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

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. Preface 6 Contents 9 1 Introduction 13 1.1 Background 13 1.2 Current Situation of Related Research 15 1.2.1 Decision Making with Hesitant Fuzzy Information 15 1.2.2 Research Status of Uncertain Reasoning 16 1.2.3 Research Status of Regression Analysis 17 1.3 Preminaries 18 1.3.1 Hesitant Fuzzy Set 18 1.3.2 Basic Operation Laws and Aggregation Operators 19 1.4 Aim and Focus of This Book 20 References 21 2 TODIM Decision Making Method Based on the Hesitant Fuzzy Psychological Distance Measure 23 2.1 Review of the Related Work 23 2.2 Distance and Similarity Measures for HFSs 24 2.3 TODIM Method Based on the Hesitant Fuzzy Psychological Distance Measure 25 2.3.1 Background of Psychological Distance 25 2.3.2 Hesitant Fuzzy Psychological Distance Measure and the Corresponding Similarity Measure 27 2.3.3 TODIM Based on the Hesitant Fuzzy Psychological Distance Measure 31 2.4 Application to the Temporary Rescue Airport Decision Making Problem 33 2.5 Remarks 40 References 40 3 Dynamic Decision Making Method Based on the Hesitant Fuzzy Decision Field Theory 42 3.1 Review of the Related Work 42 3.2 Hesitant Fuzzy Decision Field Theory 44 3.2.1 Classical DFT Method 44 3.2.2 Hesitant Fuzzy Decision Field Theory 45 3.2.3 Group Decision Making Based on the Hesitant Fuzzy Decision Field Theory 46 3.3 Application to the Route Selection of the Arctic Northwest Passage Based on the HFDFT Method 49 3.3.1 Case Study 49 3.3.2 Comparisons with the Existing Methods for HFSs 54 3.4 Remarks 57 References 58 4 Uncertain Reasoning Algorithm Under the Hesitant Fuzzy Environment 60 4.1 Motivations and Background 60 4.2 Preliminaries 62 4.3 Dynamic Hesitant Fuzzy Bayesian Network 63 4.3.1 Hesitant Fuzzy Event 63 4.3.2 Hesitant Fuzzy Bayesian Network 65 4.3.3 Dynamic Hesitant Fuzzy Bayesian Network 67 4.4 Structure Learning Algorithm of Bayesian Network Based on the Hesitant Fuzzy Information Flow 68 4.4.1 Hesitant Fuzzy Information Flow 69 4.4.2 Unconstrained Optimization Model 71 4.4.3 Improved PSO Algorithm for the Structure Learning of Bayesian Network 72 4.5 Parameter Learning and Inference Prediction 75 4.5.1 Databases and Measure of the Performance 75 4.5.2 Experimental Results and Analysis 75 4.5.3 Comparisons with Traditional Algorithms for Structure Learning 77 4.5.4 Parameter Learning of Dynamic Hesitant Fuzzy Bayesian Network 81 4.5.5 Reasoning and Prediction of Dynamic Hesitant Fuzzy Bayesian Network 82 4.6 Case Study 83 4.6.1 Background of the Optimal Investment Port Decision Making Problems of “Twenty-First-Century Maritime Silk Road” 84 4.6.2 Calculations and Results Analysis 85 4.6.3 Comparative Experiment and Results Analysis 87 4.7 Remarks 89 References 90 5 Regression Analysis Models Under the Hesitant Fuzzy Environment 93 5.1 Motivations and Background 93 5.2 Preliminaries 96 5.3 Optimized GRNN Based on FDS-FOA Under the Hesitant Fuzzy Environment 98 5.3.1 Generalized Regression Neural Network Under the Hesitant Fuzzy Environment 98 5.3.2 Fruit Fly Optimization Algorithm with Fast Decreasing Step 101 5.3.3 Optimized GRNN Based on FDS-FOA 104 5.4 Application of the Optimized GRNN Model to the Prediction of Air Quality Index 104 5.4.1 AQI Prediction Model Based on the Optimized GRNN 106 5.4.2 Case Study and Data Processing 107 5.4.3 Experiment and Comparative Analysis 109 5.4.4 Sensitivity Analysis 110 5.5 Optimized Logistic Regression Model Based on the Maximum Entropy Estimation Under the Hesitant Fuzzy Environment 112 5.5.1 Hesitant Fuzzy Information Flow 112 5.5.2 Logistic Regression Model Under the Hesitant Fuzzy Environment 115 5.5.3 Maximum Entropy Estimation 117 5.5.4 Levenberg-Marquardt Algorithm 118 5.5.5 K-S Fitting Test 121 5.6 Application of the Optimized Logistic Regression Model to the Prediction of Emergency Extreme Air Pollution Event 122 5.6.1 Factors Identification of the Emergency Extreme Air Pollution Event 122 5.6.2 Construction and Prediction Results of the Optimized Logistic Regression Model 123 5.6.3 Comparative Analysis and Sensitivity Analysis 125 5.7 Remarks 128 Appendix 128 References 131 6 Decision Making Methods Based on Probabilistic and Interval-Valued Probabilistic Hesitant Fuzzy Sets 135 6.1 Motivations and Background 135 6.2 Preliminaries 138 6.2.1 Probabilistic Hesitant Fuzzy Set 138 6.2.2 Correlation Coefficients of HFSs 138 6.2.3 Concept of Interval Value 141 6.2.4 PHFSs and Their Basic Operations 141 6.2.5 Ranking Method of PHFEs 142 6.3 Correlation Coefficients of PHFSs 142 6.3.1 Some Concepts Related to PHFEs 142 6.3.2 Correlation Coefficient of PHFSs 143 6.3.3 Weighted Correlation Coefficient Between PHFSs 146 6.3.4 Clustering Algorithm for PHFSs 148 6.4 Application of the Correlation Coefficients Between the PHFSs 150 6.4.1 Application of the Correlation Coefficients Between the PHFSs in Cluster Analysis 150 6.4.2 Comparison with Clustering Algorithm for HFSs 157 6.5 Interval-Valued Probabilistic HFS 162 6.5.1 Concept of IVPHFS 162 6.5.2 Normalization of IVPHFS 163 6.5.3 Comparison Approach of IVPHEs 164 6.5.4 Basic Operations of the IVPHEs 165 6.5.5 Some Basic Aggregation Operators for IVPHEs 167 6.5.6 MCGDM Based on IVPHFSs 169 6.6 Application and Simulation Experiment of IVPHFSs 171 6.6.1 Application of IVPHFSs to Geopolitical Risk Evaluation Problem of Arctic Area 171 6.6.2 Comparison with the Traditional Method for PDHFSs 176 6.7 Remarks 177 Appendix 179 References 184