Trends in Multiple Criteria Decision Analysis

Trends in Multiple Criteria Decision Analysis

von: Salvatore Greco, Matthias Ehrgott, José Rui Figueira

Springer-Verlag, 2010

ISBN: 9781441959041 , 412 Seiten

Format: PDF

Kopierschutz: Wasserzeichen

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Preis: 202,29 EUR

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Mehr zum Inhalt

Trends in Multiple Criteria Decision Analysis


 

Trends in Multiple Criteria Decision Analysis

1

Contents

Contents

List of Figures

7

List of Tables

9

Introduction

11

1 Introduction

11

1 Dynamic MCDM, Habitual Domains and Competence Set Analysis for Effective Decision Making in Changeable Spaces

17

1.1 Introduction

17

1.2 Three Decision Makings in Changeable Spaces

19

1.3 Dynamics of Human Behavior

20

1.3.1 A Sketch of the Behavior Mechanism

21

1.3.2 Eight Hypotheses of Brain and Mind Operation

22

1.3.3 Paradoxical Behavior

25

1.4 Habitual Domains

27

1.4.1 Definition and Stability of Habitual Domains

28

1.4.2 Elements of Habitual Domains

30

1.4.3 Expansion and Enrichment of Habitual Domains

31

1.4.3.1 Seven Self-Perpetuating Operators

31

1.4.3.2 Eight Methods for Expanding the Habitual Domains

33

1.4.3.3 Nine Principles of Deep Knowledge

34

1.5 Competence Set Analysis

35

1.5.1 Concept of Competence Set Analysis

36

1.5.2 Research Issues of Competence Set Analysis

38

1.5.3 Innovation Dynamics

40

1.6 Decision Making in Changeable Spaces

44

1.6.1 Parameters in Decision Processes

45

1.6.2 Decision Blinds and Decision Traps

47

1.7 Conclusion

48

References

49

2 The Need for and Possible Methods of Objective Ranking

52

2.1 Introduction

52

2.2 The Need for Objective Ranking and the Issue of Objectivity

54

2.3 Basic Formulations and Assumptions

57

2.4 Why Classical Approaches Are Not Applicable in This Case

59

2.5 Reference Point Approaches for Objective Ranking

61

2.6 Examples

65

2.7 Conclusions and Further Research

69

References

70

3 Preference Function Modelling: The Mathematical Foundations of Decision Theory

72

3.1 Introduction

72

3.2 Measurement of Preference

73

3.2.1 Empirical Addition – Circumventing the Issue

74

3.2.2 Applicability of Operations on Scale Values Versus Scale Operations

75

3.3 The Principle of Reflection

76

3.4 The Ordinal Utility Claim in Economic Theory

76

3.4.1 Ordinal Utility

77

3.4.2 Optimality Conditions on Indifference Surfaces

78

3.4.3 Pareto's Claim

80

3.4.4 Samuelson's Explanation

80

3.4.5 Counter-Examples

81

3.5 Shortcomings of Utility Theory

81

3.5.1 Von Neumann and Morgenstern's Utility Theory

82

3.5.2 Addition and Multiplication Are Not Applicable to Utility Scales

82

3.5.3 Barzilai's Paradox: Utility's Intrinsic Contradiction

83

3.5.4 Utility Theory Is Neither Prescriptive Nor Normative

83

3.5.5 Von Neumann and Morgenstern's Structure Is Not Operational

84

3.6 Shortcomings of Game Theory

84

3.6.1 Undefined Sums

85

3.6.2 The Utility of a Coalition

85

3.6.3 ``The'' Value of a Two-Person Zero-Sum Game Is Ill-Defined

85

3.6.4 The Characteristic Function of Game Theory is Ill-Defined

86

3.6.5 The Essential Role of Preference

86

3.6.6 Implications

87

3.6.7 On ``Utility Functions That Are Linear in Money''

88

3.6.8 The Minimax Solution of Two-Person Zero-Sum Games

88

3.6.9 Errors Not Corrected

90

3.7 Reconstructing the Foundations

90

3.7.1 Proper Scales – Straight Lines

90

3.7.2 Strong Scales – the Real Numbers

92

3.7.3 The Axioms of an Affine Straight Line

93

3.7.3.1 Groups and Fields

93

3.7.3.2 Vector and Affine Spaces

93

3.8 Measurement Theory

94

3.9 Classical Decision Theory

95

3.9.1 Utility Theory

95

3.9.2 Undefined Ratios and Pairwise Comparisons

96

3.9.3 The Analytic Hierarchy Process

96

3.9.4 Value Theory

97

3.9.5 Group Decision Making

98

3.10 Summary

98

References

99

4 Robustness in Multi-criteria Decision Aiding

102

4.1 Introduction

103

4.2 Why Is Robustness of Interest in MCDA?

104

4.3 Robustness in MCDA: Mono-dimensional Approaches

110

4.3.1 Characterizing Mono-dimensional Approaches

110

4.3.2 With an Initial Mono-criterion Preference Model

110

4.3.3 With an Initial Multi-criteria Preference Model

113

4.3.4 With an Initial Preference Model That Is Either Mono-criterion or Multi-criteria

114

4.4 Robustness in MCDA: Multi-dimensional Approaches

114

4.4.1 Characterizing Multi-dimensional Approaches

114

4.4.2 Without Any Initial Preference Model

115

4.4.3 With an Initial Mono-criterion Preference Model

116

4.4.4 With an Initial Multi-criteria Preference Model

118

4.5 Robustness in MCDA: Other Approaches

120

4.5.1 Preliminaries

120

4.5.2 Robustness in Mathematical Programming

121

4.5.3 Obtaining Robust Conclusions from a Representative Subset S

124

4.5.4 Approaches for Judging the Robustness of a Method

126

4.5.5 Approach Allowing to Formulate Robust Conclusions in the Framework of Additive Utility Functions

128

4.5.6 Approaches to Robustness Based on the Concept of Prudent Order

130

4.6 Conclusion

131

References

134

5 Preference Modelling, a Matter of Degree

137

5.1 Introduction

137

5.2 Fuzzy and Probabilistic Connectives

139

5.3 Fuzzy Preference Structures

141

5.3.1 Fuzzy Relations

141

5.3.1.1 Properties of Fuzzy Relations

142

5.3.1.2 Special Types of Fuzzy Relations

145

5.3.2 Additive Fuzzy Preference Structures: Bottom-Up Approach

147

5.3.2.1 Classical Preference Structures

147

5.3.2.2 The Quest for Fuzzy Preference Structures: The Axiomatic Approach

148

5.3.2.3 Additive Fuzzy Preference Structures and Indifference Generators

151

5.4 Reciprocal Preference Relations

154

5.4.1 Reciprocal Relations

154

5.4.1.1 Definition

154

5.4.1.2 A Fuzzy Set Viewpoint

154

5.4.1.3 A Frequentist View

155

5.4.2 The Cycle-Transitivity Framework

155

5.4.2.1 Stochastic Transitivity

155

5.4.2.2 FG-Transitivity

156

5.4.2.3 Cycle-Transitivity

157

5.4.2.4 Cycle-Transitivity Is a General Framework

158

5.4.3 Comparison of Random Variables

161

5.4.3.1 Dice-Transitivity of Winning Probabilities

161

5.4.3.2 A Method for Comparing Random Variables

162

5.4.3.3 Artificial Coupling of Random Variables

164

5.4.3.4 Comparison of Special Independent Random Variables

165

5.4.4 Mutual Ranking Probabilities in Posets

166

References

168

6 Fuzzy Sets and Fuzzy Logic-Based Methods in Multicriteria Decision Analysis

171

6.1 Introduction

171

6.2 Fuzzy Set Based Utility Functions

172

6.3 Fuzzy Quantities Based Preference Structures Constructions

176

6.4 Mean of Maxima Defuzzification Approach

180

6.5 Fuzzy Logic-Based Construction of Preference Relations

184

6.6 Concluding Remarks

186

References

187

7 Argumentation Theory and Decision Aiding

190

7.1 Introduction

190

7.2 Decision Theory and AI

191

7.2.1 Decision Process and Decision Aiding

192

7.2.2 Preferences and Decision Aiding

193

7.3 Argumentation for Decision Support

196

7.3.1 Argumentation Theory

196

7.3.2 Argumentation-Based Decision-Support Systems

200

7.4 Arguing Over Actions: A Multiple Criteria Point of View

203

7.4.1 Arguments, Criteria and Actions

204

7.4.2 Argument Schemes for Action

207

7.4.3 Argument Schemes for the Decision-Aiding Process

212

7.5 Conclusion

213

References

214

8 Problem Structuring and Multiple Criteria Decision Analysis

222

8.1 Introduction

222

8.2 The Nature of Problems and Problem Structuring for MCDA

224

8.3 How Has Problem Structuring for MCDA Been Approached?

227

8.4 Problem Structuring Methods and the Potential for Integration with MCDA

229

8.5 Implementing Problem Structuring for MCDA

233

8.6 Case Studies in Problem Structuring for MCDA

234

8.7 MCDA as Problem Structuring

247

References

248

9 Robust Ordinal Regression

253

9.1 Introduction

254

9.2 Ordinal Regression for Multiple Criteria Ranking Problems

257

9.2.1 Concepts: Definitions and Notation

258

9.2.2 The UTA Method

259

9.2.2.1 Preference Information

260

9.2.2.2 Additive Model

260

9.2.2.3 Checking for Compatible Value Functions Through Linear Programming

261

9.3 Robust Ordinal Regression for Multiple Criteria Ranking Problems

262

9.3.1 The Preference Information Provided by the Decision Maker

263

9.3.2 Possible and Necessary Rankings

264

9.3.3 Linear Programming Constraints

265

9.3.4 Computational Issues

266

9.4 Comparison of GRIP with other MCDA Methods

267

9.4.1 Comparison of GRIP with the AHP

267

9.4.2 Comparison of GRIP with MACBETH

268

9.5 Robust Ordinal Regression for Multiple Criteria Sorting Problems

270

9.6 The Most Representative Value Function

273

9.7 Nonadditive Robust Ordinal Regression

276

9.8 Robust Ordinal Regression in Interactive Multiobjective Optimization

278

9.9 Robust Ordinal Regression in Evolutionary Interactive Multiobjective Optimization

280

9.10 Robust Ordinal Regression for Outranking Methods

284

9.11 Robust Ordinal Regression for Multiple Criteria Group Decisions

287

9.12 An Illustrative Example

288

9.13 Conclusions and Further Research Directions

291

References

292

10 Stochastic Multicriteria Acceptability Analysis (SMAA)

296

10.1 Introduction

297

10.1.1 Aims and Goals of SMAA Methods

297

10.1.2 Variants of SMAA

299

10.1.3 Related Research

299

10.2 SMAA Approach

300

10.2.1 Problem Representation

300

10.2.2 Inverse Weight Space Analysis

301

10.2.3 Generic Simulation Approach

304

10.2.4 The SMAA-2 Method

305

10.3 Modelling Uncertain Information

308

10.3.1 Representing Uncertain Criteria

309

10.3.1.1 Cardinal Criteria

309

10.3.1.2 Ordinal Criteria

309

10.3.2 Incomplete Preference Information

311

10.3.2.1 Missing Weight Information

311

10.3.2.2 Intervals for Weights

312

10.3.2.3 Intervals for Trade-Off Ratios of Criteria

313

10.3.2.4 Ordinal Preference Information

313

10.3.2.5 Implicit Weight Information

315

10.3.2.6 Non-uniform Distributions

315

10.3.2.7 Combining Preference Information

315

10.4 Implementation Techniques

316

10.4.1 Accuracy of the SMAA Computations

316

10.4.2 Efficiency of Computations

317

10.5 Applications

317

10.6 Discussion and Future Research

322

References

322

11 Multiple Criteria Approaches to Group Decision and Negotiation

327

11.1 Introduction: Group Decision and Negotiation

327

11.2 Multiple Criteria Decision Analysis in Group Decision and Negotiation

330

11.3 MCDA and Group Decision Support (GDS)

333

11.4 MCDA and Negotiations

336

11.5 Examples

338

11.6 Conclusions

343

References

343

12 Recent Developments in Evolutionary Multi-Objective Optimization

349

12.1 Introduction

350

12.2 Evolutionary Multi-objective Optimization (EMO)

350

12.2.1 EMO Principles

352

12.2.2 A Posteriori MCDM Methods and EMO

353

12.3 A Brief History of EMO Methodologies

355

12.4 Elitist EMO: NSGA-II

356

12.4.1 Sample Results

357

12.4.2 Constraint Handling in EMO

358

12.5 Applications of EMO

360

12.5.1 Spacecraft Trajectory Design

360

12.6 Salient Recent Developments of EMO

362

12.6.1 Hybrid EMO Algorithms

362

12.6.2 Multi-objectivization

363

12.6.3 Uncertainty-based EMO

364

12.6.4 EMO and Decision Making

365

12.6.5 EMO for Handling a Large Number of Objectives

366

12.6.5.1 Finding a Partial Set

366

12.6.5.2 Identifying and Eliminating Redundant Objectives

367

12.6.6 Knowledge Extraction Through EMO

368

12.6.7 Dynamic EMO

368

12.6.8 Quality Estimates for EMO

369

12.6.9 Exact EMO with Run-time Analysis

370

12.6.10 EMO with Meta-models

371

12.7 Conclusions

372

References

373

13 Multiple Criteria Decision Analysis and Geographic Information Systems

379

13.1 Introduction

379

13.2 GIS: Basic Concepts

380

13.2.1 Definition of GIS

380

13.2.2 GIS Data Models

381

13.2.3 GIS Analytical Operations

382

13.3 Brief History of GIS-MCDA

383

13.3.1 Innovation: GIS and OR/MS

383

13.3.2 Integration: Cartographic Modeling and MCDA

384

13.3.3 Proliferation: The User-oriented GIS-MCDA

385

13.4 A Survey of the GIS-MCDA Literature

386

13.4.1 Taxonomy of GIS-MCDA

386

13.4.2 GIS Components of GIS-MCDA

387

13.4.3 MCDA Components of GIS-MCDA

388

13.5 Functions of MCDA in GIS

390

13.5.1 Decision Problem Structuring

390

13.5.2 Value Scaling

390

13.5.3 Criterion Weighting

391

13.5.4 Decision Rules

391

13.5.5 Sensitivity Analysis

392

13.6 Multicriteria Spatial Decision Support Systems (MC-SDSS)

392

13.6.1 Components of MC-SDSS

392

13.6.2 Integrating GIS and MCDA

393

13.7 Conclusions: Challenges and Prospects

394

References

395

Contributors

395

Index

415