This book gives a thorough and systematic introduction to the latest research results about fuzzy decision-making method based on prospect theory. It includes eight chapters: Introduction, Intuitionistic fuzzy MADM based on prospect theory, QUALIFLEX based on prospect theory with probabilistic linguistic information, Group PROMETHEE based on prospect theory with hesitant fuzzy linguistic information, Prospect consensus with probabilistic hesitant fuzzy preference information, Improved TODIM based on prospect theory and the improved TODIM with probabilistic hesitant fuzzy information, etc. This book is suitable for the researchers in the fields of fuzzy mathematics, operations research, behavioral science, management science and engineering, etc. It is also useful as a textbook for postgraduate and senior-year undergraduate students of the relevant professional institutions of higher learning.

Autorentext

Xiaoli Tian is Associate Professor of the School of Business Administration in Southwestern University of Finance and Economics, Chengdu, China. She was Academic Visitor with the Department of Computer Science and Artificial Intelligence, University of Granada, Spain, in 2017. She has published more than 15 peer-reviewed papers, many in high-quality international journals including Knowledge-Based Systems, Applied Soft Computing, Technological and Economic Development of Economy, Technological Forecasting and Social Change, etc. One of her papers has been selected as ESI Highly Cited Papers. Her current research interest includes large-scale consensus, group decision making, decision making with bounded rationality, and multiple attributes decision making under uncertainty. Dr. Tian serves as a reviewer for more than 10 international journals.

Zeshui Xu is Distinguished Young Scholar of the National Natural Science Foundation of China and Chang Jiang Scholars of the Ministry of Education of China. He is currently Professor with the Business School, Sichuan University, Chengdu, China. He has been elected as Academician of IASCYS (International academy for systems and cybernetic sciences), Fellow of IEEE (Institute of Electrical and Electronics Engineers), Fellow of IFSA (International Fuzzy Systems Association), Fellow of RSA (Royal Society of Arts), Fellow of IET (Institution of Engineering and Technology), Fellow of BCS (British Computer Society), Fellow of IAAM (International Association of Advanced Materials), Fellow of VEBLEO, and ranked 431th among World's Top 100,000 Scientists in 2019. He has contributed more than 600 SCI/SSCI articles to professional journals, and is among the world's top 1% most highly cited researchers with about 62,000 citations, his h-index is 123. He is currently the Associate Editors of IEEE Transactions on Cybernetics, IEEE Transactions on Fuzzy Systems, IEEE Access, Information Sciences, Fuzzy Optimization and Decision Making, Journal of the Operational Research Socitey, International Journal of Systems Science, Artificial Intelligence Review, etc. His current research interests include decision making, information fusion, data analysis, fuzzy systems and applications.

Inhalt

Preface 1

Chapter 1. Introduction 1

1.1 Background 1

1.1.1 Development of bounded rationality 2

1.1.2 Development of fuzzy information 3

1.1.3 Importance of research about fuzzy decision making with prospect theory 3

1.2 Corresponding preliminaries 4

1.2.1 Prospect theory 5

1.2.2 TODIM 5

1.2.3 Intuitionistic fuzzy information 7 1.2.4 Probabilistic hesitant fuzzy information 9

1.2.5 Hesitant fuzzy linguistic information 11

1.2.6 Probabilistic linguistic information 14

1.3 Aim and focus of this book 17

Chapter 2. Intuitionistic Fuzzy MADM based on PT 19

2.1 Decision-making procedure 20

2.2 Illustrative example 24

2.2.1 Decision-making attributes used by VCs 26

2.2.2 Selecting process and results derived by IFPT 28

2.2.3. Selecting process and results derived by TOPSIS 30

2.3. Remarks 33 Chapter 3. QUALIFLEX based on PT with Probabilistic Linguistic Information 35

3.1 Procedure of P-QUALIFLEX with probabilistic linguistic information 36

3.2 Procedure of the extended QUALIFLEX with probabilistic linguistic information 39

3.3 Illustrative example 41 3.3.1 Results of P-QUALIFLEX with probabilistic linguistic information 42

3.3.2 Results of the extended QUALIFLEX with probabilistic linguistic information 46

3.4 Comparative analysis 48

3.4.1 Comparison of P-QUALIFLEX with extended QUALIFLEX 48

3.4.2 Comparison of P-QUALIFLEX with TODIM 50

3.5 Remarks 55

Chapter 4. Group PROMETHEE based on PT with Hesitant Fuzzy Linguistic Information 57 4.1 GP-PROMETHEE with hesitant fuzzy linguistic information 60

4.2 G-PROMETHEE with hesitant fuzzy linguistic information 65

4.3 Illustrative example 67

4.3.1 Decision-making background 67 4.3.2 Results of the GP-PROMETHEE with hesitant fuzzy linguistic information 69

4.3.3 Results of the G-PROMETHEE with hesitant fuzzy linguistic information 75

4.3.4 Results of TODIM with hesitant fuzzy linguistic information 78 4.3.5 Comparative analysis 80

4.3.5.1 Comparative analysis based on the results of illustrative example 81

4.3.5.2 Comparative analysis based on the sensitivity of parameters 82

4.4 Simulation analysis 88

4.5 Remarks 91

Chapter 5. Prospect Consensus with Probabilistic Hesitant Fuzzy Preference Information 93

5.1 Probabilistic hesitant fuzzy preference information 93

5.2 Consensus model based on PT with P-HFPs 95

5.2.1 Prospect consensus measure with P-HFPs 96

5.2.2 Procedure of reaching prospect consensus and decision-making 100

5.3 Illustrative example 102

5.3.1 Sequential decision-making attributes 103

5.3.2 Results of prospect consensus with P-HFPs 106

5.3.3 Results of the expected consensus process with P-HFPs 114

5.3.4 Results of prospect consensus with HFPs 117

5.3.5 Results of the expected consensus with HFPs 120

5.3.6 Comparative analysis 121 5.4 Simulated analysis 124

5.5 Remarks 131

Chapter 6. An Improved TODIM based on PT 132

6.1 Procedure of the improved TODIM 133

6.2 Illustrative example 135

6.2.1 Decision-making background 135

6.2.2 Results of the improved TODIM 136

6.2.3 Results of the classical TODIM 139 6.2.4 Comparative analysis between the improved and the classical TODIM 140

6.3 Remarks 141

Chapter 7. An improved TODIM with probabilistic hesitant fuzzy information 143

7.1 Procedure of the improved TODIM with probabilistic hesitant fuzzy information 143

7.2 Procedure of the improved TODIM with hesitant fuzzy information 145

7.3 Illustrative analysis 148

7.3.1 Screening process of the improved TODIM with probabilistic hesitant fuzzy information 148 7.3.2 Screening process of the extended TODIM with probabilistic hesitant fuzzy information 150

7.3.3 Screening process of the improved TODIM with hesitant fuzzy information 153

7.3.4 Screening process of the extended TODIM with hesitant fuzzy information 154

7.3.5 Analysis 157

7.4 Comparative analysis 159

7.4.1 Comparative analysis with the TOPSIS method 159

7.4.2 Sensitivity analysis based on the parameter values 162

7.4.2.1 Sensitivity analysis of the improved TODIM and the extended TODIM with the same fuzzy information 162

7.4.2.2 Sensitivity analysis of the improved TODIM and the extended TODIM based on different types of fuzzy information 165

7.5 Simulation analysis 171

7.6 Remarks 173

Chapter 8. Conclusions 175

8.1 Summary 175

8.2 Future studies 178

References: 181