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E-raamat: Techniques of Decision Making, Uncertain Reasoning and Regression Analysis Under the Hesitant Fuzzy Environment and Their Applications

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Techniques of Decision Making, Uncertain Reasoning and Regression Analysis Under the Hesitant Fuzzy Environment and Their ApplicationsSuurem pilt
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This book mainly introduces some techniques of decision-making, uncertain reasoning and regression analysis under the hesitant fuzzy environment and expands the applications of hesitant fuzzy sets in solving practical problems. The book pursues three major objectives: (1) to introduce some techniques about decision-making, uncertain reasoning and regression analysis under the hesitant fuzzy environment, (2) to prove these techniques theoretically and (3) to apply the involved techniques to practical problems. The book is especially valuable for readers to understand how hesitant fuzzy set could be employed in decision-making, uncertain reasoning and regression analysis and motivates researchers to expand more application fields of hesitant fuzzy set.

1 Introduction
1(10)
1.1 Background
1(2)
1.2 Current Situation of Related Research
3(3)
1.2.1 Decision Making with Hesitant Fuzzy Information
3(1)
1.2.2 Research Status of Uncertain Reasoning
4(1)
1.2.3 Research Status of Regression Analysis
5(1)
1.3 Preminaries
6(2)
1.3.1 Hesitant Fuzzy Set
6(1)
1.3.2 Basic Operation Laws and Aggregation Operators
7(1)
1.4 Aim and Focus of This Book
8(3)
References
9(2)
2 TODIM Decision Making Method Based on the Hesitant Fuzzy Psychological Distance Measure
11(20)
2.1 Review of the Related Work
11(1)
2.2 Distance and Similarity Measures for HFSs
12(1)
2.3 TODIM Method Based on the Hesitant Fuzzy Psychological Distance Measure
13(8)
2.3.1 Background of Psychological Distance
13(2)
2.3.2 Hesitant Fuzzy Psychological Distance Measure and the Corresponding Similarity Measure
15(4)
2.3.3 TODIM Based on the Hesitant Fuzzy Psychological Distance Measure
19(2)
2.4 Application to the Temporary Rescue Airport Decision Making Problem
21(7)
2.5 Remarks
28(3)
References
28(3)
3 Dynamic Decision Making Method Based on the Hesitant Fuzzy Decision Field Theory
31(18)
3.1 Review of the Related Work
31(2)
3.2 Hesitant Fuzzy Decision Field Theory
33(5)
3.2.1 Classical DFT Method
33(1)
3.2.2 Hesitant Fuzzy Decision Field Theory
34(1)
3.2.3 Group Decision Making Based on the Hesitant Fuzzy Decision Field Theory
35(3)
3.3 Application to the Route Selection of the Arctic Northwest Passage Based on the HFDFT Method
38(8)
3.3.1 Case Study
38(5)
3.3.2 Comparisons with the Existing Methods for HFSs
43(3)
3.4 Remarks
46(3)
References
47(2)
4 Uncertain Reasoning Algorithm Under the Hesitant Fuzzy Environment
49(34)
4.1 Motivations and Background
49(2)
4.2 Preliminaries
51(1)
4.3 Dynamic Hesitant Fuzzy Bayesian Network
52(5)
4.3.1 Hesitant Fuzzy Event
52(2)
4.3.2 Hesitant Fuzzy Bayesian Network
54(2)
4.3.3 Dynamic Hesitant Fuzzy Bayesian Network
56(1)
4.4 Structure Learning Algorithm of Bayesian Network Based on the Hesitant Fuzzy Information Flow
57(7)
4.4.1 Hesitant Fuzzy Information Flow
58(2)
4.4.2 Unconstrained Optimization Model
60(1)
4.4.3 Improved PSO Algorithm for the Structure Learning of Bayesian Network
61(3)
4.5 Parameter Learning and Inference Prediction
64(8)
4.5.1 Databases and Measure of the Performance
64(1)
4.5.2 Experimental Results and Analysis
64(2)
4.5.3 Comparisons with Traditional Algorithms for Structure Learning
66(4)
4.5.4 Parameter Learning of Dynamic Hesitant Fuzzy Bayesian Network
70(1)
4.5.5 Reasoning and Prediction of Dynamic Hesitant Fuzzy Bayesian Network
71(1)
4.6 Case Study
72(6)
4.6.1 Background of the Optimal Investment Port Decision Making Problems of "Twenty-First-Century Maritime Silk Road"
73(1)
4.6.2 Calculations and Results Analysis
74(2)
4.6.3 Comparative Experiment and Results Analysis
76(2)
4.7 Remarks
78(5)
References
79(4)
5 Regression Analysis Models Under the Hesitant Fuzzy Environment
83(42)
5.1 Motivations and Background
83(3)
5.2 Preliminaries
86(2)
5.3 Optimized GRNN Based on FDS-FOA Under the Hesitant Fuzzy Environment
88(6)
5.3.1 Generalized Regression Neural Network Under the Hesitant Fuzzy Environment
88(3)
5.3.2 Fruit Fly Optimization Algorithm with Fast Decreasing Step
91(3)
5.3.3 Optimized GRNN Based on FDS-FOA
94(1)
5.4 Application of the Optimized GRNN Model to the Prediction of Air Quality Index
94(8)
5.4.1 AQI Prediction Model Based on the Optimized GRNN
96(1)
5.4.2 Case Study and Data Processing
97(2)
5.4.3 Experiment and Comparative Analysis
99(1)
5.4.4 Sensitivity Analysis
100(2)
5.5 Optimized Logistic Regression Model Based on the Maximum Entropy Estimation Under the Hesitant Fuzzy Environment
102(10)
5.5.1 Hesitant Fuzzy Information Flow
102(3)
5.5.2 Logistic Regression Model Under the Hesitant Fuzzy Environment
105(2)
5.5.3 Maximum Entropy Estimation
107(1)
5.5.4 Levenberg-Marquardt Algorithm
108(3)
5.5.5 K-S Fitting Test
111(1)
5.6 Application of the Optimized Logistic Regression Model to the Prediction of Emergency Extreme Air Pollution Event
112(6)
5.6.1 Factors Identification of the Emergency Extreme Air Pollution Event
112(1)
5.6.2 Construction and Prediction Results of the Optimized Logistic Regression Model
113(2)
5.6.3 Comparative Analysis and Sensitivity Analysis
115(3)
5.7 Remarks
118(7)
Appendix
118(3)
References
121(4)
6 Decision Making Methods Based on Probabilistic and Interval-Valued Probabilistic Hesitant Fuzzy Sets
125
6.1 Motivations and Background
125(3)
6.2 Preliminaries
128(4)
6.2.1 Probabilistic Hesitant Fuzzy Set
128(1)
6.2.2 Correlation Coefficients of HFSs
128(3)
6.2.3 Concept of Interval Value
131(1)
6.2.4 PHFSs and Their Basic Operations
131(1)
6.2.5 Ranking Method of PHFEs
132(1)
6.3 Correlation Coefficients of PHFSs
132(8)
6.3.1 Some Concepts Related to PHFEs
132(1)
6.3.2 Correlation Coefficient of PHFSs
133(3)
6.3.3 Weighted Correlation Coefficient Between PHFSs
136(2)
6.3.4 Clustering Algorithm for PHFSs
138(2)
6.4 Application of the Correlation Coefficients Between the PHFSs
140(12)
6.4.1 Application of the Correlation Coefficients Between the PHFSs in Cluster Analysis
140(7)
6.4.2 Comparison with Clustering Algorithm for HFSs
147(5)
6.5 Interval-Valued Probabilistic HFS
152(9)
6.5.1 Concept of IVPHFS
152(1)
6.5.2 Normalization of IVPHFS
153(1)
6.5.3 Comparison Approach of IVPHEs
154(1)
6.5.4 Basic Operations of the IVPHEs
155(2)
6.5.5 Some Basic Aggregation Operators for IVPHEs
157(2)
6.5.6 MCGDM Based on IVPHFSs
159(2)
6.6 Application and Simulation Experiment of IVPHFSs
161(6)
6.6.1 Application of IVPHFSs to Geopolitical Risk Evaluation Problem of Arctic Area
161(5)
6.6.2 Comparison with the Traditional Method for PDHFSs
166(1)
6.7 Remarks
167
Appendix
169(5)
References
174
Chenyang Song received the Bachelor Degree in meteorology from PLA University of Science and Technology, Nanjing, China, in 2014, the Master Degree in meteorology from PLA University of Science and Technology, Nanjing, China, in 2017, and the Ph.D degree in computer science from the Army Engineering University of PLA, Nanjing, China, in 2020. He is currently an engineer at the Army Aviation Institute, Beijing, China. He has published more than ten peer reviewed papers, and his research works has been published in Applied Soft Computing, International Journal of Intelligent Systems, International Journal of Fuzzy Systems, Applied Intelligence, International Journal of Machine Learning and Cybernetics, Journal of Intelligent and Fuzzy Systems, etc. His current research interests include decision analysis, optimization and data fusion. Zeshui Xu received the Ph. D degree in management science and engineering from Southeast University, Nanjing, China, in 2003.From October 2005 to December 2007, he was a Postdoctoral Researcher with School of Economics and Management, Tsinghua University, China. He was a Distinguished Young Scholar of the National Natural Science Foundation of China and the Chang Jiang Scholar of the Ministry of Education of China. He is currently a Professor with the Business School, Sichuan University, Chengdu. He has been elected as Academician of IASCYS, Fellow of IEEE, IFSA, RSA, IET, ORS, BCS, VEBLEO, IAAM, AAIA, and ranked 30th in 2019 single year scientific impact and 258th in career scientific impact among Worlds top 100,000 Scientists, and ranked 57th among Worlds top 1,000 Scientists in Computer Science & Electronics in 2020. He has published 17 monographs by Springer and contributed more than 650 SCI/SSCI articles to professional journals. He is among the worlds top 1% most highly cited researchers with about 67,000 citations in Google Scholar, his h-index is 133. He is currently the Associate Editors of IEEE Transactions on Cybernetics, IEEE Transactions on Fuzzy Systems, IEEE Access, Information Sciences, Artificial Intelligence Review, Cognitive Computation, Applied Intelligence, Journal of the Operational Research, Fuzzy Optimization and Decision Making, etc. His current research interests include Decision-making theory and methodology, optimization algorithms, information fusion, and big data analytics.
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