Hesitant Fuzzy and Probabilistic Information Fusion Theory and Applications

✍ Scribed by Zhan Su, Zeshui Xu, Shen Zhang

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 155
• Series: Uncertainty and Operations Research
• Category: Library

✦ Synopsis

This book introduces the current research progress on hesitant fuzzy decision-making based on probability theory and methods. From the perspectives of theory expansion, information fusion, and information mining, it explores novel perspectives, ideas, and techniques for addressing hesitant fuzzy uncertain decision-making problems and demonstrates them through practical applications and case studies. It aims to provide a reference for researchers, practitioners, and graduate students in the fields of decision analysis, fuzzy theory, and information fusion.

✦ Table of Contents

Preface
Contents
List of Figures
1 Introduction
1.1 Background
1.1.1 Cognition of Uncertainty
1.1.2 The Uncertainty in Decision-Making
1.2 Literature Reviews
1.2.1 Hesitant Fuzzy Theory
1.2.2 Probabilistic Expansion of HFSs
1.2.3 Application of Probability in Fuzzy Decision-Making Problems
1.3 Raised Issues
1.4 Research Design
References
2 Probability-Based Hesitant Fuzzy Opinion Dynamics Decision-Making Method
2.1 HFSs and Opinion Dynamics
2.1.1 HFSs
2.1.2 DeGroot Model
2.2 The Evaluation of the Hesitant Fuzzy Opinion
2.2.1 Multiplication Between the Real Matrix and Hesitant Fuzzy Matrix
2.2.2 HF-DeGroot Model
2.3 Decision-Making Method Based on the HF-DeGroot Model
2.3.1 Composition of the Transition Matrix
2.3.2 Evolution Analysis of the HF-DeGroot Model
2.3.3 The Decision-Making Methods Based on the HF-DeGroot Model
2.4 Numerical Examples and Analysis
2.4.1 Problem Description
2.4.2 The Solution Based on Algorithm II
2.4.3 The Solution Based on Algorithm III
2.4.4 The Solution Based on Algorithm IV
2.5 Comparative Analysis
2.5.1 Comparison Between Algorithms
2.5.2 Sensitivity Analysis Based on Parameter Values
2.6 Conclusions
References
3 Distribution-Based Decision-Making Method for Dual Hesitant Fuzzy Information
3.1 DHFSs
3.2 Probability Distribution-Based Decision-Making Method for DHFSs
3.2.1 Mean and Standard Deviation of DHFEs
3.2.2 Three Weighting Methods Based on DHFEs
3.2.3 Probability Distribution-Based Decision-Making Methods for DHFSs
3.3 Probability Distribution-Based Decision-Making Methods for HFEs
3.3.1 Mean and Standard Deviation of HFEs
3.3.2 Three Weighting Methods for HFSs
3.4 Numerical Examples and Analysis
3.4.1 Numerical Examples for DHFEs
3.4.2 Numerical Examples for HFEs
3.5 Conclusions
References
4 Multi-Attribute Decision-Making Method Based on Probabilistic Hesitant Fuzzy Entropy
4.1 PHFE
4.2 The Membership Degree-Based Fuzzy Entropies
4.2.1 Classical Fuzzy Entropy Theory
4.2.2 The Membership Degree-Based Entropies for PHFEs
4.3 The Distance-Based Fuzzy Entropies
4.3.1 Distance Measures for PHFEs
4.3.2 The Symmetry in the Circumstances of HFEs and PHFEs
4.3.3 Like-Distance Measure for PHFEs
4.3.4 The Distance-Based Entropies for PHFEs
4.4 Multi-Attribute Decision-Making Method Based on Probability Hesitant Fuzzy Entropy
4.5 Numerical Examples and Analysis
4.5.1 The Solution Based on Algorithm I
4.5.2 The Solution Based on Algorithm II
4.5.3 Comparison and Analysis
4.6 Conclusions
References
5 Probability-Based Integration for Continuous Hesitant Fuzzy Information in Group Decision-Making
5.1 Problem Analysis
5.2 Detailed Explanation of CHFEs
5.2.1 CHFE
5.2.2 Uniform Hesitant Fuzzy Elements and CHFEs with Uniform Distribution
5.2.3 Further Discussion of CHFEs
5.3 Operation and Aggregation Methods of CHFEs
5.3.1 Operation and Aggregation Methods of CHFEs Based on Mathematical Derivation
5.3.2 Operation and Aggregation Methods of CHFEs Based on Computer Simulation
5.4 Numerical Examples and Analysis
5.4.1 Problem Description
5.4.2 The Solution Based on the Probability-Based Multi-Attribute Decision-Making Method
5.4.3 Comparison and Analysis
5.5 Conclusions
References
6 Probability-Based Political Risk Assessment in the Belt and Road Investment
6.1 Problem Analysis
6.1.1 Necessity and Feasibility of Political Risk Assessment for BRI
6.1.2 Uncertainty in the Political Risk Assessment
6.2 The Choice of Multi-Attribute Decision-Making Method for Political Risk Assessment
6.2.1 Prospect Theory
6.2.2 The Index System for Hesitant Fuzzy Political Risk Assessment
6.2.3 A Probability-Based Hesitant Fuzzy Political Risk Assessment Model
6.2.4 The Solution for the Probability-Based Political Risk Assessment Case
6.3 Comparative Analysis
6.4 Conclusions
References
Appendix A
Appendix B