Multiple Attribute Decision Making: Methods and Applications

350 Pages·2011·3.85 MB·English

by  Gwo-Hshiung Tzeng

Multiple Attribute
Decision Making
M e t h o d s a n d a p p l i c a t i o n s

Multiple Attribute
Decision Making
M e t h o d s a n d a p p l i c a t i o n s
Gwo-Hshiung Tzeng
Jih-Jeng Huang
CRC Press
Taylor & Francis Group
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Contents
Preface.......................................................................................................................xi
Authors ...................................................................................................................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 α-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
v
vi Contents
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 I .............................................................................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 I..........................................................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
Contents 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
and ANP ...........................................................................................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 ........................................................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 Contents
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 Geothermal 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
Contents 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 λ ...................................................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