Multiple Attribute Decision Making M E T H O D S AND A P P L I C A T I O N S Gwo-Hshiung Tzeng Jih-Jeng Huang CRC Press Taylor Si Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A CHAPMAN St HALL BOOK
Preface Authors xi xiii Chapter 1 Introduction 1 1.1 Profile of Multiple Criterion Decision Making 1 1.2 Historical Development of Multiple Attribute Decision Making 2 1.3 Historical Development of Multiple Objective Decision Making 4 1.4 Introduction to Fuzzy Sets 7 1.4.1 Basic Concepts 7 1.4.2 Fuzzy Arithmetic Operations 9 1.4.3 Extension Principle 9 1.4.4 a-cut Arithmetic 10 1.4.5 Ranking Fuzzy Numbers 11 1.5 Outline of this Book 11 Part I Concepts and Theory of MADM Chapter 2 Analytic Hierarchy Process 15 2.1 Eigenvalue Method 15 2.2 Geometric Mean Method 20 2.3 Linear Programming Method 22 2.4 Fuzzy Lambda-Max Method 25 Chapter 3 Analytic Network Process and Fuzzy Analytic Network Process 29 3.1 Analytic Network Process 29 3.2 Fuzzy Analytic Network Process 35 3.3 Matrix Method for Fuzzy Analytic Network Process 44 Chapter 4 Simple Additive Weighting Method ^. 55 4.1 Simple Additive Weighting Method 55 4.2 Fuzzy Simple Additive Weighting 57 4.3 Fuzzy Simple Additive Weighting for the Best Plan: Example of an Environment-Watershed Plan 60 4.3.1 Building a Hierarchical Structure of Environment-Watershed Evaluation Criteria 61
VI 4.3.1.1 Determining the Evaluation Criteria Weights 62 4.3.2 Fuzzy Numbers 63 4.3.3 Linguistic Variables 64 4.3.4 Fuzzy Analytic Hierarchy Process 65 4.4 Fuzzy Multiple Criteria Decision-Making 66 Chapter 5 TOPSIS and VIKOR 69 5.1 TOPSIS 69 5.2 VIKOR 71 5.3 Comparing VIKOR and TOPSIS 75 5.4 Fuzzy TOPSIS 76 Chapter 6 ELECTRE Method 81 6.1 ELECTRE 1 81 6.2 ELECTRE II 82 6.3 ELECTRE III 86 6.4 ELECTRE IV 90 Chapter 7 PROMETHEE Method 95 7.1 The Notion of the PROMETHEE Method 95 7.2 PROMETHEE I, II, III, IV 96 7.2.1 PROMETHEE 1 98 7.2.2 PROMETHEE II 99 7.2.3 PROMETHEE III 99 7.2.4 PROMETHEE IV 100 7.3 Example for House Selection 102 Chapter 8 Gray Relational Model 103 8.1 Concepts of Gray System and Gray Relation 103 8.2 Gray Relation Model 104 8.3 Gray Relation for Multiple Criteria Evaluation 105 8.4 Example for Car Selection 107 Chapter 9 Fuzzy Integral Technique 109 9.1 Fuzzy Integral 109 9.2 Hierarchical Fuzzy Integral 114 Chapter 10 Rough Sets 123 10.1 Information System 124 10.2 Indiscernible Relation 124
vii 10.3 Approximation of Sets and Approximation of Accuracy 125 10.4 Reduction of Attributes 126 10.5 Decision Table and Decision Rules 126 10.6 The Analytical Procedure of Data Analysis 127 Chapter 11 Structural Model 131 11.1 Interpretive Structural Modeling Method 131 11.2 DEMATEL Method 134 11.3 Fuzzy Cognition Maps 138 Part II Applications of MADM Chapter 12 AHP: An Application 143 12.1 Introduction 143 12.2 Planning and Design Alternatives Evaluation Model 144 12.2.1 Building Hierarchical Structure of Evaluation Criteria 144 12.2.2 Determining the Evaluation Criteria Weights 144 12.3 Case of Selecting the Engineering Service for Public Buildings 146 12.3.1 Weights Calculation of the Evaluation Criteria 146 12.3.2 Estimating the Performance Matrix 152 12.3.3 Ranking the Alternatives 154 12.4 Discussions 154 12.5 Conclusion 156 Chapter 13 VIKOR Technique with Applications Based on DEMATEL andanp 157 13.1 Introduction 157 13.2 Novel Hybrid Multiple Criteria Decision Making model 158 13.2.1 DEMATEL 158 13.2.2 Analytic Network Process 161 13.2.3 VIKOR Method i 164 13.3 Numerical Example with Applications 166 13.4 Discussions and Comparisons 169 13.5 Conclusions 171 Chapter 14 TOPSIS and VIKOR: An Application 173 14.1 Alternative Solutions 174 14.2 Evaluation Criteria 177 14.2.1 Establishing the Evaluation Criteria 177
viii 14.2.2 Assessment of Criteria Weights 178 14.3 Evaluation of the Alternatives 179 14.4 Multicriteria Optimization 179 14.4.1 Comparison of TOPSIS and VIKOR 181 14.4.2 Compromise Solution 182 14.4.3 Discussions 183 14.5 Conclusions 184 Chapter 15 ELECTRE: An Application 187 15.1 Introduction 187 15.2 Multiple Objective Equilibrium Network Design Problem... 188 15.3 Modeling the Network Improvement Problem with Multiobjective Decision Making 190 15.4 Model and the Solution of the Bilevel Multiobjective Network Design 191 15.5 Evaluation and Group Decision Making for Network Improvement Project 194 15.5.1 Consensus Ranking of Cook and Seiford 194 15.5.2 Case Study of Metropolitan Taipei 195 15.5.3 Non-inferior Solutions of Network Improvement Alternatives 196 15.5.4 Evaluation Criteria of the Network Improvement Alternatives 197 15.5.4.1 Total Travel Time Saved 197 15.5.4.2 Total Investment Cost 198 15.5.4.3 Improvement of Air Pollution 198 15.5.4.4 Complexity of Underground Cables 199 15.6 Conclusions and Recommendations 200 Chapter 16 PROMETEE: An Application 203 16.1 Introduction.^..203 16.1.1 Solar Thermal Energy 203 16.1.2 Solar Photovoltaics 204 16.1.3 Fuel Cells 204 16.1.4 Wind Energy 205 16.1.5 Biofuels 205 16.1.6 Geotherfhal Energy 205 16.1.7 Ocean Energy 206 16.1.8 Hydrogen Energy 206 16.2 Evaluation of New Energy-Development Alternatives 207 16.2.1 Application of AHP 208 16.2.2 Application of PROMETHEE 208 16.3 Conclusions 216
ix Chapter 17 Fuzzy Integral and Gray Relation: An Application 217 17.1 Introduction 217 17.2 Non-additive Type Fuzzy Multicriteria Evaluation 219 17.3 Multicriteria Evaluation through the Fuzzy Integral 219 17.4 Multiple Criteria Evaluation of the Gray Relation Model 220 17.5 Constructing the Gray Relation Model with Non- Additive Measures 220 17.6 Empirical Analysis: A Case Study of Taiwan's Junior Colleges 221 17.7 Problem Descriptions 221 17.8 Constructing Multiple Criteria Evaluation Systems 222 17.9 Analysis Procedures 222 17.10 Analysis Results and Discussions 224 17.11 Conclusions 227 Appendices 228 Chapter 18 Fuzzy Integral: An Application 233 18.1 Introduction 233 18.2 Modeling the Hierarchical Structure of the Choquet Integral... 234 18.3 Algorithm for Identifying A, 235 18.4 Empirical Case: Fuzzy Integral for Enterprise Intranet Websites 235 18.4.1 Background and Problem Statement 235 18.4.2 Constructing a Hierarchical Multiattribute Evaluation System 236 18.4.2.1 Generating Aspects and Performance Scores for Criteria 236 18.4.2.2 Determining the Grade of Criteria /Importance 236 18.4.2.3 Choquet Integral for Evaluating the Case Enterprise Intranet Websites 238 18.4.3 Results and Discussions?. 238 18.5 Conclusions 240 Appendix 18.1 241 Appendix 18.2 241 Appendix 18.3 243 Chapter 19 Rough Sets: An Application 245 19.1 Introduction 245 19.2 Illustrative Empirical Study: A Case for Making Insurance Marketing Decisions 246 19.2.1 Problem Descriptions 246 19.2.2 Empirical Process 247
x 19.3 Study of Customer Needs and Reason for No Purchase 247 19.4 Empirical Result 249 19.5 Discussions 251 19.6 Conclusions 255 Appendix 19.1 256 Appendix 19.2 256 Chapter 20 Extending the DEMATEL Method for Group Decision Making in Fuzzy Environments 257 20.1 Introduction 257 20.2 DEMATEL and Fuzzy Group Decision Making 258 20.2.1 DEMATEL Method 258 20.2.2 Fuzzy Group Decision Making 261 20.3 Analytical Procedure of the Proposed Methodology 264 20.4 Application of the Proposed Methodology 266 20.4.1 Empirical Study of an Application of the Proposed Methodology 266 20.4.2 Discussions 268 20.5 Conclusions 270 Appendix 20.1 Total-Relation Matrix T 271 Appendix 273 Bibliography 309 Index 333