Techniques of Decision Making, Uncertain Reasoning and Regression Analysis Under the Hesitant Fuzzy Environment and Their Applications (Uncertainty and Operations Research)

✍ Scribed by Chenyang Song, Zeshui Xu

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 186
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface
Contents
1 Introduction
1.1 Background
1.2 Current Situation of Related Research
1.2.1 Decision Making with Hesitant Fuzzy Information
1.2.2 Research Status of Uncertain Reasoning
1.2.3 Research Status of Regression Analysis
1.3 Preminaries
1.3.1 Hesitant Fuzzy Set
1.3.2 Basic Operation Laws and Aggregation Operators
1.4 Aim and Focus of This Book
References
2 TODIM Decision Making Method Based on the Hesitant Fuzzy Psychological Distance Measure
2.1 Review of the Related Work
2.2 Distance and Similarity Measures for HFSs
2.3 TODIM Method Based on the Hesitant Fuzzy Psychological Distance Measure
2.3.1 Background of Psychological Distance
2.3.2 Hesitant Fuzzy Psychological Distance Measure and the Corresponding Similarity Measure
2.3.3 TODIM Based on the Hesitant Fuzzy Psychological Distance Measure
2.4 Application to the Temporary Rescue Airport Decision Making Problem
2.5 Remarks
References
3 Dynamic Decision Making Method Based on the Hesitant Fuzzy Decision Field Theory
3.1 Review of the Related Work
3.2 Hesitant Fuzzy Decision Field Theory
3.2.1 Classical DFT Method
3.2.2 Hesitant Fuzzy Decision Field Theory
3.2.3 Group Decision Making Based on the Hesitant Fuzzy Decision Field Theory
3.3 Application to the Route Selection of the Arctic Northwest Passage Based on the HFDFT Method
3.3.1 Case Study
3.3.2 Comparisons with the Existing Methods for HFSs
3.4 Remarks
References
4 Uncertain Reasoning Algorithm Under the Hesitant Fuzzy Environment
4.1 Motivations and Background
4.2 Preliminaries
4.3 Dynamic Hesitant Fuzzy Bayesian Network
4.3.1 Hesitant Fuzzy Event
4.3.2 Hesitant Fuzzy Bayesian Network
4.3.3 Dynamic Hesitant Fuzzy Bayesian Network
4.4 Structure Learning Algorithm of Bayesian Network Based on the Hesitant Fuzzy Information Flow
4.4.1 Hesitant Fuzzy Information Flow
4.4.2 Unconstrained Optimization Model
4.4.3 Improved PSO Algorithm for the Structure Learning of Bayesian Network
4.5 Parameter Learning and Inference Prediction
4.5.1 Databases and Measure of the Performance
4.5.2 Experimental Results and Analysis
4.5.3 Comparisons with Traditional Algorithms for Structure Learning
4.5.4 Parameter Learning of Dynamic Hesitant Fuzzy Bayesian Network
4.5.5 Reasoning and Prediction of Dynamic Hesitant Fuzzy Bayesian Network
4.6 Case Study
4.6.1 Background of the Optimal Investment Port Decision Making Problems of “Twenty-First-Century Maritime Silk Road”
4.6.2 Calculations and Results Analysis
4.6.3 Comparative Experiment and Results Analysis
4.7 Remarks
References
5 Regression Analysis Models Under the Hesitant Fuzzy Environment
5.1 Motivations and Background
5.2 Preliminaries
5.3 Optimized GRNN Based on FDS-FOA Under the Hesitant Fuzzy Environment
5.3.1 Generalized Regression Neural Network Under the Hesitant Fuzzy Environment
5.3.2 Fruit Fly Optimization Algorithm with Fast Decreasing Step
5.3.3 Optimized GRNN Based on FDS-FOA
5.4 Application of the Optimized GRNN Model to the Prediction of Air Quality Index
5.4.1 AQI Prediction Model Based on the Optimized GRNN
5.4.2 Case Study and Data Processing
5.4.3 Experiment and Comparative Analysis
5.4.4 Sensitivity Analysis
5.5 Optimized Logistic Regression Model Based on the Maximum Entropy Estimation Under the Hesitant Fuzzy Environment
5.5.1 Hesitant Fuzzy Information Flow
5.5.2 Logistic Regression Model Under the Hesitant Fuzzy Environment
5.5.3 Maximum Entropy Estimation
5.5.4 Levenberg-Marquardt Algorithm
5.5.5 K-S Fitting Test
5.6 Application of the Optimized Logistic Regression Model to the Prediction of Emergency Extreme Air Pollution Event
5.6.1 Factors Identification of the Emergency Extreme Air Pollution Event
5.6.2 Construction and Prediction Results of the Optimized Logistic Regression Model
5.6.3 Comparative Analysis and Sensitivity Analysis
5.7 Remarks
Appendix
References
6 Decision Making Methods Based on Probabilistic and Interval-Valued Probabilistic Hesitant Fuzzy Sets
6.1 Motivations and Background
6.2 Preliminaries
6.2.1 Probabilistic Hesitant Fuzzy Set
6.2.2 Correlation Coefficients of HFSs
6.2.3 Concept of Interval Value
6.2.4 PHFSs and Their Basic Operations
6.2.5 Ranking Method of PHFEs
6.3 Correlation Coefficients of PHFSs
6.3.1 Some Concepts Related to PHFEs
6.3.2 Correlation Coefficient of PHFSs
6.3.3 Weighted Correlation Coefficient Between PHFSs
6.3.4 Clustering Algorithm for PHFSs
6.4 Application of the Correlation Coefficients Between the PHFSs
6.4.1 Application of the Correlation Coefficients Between the PHFSs in Cluster Analysis
6.4.2 Comparison with Clustering Algorithm for HFSs
6.5 Interval-Valued Probabilistic HFS
6.5.1 Concept of IVPHFS
6.5.2 Normalization of IVPHFS
6.5.3 Comparison Approach of IVPHEs
6.5.4 Basic Operations of the IVPHEs
6.5.5 Some Basic Aggregation Operators for IVPHEs
6.5.6 MCGDM Based on IVPHFSs
6.6 Application and Simulation Experiment of IVPHFSs
6.6.1 Application of IVPHFSs to Geopolitical Risk Evaluation Problem of Arctic Area
6.6.2 Comparison with the Traditional Method for PDHFSs
6.7 Remarks
Appendix
References