certification (ISO), New business density (NBD), High-tech and medium high-tech output (HTO),

and the effect group criteria contains: • Growth rate of GDP per person engaged (GRR). From Table 6.7 it can be seen that IC E = F DI > I P R = HT E which means that “ICT service exports (ICE) and Foreign direct investment net outflows (FDI) “ are greater than “Intellectual property receipts (IPR) and High-tech exports (THE)”. Figure 6.6 shows that the cause group criteria are: • Intellectual property receipts (IPR), • High-tech exports (HTE), and the effect group criteria are: • ICT service exports (ICE), • Foreign direct investment net outflows (FDI).

6.3 Analysis of the Cause-Effect Relationship

113

The application of tool and techniques of the theory of intuitionistic fuzzy sets and the DEMATEL methods to evaluate the impact level of indicators’ sub-indices that formulate the “human capital” and “knowledge and technology” as development resources of information economy, gives us a possibility to define the direction of investments in particular sub-sectors.

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