Linguistic Decision Making : Numerical Scale Model and Consistency-Driven Methodology

This book proposes a novel CWW model to personalize individual semantics in linguistic decision making, based on two new concepts: numerical scale and consistency-driven methodology. The numerical scale model provides a unified framework to connect different linguistic symbolic computational models for CWW, and the consistency-driven methodology customizes individuals' semantics to support linguistic group decision making by setting personalized numerical scales. The book is a valuable resource for researchers and postgraduates who are interested in CWW in linguistic decision making.-- Provided by publisher Preface 5 References 6 Contents 7 1 Introduction 9 1.1 Computing with Words in Decision Making 9 1.2 Linguistic Symbolic Computational Models 11 1.2.1 The 2-Tuple Linguistic Model 11 1.2.2 The Proportional 2-Tuple Linguistic Model 13 1.2.3 Linguistic Hierarchy 15 1.2.4 Hesitant Linguistic Term Set 17 1.3 A Core Problem in Linguistic Decision Making 18 References 21 2 Numerical Scale Model 25 2.1 Numerical Scale 25 2.1.1 The Definition of Numerical Scale 25 2.1.2 Interval Numerical Scale 28 2.1.2.1 Interval Numerical Scale 28 2.1.2.2 Generalized Inverse Operation of Interval Numerical Scale 30 2.2 Linguistic Computational Model 32 2.2.1 Linguistic Computational Framework 32 2.2.2 Linguistic Aggregation 33 2.2.3 Illustrative Example 36 2.3 Setting the Interval Numerical Scale Based on IT2 FSs 37 2.3.1 Generalizing the Wang and Hao Model 37 2.3.2 Comparative Study 38 References 44 3 A Unified Framework 46 3.1 Connecting Numerical Scale Model to Linguistic Hierarchy 46 3.1.1 Definition of Unbalanced Linguistic Term Sets 48 3.1.2 The Revised Retranslation Processin Linguistic Hierarchy 48 3.1.3 Equivalence Between Numerical Scale Model and Linguistic Hierarchy 51 3.1.3.1 Equivalence for Aggregation Operators 51 3.1.3.2 Equivalence for Negation Operators 53 3.1.3.3 Illustrative Example 54 3.2 Hesitant Unbalanced Linguistic Information 55 3.2.1 Possibility Degree Formulas 55 3.2.2 Unbalanced Hesitant Linguistic Aggregation 62 3.2.2.1 Hesitant Unbalanced Linguistic Aggregation Operators 63 3.2.2.2 An Algorithm for Obtaining the Aggregation Results of the Novel HLWA and HLOWA Operators 67 References 71 4 Consistency of Interval-Like Reciprocal Preference Relations 73 4.1 Consistency of Interval-Valued Reciprocal Preference Relations 73 4.1.1 Interval-Valued Reciprocal Preference Relations 74 4.1.1.1 Definitions of IVRPRs 74 4.1.1.2 Consistency Measures of IVRPRs 75 4.1.2 Average-Case Consistency Measure 76 4.1.2.1 Average Consistency Index of IVRPRs 76 4.1.2.2 Numerical Examples for Consistency Measurement 82 4.1.2.3 Comparative Study 82 4.1.3 Average-Case Consistency Improving Method 86 4.1.3.1 A Method to Improve ACI 86 4.1.3.2 Numerical Example for Consistency Improvement 88 4.1.3.3 Simulation Experiments 90 4.2 Consistency of Hesitant Linguistic Preference Relations 92 4.2.1 Hesitant Linguistic Preference Relations 93 4.2.1.1 Linguistic Preference Relation and Its Consistency Index 93 4.2.1.2 Hesitant Fuzzy Linguistic Preference Relation and the Normalization Method 95 4.2.2 Interval Consistency Measure 97 4.2.2.1 The Approach to Obtain the Interval Consistency Level of HFLPRs 98 4.2.2.2 Illustrative Examples 101 4.2.3 Interval Consistency Measure vs Normalization Method 104 4.2.3.1 Illustrate the Essence of the Normalization Method 104 4.2.3.2 Connection Among ICI, NCI, and ACI 105 References 111 5 Consistency-Driven Methodology 113 5.1 Personalized Individual Semantics in Linguistic Term Sets 113 5.1.1 Consistency-Driven Methodology to Set Personalized Interval Numerical Scales 114 5.1.1.1 Connecting Linguistic Preference Relations to Interval Numerical Preference Relations 115 5.1.1.2 Premises and Basic Ideas 115 5.1.1.3 Linear Programming Model 117 5.1.1.4 Example 119 5.1.2 A CWW Framework with PISs 121 5.1.2.1 A 2-Tuple Linguistic Framework Based on Yager's CWW Scheme 121 5.1.2.2 Comparison and Aggregation: The Personalized 2-Tuple Linguistic Operators 123 5.2 Personalized Individual Semantics in HesitantLinguistic Contexts 127 5.2.1 Personalizing Hesitant Individual Semantics 128 5.2.1.1 Framework 128 5.2.1.2 Setting Personalized Numerical Scales of Linguistic Terms in GDM 129 5.2.1.3 Personalizing Individual Semantics with HFLTSs in GDM 133 5.2.2 Numerical Examples and Analysis 135 5.2.2.1 Numerical Examples 135 5.2.2.2 Comparative Study 142 5.2.3 Discussion: Advantages and Limitations 143 References 144 6 Applications in Various Decision Problems 147 6.1 The Analytic Hierarchy Process 147 6.1.1 Basic Knowledge 148 6.1.1.1 The Framework of AHP 149 6.1.1.2 2-Tuple Linguistic Modelling of the AHP Scale Problem 151 6.1.2 The Framework of the AHP with PISs 153 6.1.2.1 Consistency Test Regarding Linguistic Preference Relations 154 6.1.2.2 Consistency-Driven Approach to Obtain the Numerical Scale with PIS 155 6.1.3 Consistency-Driven Methodology to Deal with PISs 156 6.1.3.1 Consistency-Driven Optimization Model 156 6.1.3.2 Further Discussion 159 6.1.3.3 Practical Example 163 6.1.3.4 Simulation and Comparison Analysis 167 6.1.4 Personalized AHP Interval Numerical Scales 170 6.1.4.1 Using the Consistency-Driven Methodology to Set AHP Interval Numerical Scale 170 6.1.4.2 Framework for the Use of the Consistency-Driven Methodology in Linguistic GDM Problems 174 6.1.4.3 Example I 175 6.1.4.4 Example II 177 6.2 Consensus Model in Linguistic GDM Problem 180 6.2.1 A GDM Framework with PISs 180 6.2.2 Consensus Reaching Process 182 6.3 MAGDM with Linguistic Preference Information on Alternatives 189 6.3.1 MAGDM with Numerical Preference Information 191 6.3.2 A PIS Based MAGDM Framework 193 6.3.2.1 Description of the Problem: MAGDM with Linguistic Preference Information on Alternatives 193 6.3.2.2 The Proposed Framework 193 6.3.3 Obtaining the Individual Numerical Scales with PISs 195 6.3.3.1 Modelling 196 6.3.3.2 Further Discussion Regarding Model P1 199 6.3.3.3 Numerical Example 203 6.3.4 Numerical and Simulation Analysis 205 6.3.4.1 Comparison Criteria 205 6.3.4.2 Numerical Analysis 206 6.3.4.3 Simulation Analysis 208 References 211 Front Matter ....Pages i-viii Introduction (Yucheng Dong, Jiuping Xu)....Pages 1-16 Numerical Scale Model (Yucheng Dong, Jiuping Xu)....Pages 17-37 A Unified Framework (Yucheng Dong, Jiuping Xu)....Pages 39-65 Consistency of Interval-Like Reciprocal Preference Relations (Yucheng Dong, Jiuping Xu)....Pages 67-106 Consistency-Driven Methodology (Yucheng Dong, Jiuping Xu)....Pages 107-140 Applications in Various Decision Problems (Yucheng Dong, Jiuping Xu)....Pages 141-209