E-Book, Englisch, Band 233, 1356 Seiten, eBook
Reihe: International Series in Operations Research & Management Science
State of the Art Surveys
E-Book, Englisch, Band 233, 1356 Seiten, eBook
Reihe: International Series in Operations Research & Management Science
ISBN: 978-1-4939-3094-4
Verlag: Springer US
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)
José Rui Figueira is an Associate Professor at the Technical University of Lisbon, Portugal, and researcher at CEG-IST, Center for Management Studies of Instituto Superior Técnico and LAMSADE, University of Paris-Dauphine, France. He obtained his Ph.D. in Operations Research from University of Paris-Dauphine. Professor Figueira's current research interests are in decision analysis, integer programming, network flows and multiple criteria decision aiding. His research has been published in such journals as European Journal of Operational Research, Computers & Operations Research, Journal of the Operational Research Society, Journal of Mathematical Modeling and Algorithms, European Business Review, Annals of Operations Research, Fuzzy Sets and Systems, 4OR, Socio-Economic Planning Sciences, Journal of Multi-Criteria Decision Analysis,and OMEGA. He is the co-editor of the book, 'Multiple Criteria Decision Analysis: State of the Art Surveys, Springer Science + Business Media, Inc, 2005. He is the currently serves as Editor of the Newsletter of the European Working Group on Multiple Criteria Decision Aiding and one of the coordinators of this group. He is also member of the Executive Committee of the International Society of Multiple Criteria Decision Making.Salvatore Greco is a full professor at the Department of Economics, Catania University. His main research interests are in the field of multicriteria decision aid, in the application of the rough set approach to decision analysis, in the axiomatic foundation of multicriteria methodology and in the fuzzy integral approach to MCDA. In these fields he cooperates with many researchers of different countries He received the Best Theoretical Paper Award, by the Decision Sciences Institute (Athens, 1999). Together with Benedetto Matarazzo, he organized the VII International Summer School on MCDA (Catania, 2000). He is author of many articles published in important international journals and specialized books. He has been invited professor at Poznan Technical University and at the University of Paris Dauphine. He has been invited speakers in important international conferences. He is referee of the most relevant journals in the field of decision analysis.Matthias Ehrgott grew up in the Palatinate region of Germany. He studied mathematics, computer science and economics at the University of Kaiserslautern in Germany. In 2000 Matthias joined the Department of Engineering Science as a Lecturer. In 2002 he was promoted to Senior Lecturer and in 2004 to Associate Professor. From 2006 to 2008 he also held the position of directeur de recherche at Laboratoire d'Informatique de Nantes Atlantique in France. In 2011 he became Professor and the seventh Head of the Department of Engineering Science. Matthias left the University of Auckland in 2013 to take up a professorship in the Department of Management Science at the University of Lancaster.
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Weitere Infos & Material
1;Contents;6
2;List of Figures;10
3;List of Tables;16
4;Introduction;20
4.1;1 Ten Years of Success of Multiple Criteria Decision Analysis and Reasons for This New Edition;20
4.2;2 Human Reflection About Decision;21
4.3;3 Technical Reflection About Decision: MCDA Researchers Before MCDA;22
4.4;4 Reasons for This Collection of State-of-the-Art Surveys;24
4.5;5 A Guided Tour of the Book;25
4.5.1;5.1 Part I: The History and Current State of MCDA;25
4.5.2;5.2 Part II: Foundations of MCDA;26
4.5.3;5.3 Part III: Outranking Methods;26
4.5.4;5.4 Part IV: Multi-attribute Utility and Value Theories;27
4.5.5;5.5 Part V: Non-classical MCDA Approaches;28
4.5.6;5.6 Part VI: Multiobjective Optimization;29
4.5.7;5.7 Part VII: Applications;31
4.5.8;5.8 Part VIII: MCDM Software;33
4.6;References;33
5;Part I The History and Current State of MCDA;35
5.1;1 An Early History of Multiple Criteria Decision Making;36
5.1.1;1.1 Introduction;36
5.1.2;1.2 Early Developments;37
5.1.2.1;1.2.1 Moral Algebra;38
5.1.2.2;1.2.2 Some Early Voting Results;38
5.1.2.3;1.2.3 Pareto-Optimality;39
5.1.2.4;1.2.4 Indifference Curves and Edgeworth Box;40
5.1.2.5;1.2.5 Set Theory, Number Theory;40
5.1.3;1.3 Origins of Decision Analysis, Utility Theory;41
5.1.3.1;1.3.1 Economics as a Modern Science;41
5.1.3.2;1.3.2 Expected Subjective Utility;41
5.1.3.3;1.3.3 Theory of Games;42
5.1.3.4;1.3.4 Revealed Preferences;42
5.1.3.5;1.3.5 Bounded Rationality;43
5.1.3.6;1.3.6 Social Choice and Individual Values;44
5.1.3.7;1.3.7 Theory of Value;44
5.1.3.8;1.3.8 Games and Decisions;44
5.1.3.9;1.3.9 Behavioral Decision Theory;45
5.1.3.10;1.3.10 Utility Theory;46
5.1.3.11;1.3.11 The `Outranking Methods';46
5.1.4;1.4 Origins of Multiple Objective Mathematical Programming;47
5.1.4.1;1.4.1 Efficient Vectors;47
5.1.4.2;1.4.2 Goal Programming;48
5.1.4.3;1.4.3 Parametric Programming;48
5.1.4.4;1.4.4 Automatic Control;49
5.1.4.5;1.4.5 Restricted Bargaining;49
5.1.5;1.5 Conclusion;49
5.2;2 Paradigms and Challenges;51
5.2.1;2.1 What Are the Expectations that Multicriteria Decision Aiding (MCDA) Responds To?;52
5.2.1.1;2.1.1 What Is Reasonable to Expect from Decision Aiding (DA)?;52
5.2.1.2;2.1.2 Why Is DA More Often Multicriteria than Monocriterion?;53
5.2.1.3;2.1.3 Can MCDA Be Always Totally Objective?;54
5.2.2;2.2 Three Basic Concepts;55
5.2.2.1;2.2.1 Alternative, and More Generally, Potential Action;55
5.2.2.2;2.2.2 Criterion and Family of Criteria;56
5.2.2.3;2.2.3 Problematic as a Way in Which DA May Be Envisaged;58
5.2.3;2.3 How to Take into Account Imperfect Knowledge and Ill-Determination?;59
5.2.4;2.4 An Operational Point of View;61
5.2.4.1;2.4.1 About Multicriteria Aggregation Procedures;62
5.2.4.2;2.4.2 Approach Based on a Synthesizing Criterion;63
5.2.4.3;2.4.3 The Operational Approach Based on a Synthesizing Preference Relational System;64
5.2.4.4;2.4.4 About Other Operational Approaches;65
5.2.5;2.5 Conclusion;65
5.2.6;References;67
6;Part II Foundations of MCDA;72
6.1;3 Preference Modelling;73
6.1.1;3.1 Introduction;74
6.1.2;3.2 Purpose;74
6.1.3;3.3 Nature of Information;76
6.1.4;3.4 Notation and Basic Definitions;77
6.1.5;3.5 Languages;79
6.1.5.1;3.5.1 Classic Logic;80
6.1.5.2;3.5.2 Fuzzy Sets;80
6.1.5.3;3.5.3 Four-Valued Logics;84
6.1.6;3.6 Preference Structures;84
6.1.6.1;3.6.1 "426830A P, I "526930B Structures;85
6.1.6.2;3.6.2 Extended Structures;88
6.1.6.2.1;3.6.2.1 Preference Relations on n Ordered Points;88
6.1.6.2.2;3.6.2.2 Several Preference Relations;89
6.1.6.2.3;3.6.2.3 Incomparability;90
6.1.6.3;3.6.3 Valued Structures;91
6.1.7;3.7 Domains and Numerical Representations;95
6.1.7.1;3.7.1 Representation Theorems;95
6.1.7.2;3.7.2 Minimal Representation;99
6.1.7.2.1;3.7.2.1 Total Order, Weak Order;99
6.1.7.2.2;3.7.2.2 Semi-order;100
6.1.7.2.3;3.7.2.3 Interval Order;102
6.1.7.2.4;3.7.2.4 PQI Interval Order;102
6.1.8;3.8 Extending Preferences to Sets;103
6.1.8.1;3.8.1 Complete Uncertainty;104
6.1.8.2;3.8.2 Opportunity Sets;106
6.1.8.3;3.8.3 Sets as Final Outcomes;107
6.1.8.4;3.8.4 An Overview to Related Theories;108
6.1.9;3.9 Logic of Preferences;110
6.1.10;3.10 Conclusion;113
6.1.11;References;114
6.2;4 Conjoint Measurement Tools for MCDM;126
6.2.1;4.1 Introduction and Motivation;126
6.2.1.1;4.1.1 Conjoint Measurement Models in Decision Theory;127
6.2.1.2;4.1.2 An Aside: Measuring Length;130
6.2.1.3;4.1.3 An Example: Even Swaps;135
6.2.2;4.2 Definitions and Notation;141
6.2.2.1;4.2.1 Binary Relations;141
6.2.2.2;4.2.2 Binary Relations on Product Sets;142
6.2.2.3;4.2.3 Independence and Marginal Preferences;142
6.2.3;4.3 The Additive Value Model in the ``Rich'' Case;144
6.2.3.1;4.3.1 Outline of Theory;144
6.2.3.1.1;4.3.1.1 The Case of Two Attributes;144
6.2.3.1.2;4.3.1.2 The Case of More Than Two Attributes;149
6.2.3.2;4.3.2 Statement of Results;150
6.2.3.3;4.3.3 Implementation: Standard Sequences and Beyond;153
6.2.4;4.4 The Additive Value Model in the ``Finite'' Case;154
6.2.4.1;4.4.1 Outline of Theory;154
6.2.4.2;4.4.2 Implementation: LP-Based Assessment;157
6.2.4.2.1;4.4.2.1 UTA JacquetLagrezeSiskos82UTA;159
6.2.4.2.2;4.4.2.2 MACBETH BanaVansnick94MACBETH;161
6.2.5;4.5 Extensions;163
6.2.5.1;4.5.1 Transitive Decomposable Models;164
6.2.5.2;4.5.2 Intransitive Indifference;165
6.2.5.3;4.5.3 Nontransitive Preferences;166
6.2.6;References;170
7;Part III Outranking Methods;181
7.1;5 ELECTRE Methods;182
7.1.1;5.1 Introduction: A Brief History;183
7.1.2;5.2 Main Features of ELECTRE Methods;185
7.1.2.1;5.2.1 In What Context Are ELECTRE Methods Relevant?;185
7.1.2.2;5.2.2 Modeling Preferences Using an Outranking Relation;186
7.1.2.3;5.2.3 Structure of ELECTRE Methods;186
7.1.2.4;5.2.4 About the Relative Importance of Criteria;187
7.1.2.5;5.2.5 Discriminating Thresholds;187
7.1.3;5.3 A Short Description of ELECTRE Methods;188
7.1.3.1;5.3.1 Choice Problematic;188
7.1.3.1.1;5.3.1.1 ELECTRE I;189
7.1.3.1.2;5.3.1.2 ELECTRE Iv;190
7.1.3.1.3;5.3.1.3 ELECTRE IS;191
7.1.3.2;5.3.2 Ranking Problematic;192
7.1.3.2.1;5.3.2.1 ELECTRE II;193
7.1.3.2.2;5.3.2.2 ELECTRE III;194
7.1.3.2.3;5.3.2.3 ELECTRE IV;196
7.1.3.3;5.3.3 Sorting Problematic;196
7.1.3.3.1;5.3.3.1 ELECTRE TRI;197
7.1.3.3.2;5.3.3.2 ELECTRE TRI C and ELECTRE TRI nC;198
7.1.4;5.4 Recent Developments;199
7.1.4.1;5.4.1 Robustness Concerns;199
7.1.4.2;5.4.2 Elicitation of Parameter Values;200
7.1.4.2.1;5.4.2.1 Direct Elicitation Techniques;200
7.1.4.2.2;5.4.2.2 Indirect Elicitation Techniques;200
7.1.5;5.5 Software and Applications;202
7.1.5.1;5.5.1 ELECTRE Software;202
7.1.5.2;5.5.2 The Decision Deck Project;203
7.1.5.3;5.5.3 Applications;204
7.1.6;5.6 Conclusion;204
7.1.7;References;205
7.2;6 PROMETHEE Methods;213
7.2.1;6.1 Preamble;214
7.2.2;6.2 History;214
7.2.3;6.3 Multicriteria Problems;215
7.2.4;6.4 The PROMETHEE Preference Modelling Information;218
7.2.4.1;6.4.1 Information Between the Criteria;218
7.2.4.2;6.4.2 Information Within the Criteria;219
7.2.5;6.5 The PROMETHEE I and II Rankings;222
7.2.5.1;6.5.1 Aggregated Preference Indices;222
7.2.5.2;6.5.2 Outranking Flows;223
7.2.5.3;6.5.3 The PROMETHEE I Partial Ranking;224
7.2.5.4;6.5.4 The PROMETHEE II Complete Ranking;225
7.2.5.5;6.5.5 The Profiles of the Alternatives;225
7.2.6;6.6 A Few Words About Rank Reversal;226
7.2.7;6.7 The GAIA Visual Interactive Module;228
7.2.7.1;6.7.1 The GAIA Plane;228
7.2.7.2;6.7.2 Graphical Display of the Alternatives and of the Criteria;229
7.2.7.3;6.7.3 The PROMETHEE Decision Stickdecision stick |205. The PROMETHEE Decision Axisdecision axis |205;231
7.2.8;6.8 The PROMETHEE VI Sensitivity Tool (the ``Human Brain'');233
7.2.9;6.9 PROMETHEE V: MCDA Under Constraints;234
7.2.10;6.10 FlowSort;235
7.2.11;6.11 The PROMETHEE GDSS Procedure;238
7.2.11.1;6.11.1 Phase I: Generation of Alternatives and Criteria;238
7.2.11.2;6.11.2 Phase II: Individual Evaluation by Each DM;239
7.2.11.3;6.11.3 Phase III: Global Evaluation by the Group;239
7.2.12;6.12 The D-Sight Software;240
7.2.13;References;243
7.3;7 Other Outranking Approaches;246
7.3.1;7.1 Introduction;246
7.3.2;7.2 Other Outranking Methods;247
7.3.2.1;7.2.1 QUALIFLEX;248
7.3.2.2;7.2.2 REGIME;251
7.3.2.3;7.2.3 ORESTE;255
7.3.2.4;7.2.4 ARGUS;258
7.3.2.5;7.2.5 EVAMIX;263
7.3.2.6;7.2.6 TACTIC;266
7.3.2.7;7.2.7 MELCHIOR;267
7.3.3;7.3 Pairwise Criterion Comparison Approach (PCCA);269
7.3.3.1;7.3.1 MAPPAC;273
7.3.3.2;7.3.2 PRAGMA;286
7.3.3.3;7.3.3 IDRA;293
7.3.3.4;7.3.4 PACMAN;296
7.3.4;7.4 One Outranking Method for Stochastic Data;300
7.3.4.1;7.4.1 Martel and Zaras' Method;300
7.3.5;7.5 Conclusions;305
7.3.6;References;305
8;Part IV Multiattribute Utility and Value Theories;308
8.1;8 Multiattribute Utility Theory (MAUT);309
8.1.1;8.1 Introduction;309
8.1.2;8.2 Preference Representations Under Certainty and Under Risk;311
8.1.2.1;8.2.1 Preference Functions for Certainty (Value Functions);313
8.1.2.2;8.2.2 Preference Functions for Risky Choice (Utility Functions);315
8.1.2.3;8.2.3 Comment;316
8.1.3;8.3 Ordinal Multiattribute Preference Functions for the Case of Certainty;317
8.1.3.1;8.3.1 Preference Independence;317
8.1.3.2;8.3.2 Assessment Methodologies;319
8.1.4;8.4 Cardinal Multiattribute Preference Functions for the Case of Risk;321
8.1.4.1;8.4.1 Utility Independence;322
8.1.4.2;8.4.2 Additive Independence;323
8.1.4.3;8.4.3 Assessment Methodologies;324
8.1.5;8.5 Measurable Multiattribute Preference Functions for the Case of Certainty;324
8.1.5.1;8.5.1 Weak Difference Independence;325
8.1.5.2;8.5.2 Difference Independence;326
8.1.5.3;8.5.3 Assessment Methodologies;328
8.1.5.3.1;8.5.3.1 Verification of the Independence Conditions;328
8.1.5.3.2;8.5.3.2 Assessment of the Measurable Value Functions;329
8.1.5.4;8.5.4 Goal Programming and Measurable Multiattribute Value Functions;330
8.1.5.4.1;8.5.4.1 Goal Programming as an Approximation to Multiattribute Preferences;331
8.1.6;8.6 The Relationships among the Multiattribute Preference Functions;334
8.1.6.1;8.6.1 The Additive Functions;334
8.1.6.2;8.6.2 The Multiplicative Functions;335
8.1.7;8.7 Concluding Remarks;336
8.1.8;References;337
8.2;9 UTA Methods;339
8.2.1;9.1 Introduction;340
8.2.1.1;9.1.1 General Philosophy;340
8.2.1.2;9.1.2 The Disaggregation-Aggregation Paradigm;341
8.2.1.3;9.1.3 Historical Background;342
8.2.2;9.2 The UTA Method;344
8.2.2.1;9.2.1 Principles and Notation;344
8.2.2.2;9.2.2 Development of the UTA Method;345
8.2.2.3;9.2.3 The UTASTAR Algorithm;348
8.2.2.4;9.2.4 Robustness Analysis;351
8.2.2.5;9.2.5 A Numerical Example;352
8.2.3;9.3 Variants of the UTA Method;356
8.2.3.1;9.3.1 Alternative Optimality Criteria;356
8.2.3.2;9.3.2 Meta-UTA Techniques;360
8.2.3.3;9.3.3 Stochastic UTA Method;361
8.2.3.4;9.3.4 UTA-Type Sorting Methods;363
8.2.3.5;9.3.5 Other Variants and Extensions;366
8.2.3.6;9.3.6 Other Disaggregation Methods;367
8.2.4;9.4 Applications and UTA-Based DSS;370
8.2.5;9.5 Concluding Remarks and Future Research;378
8.2.6;References;379
8.3;10 The Analytic Hierarchy and Analytic Network Processes for the Measurement of Intangible Criteria and for Decision-Making;387
8.3.1;10.1 Introduction;388
8.3.2;10.2 Pairwise Comparisons; Inconsistency and the Principal Eigenvector;390
8.3.3;10.3 Stimulus Response and the Fundamental Scale;395
8.3.3.1;10.3.1 Validation Example;398
8.3.3.2;10.3.2 Clustering and Homogeneity; Using Pivots to Extend the Scale from 1–9 to 1–?;399
8.3.4;10.4 Hospice Decision;400
8.3.5;10.5 Rating Alternatives One at a Time in the AHP: Absolute\ Measurement;409
8.3.5.1;10.5.1 Evaluating Employees for Salary Raises;410
8.3.6;10.6 Paired Comparisons Imply Dependence;411
8.3.7;10.7 When Is a Positive Reciprocal Matrix Consistent?;413
8.3.8;10.8 In the Analytic Hierarchy Process Additive Composition Is Necessary;415
8.3.9;10.9 Benefits, Opportunities, Costs and Risks;416
8.3.10;10.10 On the Admission of China to the World Trade Organization;417
8.3.11;10.11 The Analytic Network Process;421
8.3.11.1;10.11.1 The Classic AHP School Example as an ANP Model;426
8.3.11.2;10.11.2 Criteria Weights Automatically Derived from Supermatrix;427
8.3.12;10.12 Two Examples of Estimating Market Share: The ANP with a Single Benefits Control Criterion;428
8.3.12.1;10.12.1 Example 1: Estimating the Relative Market Share of Walmart, Kmart and Target;429
8.3.12.1.1;10.12.1.1 The Unweighted Supermatrix;429
8.3.12.1.2;10.12.1.2 The Cluster Matrix;430
8.3.12.1.3;10.12.1.3 The Weighted Supermatrix;431
8.3.12.1.4;10.12.1.4 Synthesized Results from the Limit Supermatrix;433
8.3.12.2;10.12.2 Example 2: US Athletic Footwear Market in 2000;434
8.3.12.2.1;10.12.2.1 Clusters and Elements (Nodes);434
8.3.13;10.13 Outline of the Steps of the ANP;436
8.3.14;10.14 Complex Decisions with Dependence and Feedback;439
8.3.14.1;10.14.1 The National Missile Defense Example;439
8.3.15;10.15 Synthesis of Individual Judgments into a Representative Group Judgment;441
8.3.16;10.16 Conclusions;442
8.3.17;References;443
8.4;11 On the Mathematical Foundations of MACBETH;444
8.4.1;11.1 Introduction;444
8.4.2;11.2 Previous Research and Software Evolution;447
8.4.3;11.3 Types of Preferential Information;448
8.4.3.1;11.3.1 Type 1 Information;448
8.4.3.2;11.3.2 Type 1+2 Information;449
8.4.4;11.4 Numerical Representation of the Preferential Information;449
8.4.4.1;11.4.1 Type 1 Scale;449
8.4.4.2;11.4.2 Type 1+2 Scale;450
8.4.5;11.5 Consistency: Inconsistency;450
8.4.6;11.6 Consistency Test for Preferential Information;452
8.4.6.1;11.6.1 Testing Procedures;452
8.4.6.2;11.6.2 Pre-test of the Preferential Information;452
8.4.6.3;11.6.3 Consistency Test for Type 1 Information;453
8.4.6.3.1;11.6.3.1 Consistency Test for Incomplete (? = ?) Type 1 Information;453
8.4.6.3.2;11.6.3.2 Consistency Test for Complete (? = ?) Type 1 Information;453
8.4.6.4;11.6.4 Consistency Test for Type 1+2 Information;454
8.4.7;11.7 Dealing with Inconsistency;454
8.4.7.1;11.7.1 Systems of Incompatible Constraints;455
8.4.7.2;11.7.2 Example 1;456
8.4.7.3;11.7.3 Identifying Constraints which Cause Inconsistency;458
8.4.7.4;11.7.4 Augmentation: Reduction in a Judgement with p Categories;461
8.4.7.4.1;11.7.4.1 Preliminaries;461
8.4.7.4.2;11.7.4.2 Exploitation of the Constraints of SEI;462
8.4.7.4.3;11.7.4.3 Search for Suggestions;463
8.4.7.5;11.7.5 Example 2;465
8.4.8;11.8 The MACBETH Scale;466
8.4.8.1;11.8.1 Definition of the MACBETH Scale;466
8.4.8.2;11.8.2 Discussing the Uniqueness of the Basic MACBETH Scale;467
8.4.8.3;11.8.3 Presentation of the MACBETH Scale;468
8.4.8.4;11.8.4 Determining by Hand the Basic MACBETH Scale;469
8.4.9;11.9 Discussion About a Scale;473
8.4.10;11.10 MACBETH and MCDA;474
8.4.11;References;476
9;Part V Non-classical MCDA Approaches;487
9.1;12 Dealing with Uncertainties in MCDA;488
9.1.1;12.1 What is Uncertainty?;489
9.1.1.1;12.1.1 Internal Uncertainty;490
9.1.1.2;12.1.2 External Uncertainty;490
9.1.2;12.2 Sensitivity Analysis and Related Methods;493
9.1.3;12.3 Probabilistic Models and Expected Utility;495
9.1.4;12.4 Pairwise Comparisons;500
9.1.5;12.5 Risk Measures as Surrogate Criteria;503
9.1.6;12.6 Scenario Planning and MCDA;506
9.1.7;12.7 Implications for Practice;512
9.1.8;References;513
9.2;13 Decision Rule Approach;518
9.2.1;13.1 Introduction;519
9.2.2;13.2 Dominance-Based Rough Set Approach (DRSA);522
9.2.2.1;13.2.1 Data Table;522
9.2.2.2;13.2.2 Dominance Principle;524
9.2.2.3;13.2.3 Decision Rules;525
9.2.2.4;13.2.4 Rough Approximations;526
9.2.2.5;13.2.5 Properties of Rough Approximations;529
9.2.2.6;13.2.6 Quality of Approximation, Reducts and Core;532
9.2.2.7;13.2.7 Importance and Interaction Among Criteria;534
9.2.3;13.3 Variable Consistency Dominance-Based Rough Set Approach (VC-DRSA);535
9.2.4;13.4 Induction of Decision Rules from Rough Approximations of Upward and Downward Unions of Decision Classes;537
9.2.4.1;13.4.1 A Syntax of Decision Rules Involving Dominance with Respect to Partial Profiles;537
9.2.4.2;13.4.2 Different Strategies of Decision Rule Induction;541
9.2.4.3;13.4.3 Application of Decision Rules;541
9.2.4.4;13.4.4 Decision Trees: An Alternative to Decision Rules;544
9.2.5;13.5 Extensions of DRSA;545
9.2.5.1;13.5.1 DRSA with Joint Consideration of Dominance, Indiscernibility and Similarity Relations;545
9.2.5.2;13.5.2 DRSA and Interval Orders;547
9.2.5.3;13.5.3 Fuzzy DRSA: Rough Approximations by Means of Fuzzy Dominance Relations;548
9.2.5.4;13.5.4 DRSA with Missing Values: Multiple-Criteria Classification Problem with Missing Values;550
9.2.5.5;13.5.5 DRSA for Decision Under Uncertainty;551
9.2.5.6;13.5.6 DRSA for Hierarchical Structure of Attributes and Criteria;552
9.2.6;13.6 DRSA for Multiple-Criteria Choice and Ranking;553
9.2.6.1;13.6.1 Pairwise Comparison Table (PCT) as a Preference Information and a Learning Sample;554
9.2.6.2;13.6.2 Multigraded Dominance;555
9.2.6.3;13.6.3 Induction of Decision Rules from Rough Approximations of Graded Preference Relations;557
9.2.6.4;13.6.4 Use of Decision Rules for Decision Support;558
9.2.6.5;13.6.5 Illustrative Example;559
9.2.6.6;13.6.6 Fuzzy Preferences;562
9.2.6.7;13.6.7 Preferences Without Degree of Preferences;563
9.2.7;13.7 DRSA and Operations Research Problems;563
9.2.7.1;13.7.1 DRSA to Interactive Multiobjective Optimization (IMO-DRSA);564
9.2.7.2;13.7.2 DRSA to Interactive Evolutionary Multiobjective Optimization;564
9.2.7.3;13.7.3 DRSA to Decision Under Uncertainty and Time Preference;565
9.2.8;13.8 Conclusions;566
9.2.9;References;568
9.3;14 Fuzzy Measures and Integrals in MCDA;574
9.3.1;14.1 Introduction;574
9.3.2;14.2 Measurement Theoretic Foundations;577
9.3.2.1;14.2.1 Basic Notions of Measurement, Scales;577
9.3.2.2;14.2.2 Bipolar and Unipolar Scales;579
9.3.2.3;14.2.3 Construction of the Measurement Scales and Absolute References Levels;580
9.3.3;14.3 Unipolar Scales;581
9.3.3.1;14.3.1 Notion of Interaction: A Motivating Example;581
9.3.3.2;14.3.2 Capacities and Choquet Integral;582
9.3.3.3;14.3.3 Construction of Utility Functions;584
9.3.3.3.1;14.3.3.1 Difficulty of the Construction of Utility Functions;584
9.3.3.3.2;14.3.3.2 General Method for Building Utility Functions;585
9.3.3.3.3;14.3.3.3 Construction of Utility Functions Without any Commensurability Assumption;586
9.3.3.4;14.3.4 Justification of the Use of the Choquet Integral;586
9.3.3.4.1;14.3.4.1 Justification Through Information on the Binary Alternatives;586
9.3.3.4.2;14.3.4.2 Axiomatization of the Choquet Integral as an Aggregation Function;588
9.3.3.4.3;14.3.4.3 Axiomatizations of the Choquet Integral with Utility Functions;589
9.3.3.5;14.3.5 Shapley Value and Interaction Index;590
9.3.3.6;14.3.6 k-Additive Measures;593
9.3.3.6.1;14.3.6.1 Definition of the k-Additive Measures;593
9.3.3.6.2;14.3.6.2 Axiomatic Characterization of the Choquet Integral w.r.t. 2-Additive Measures;594
9.3.3.7;14.3.7 Final Recommendation and Identification of Capacities;595
9.3.3.7.1;14.3.7.1 Preferential Information;595
9.3.3.7.2;14.3.7.2 Identification of a Capacity, and Associated Recommendation;596
9.3.3.7.3;14.3.7.3 Robust Preference Relations;596
9.3.3.7.4;14.3.7.4 Explanation of the Recommendation;597
9.3.4;14.4 Bipolar Scales;598
9.3.4.1;14.4.1 A Motivating Example;598
9.3.4.2;14.4.2 The Symmetric Choquet Integral and Cumulative Prospect Theory;599
9.3.4.2.1;14.4.2.1 Definitions;599
9.3.4.2.2;14.4.2.2 Application to the Example;600
9.3.4.3;14.4.3 Bi-capacities and the Corresponding Integral;601
9.3.4.4;14.4.4 Representation of the Motivating Example;603
9.3.4.5;14.4.5 General Method for Building Utility Functions;605
9.3.4.6;14.4.6 Justification of the Use of the Generalized Choquet Integral;606
9.3.4.6.1;14.4.6.1 Required Information;606
9.3.4.6.2;14.4.6.2 Measurement Conditions;607
9.3.4.7;14.4.7 Shapley Value and Interaction Index;608
9.3.4.8;14.4.8 Particular Models;609
9.3.4.9;14.4.9 Identification of Bi-capacities;610
9.3.5;14.5 Ordinal Scales;610
9.3.5.1;14.5.1 Introduction;610
9.3.5.2;14.5.2 The Sugeno Integral;612
9.3.5.3;14.5.3 Symmetric Ordinal Scales and the Symmetric Sugeno Integral;613
9.3.5.4;14.5.4 A Model of Decision Based on the Sugeno Integral;615
9.3.5.5;14.5.5 The Lexicographic Sugeno Integral;616
9.3.5.6;14.5.6 Identification of Capacities;618
9.3.6;14.6 Concluding Remarks;618
9.3.7;References;619
9.4;15 Verbal Decision Analysis;625
9.4.1;15.1 Introduction;625
9.4.1.1;15.1.1 Features of Unstructured Decision Problems;626
9.4.2;15.2 Main Principles of Verbal Decision Analysis;627
9.4.2.1;15.2.1 Natural Language of a Problem Description;627
9.4.2.2;15.2.2 Psychological Basis for Decision Rules Elaboration;628
9.4.2.3;15.2.3 Theoretical Basis for Decision Rules Elaboration;629
9.4.2.4;15.2.4 Consistency Check of Decision Maker's Information;630
9.4.2.5;15.2.5 Explanation of the Analysis Result;631
9.4.3;15.3 Decision Methods for Multiple Criteria Alternatives' Ranking;631
9.4.3.1;15.3.1 Problem Formulation;631
9.4.3.2;15.3.2 The Joint Ordinal Scale: Method ZAPROS-LM;633
9.4.3.2.1;15.3.2.1 Verification of the Structure of the Decision Maker's Preferences;636
9.4.3.3;15.3.3 Joint Scale for Quality Variation: ZAPROS III;637
9.4.3.4;15.3.4 Goal Oriented Process for Quality Variations: STEP-ZAPROS;639
9.4.3.5;15.3.5 Working in the Space of Real Alternatives: UniCombos;641
9.4.4;15.4 Decision Methods for Multiple Criteria Alternatives' Classification;642
9.4.4.1;15.4.1 Problem Formulation;643
9.4.4.2;15.4.2 An Ordinal Classification Approach: ORCLASS;643
9.4.4.3;15.4.3 Effectiveness of Preference Elicitation;644
9.4.4.4;15.4.4 Class Boundaries;645
9.4.4.5;15.4.5 Real Alternatives Classification: SAC and CLARA;646
9.4.4.6;15.4.6 Hierarchical Ordinal Classification;647
9.4.5;15.5 Place of Verbal Decision Analysis in MCDA;648
9.4.5.1;15.5.1 Multi Attribute Utility Theory and Verbal Decision Analysis Methods;648
9.4.5.2;15.5.2 Practical Value of the Verbal Decision Analysis Approach;652
9.4.6;15.6 Conclusion;653
9.4.7;References;653
9.5;16 A Review of Fuzzy Sets in Decision Sciences: Achievements, Limitations and Perspectives;657
9.5.1;16.1 Introduction;657
9.5.2;16.2 Membership Functions in Decision-Making;660
9.5.2.1;16.2.1 Membership Functions and Truth Sets in Decision Analysis;660
9.5.2.2;16.2.2 Truth-Sets as Value Scales: The Meaning of End-Points;661
9.5.2.3;16.2.3 Truth-Sets as Value Scales: Quantitative or Qualitative?;662
9.5.2.4;16.2.4 From Numerical to Fuzzy Value Scales;664
9.5.2.4.1;16.2.4.1 Evaluations by Pairs of Values;664
9.5.2.4.2;16.2.4.2 Linguistic vs. Numerical Scales;665
9.5.3;16.3 The Two Meanings of Fuzzy Preference Relations;667
9.5.3.1;16.3.1 Unipolar vs. Bipolar Fuzzy Relations;667
9.5.3.2;16.3.2 Fuzzy Strict Preference Relations;668
9.5.3.3;16.3.3 Fuzzy Preference Relations Expressing Uncertainty;669
9.5.3.4;16.3.4 Transitivity and Arrow's Theorem;670
9.5.4;16.4 Fuzzy Outranking Relations in Multicriteria Decision Problems;672
9.5.4.1;16.4.1 Fuzzy Concordance Relations;673
9.5.4.2;16.4.2 Fuzzy Discordance Relations and the Veto Principle;675
9.5.4.3;16.4.3 Choosing, Ranking and Sorting with Fuzzy Preference Relations;677
9.5.5;16.5 Fuzzy Connectives for Decision Evaluation in the Qualitative Setting;680
9.5.5.1;16.5.1 Aggregation Operations: Qualitative or Quantitative;681
9.5.5.2;16.5.2 Refinements of Qualitative Aggregation Operations;682
9.5.5.3;16.5.3 Numerical Encoding of Qualitative Aggregation Functions;686
9.5.5.4;16.5.4 Bipolarity in Qualitative Evaluation Processes;688
9.5.6;16.6 Uncertainty Handling in Decision Evaluation Using Fuzzy Intervals;690
9.5.6.1;16.6.1 Fuzzy Weighted Averages;690
9.5.6.2;16.6.2 Fuzzy Extensions of the Analytical Hierarchy Process;695
9.5.7;16.7 Comparing Fuzzy Intervals: A Constructive Setting;698
9.5.7.1;16.7.1 Four Views of Fuzzy Intervals;699
9.5.7.2;16.7.2 Constructing Fuzzy Interval Ranking Methods;701
9.5.7.2.1;16.7.2.1 Metric Approach;702
9.5.7.2.2;16.7.2.2 Random Interval Approach;703
9.5.7.2.3;16.7.2.3 Imprecise Probability Approach;703
9.5.7.2.4;16.7.2.4 Gradual Number Approach;704
9.5.8;16.8 Conclusion;705
9.5.9;References;706
10;Part VI Multiobjective Optimization;712
10.1;17 Vector and Set Optimization;713
10.1.1;17.1 Introduction;713
10.1.2;17.2 Pre- and Partial Orders;715
10.1.3;17.3 Vector Optimization;718
10.1.3.1;17.3.1 Optimality Concepts;718
10.1.3.2;17.3.2 Existence Results;723
10.1.3.3;17.3.3 Application: Field Design of a Magnetic Resonance System;732
10.1.3.4;17.3.4 Vector Optimization with a Variable Ordering Structure;735
10.1.4;17.4 Set Optimization;746
10.1.4.1;17.4.1 Vector Approach;746
10.1.4.2;17.4.2 Set Approach;748
10.1.5;References;753
10.2;18 Continuous Multiobjective Programming;756
10.2.1;18.1 Introduction;756
10.2.2;18.2 Problem Formulation and Solution Concepts;758
10.2.2.1;18.2.1 Partial Orders and Pareto Optimality;758
10.2.2.2;18.2.2 Cones and Nondominated Outcomes;759
10.2.2.3;18.2.3 Domination Sets and Variable Cones;761
10.2.2.4;18.2.4 Local, Proper, and Approximate Solutions;762
10.2.3;18.3 Properties of the Solution Sets;763
10.2.4;18.4 Conditions for Efficiency;765
10.2.4.1;18.4.1 First Order Conditions;765
10.2.4.2;18.4.2 Second Order Conditions;767
10.2.5;18.5 Generation of the Solution Sets;767
10.2.5.1;18.5.1 Scalarization Methods;767
10.2.5.1.1;18.5.1.1 The Weighted-Sum Approach;768
10.2.5.1.2;18.5.1.2 The Weighted t-th Power Approach;768
10.2.5.1.3;18.5.1.3 The Weighted Quadratic Approach;769
10.2.5.1.4;18.5.1.4 The Guddat et al. Approach;769
10.2.5.1.5;18.5.1.5 The -Constraint Approach;770
10.2.5.1.6;18.5.1.6 The Improved -Constraint Approach;770
10.2.5.1.7;18.5.1.7 The Penalty Function Approach;771
10.2.5.1.8;18.5.1.8 The Benson Approach;772
10.2.5.1.9;18.5.1.9 Reference Point Approaches;772
10.2.5.1.10;18.5.1.10 Direction-Based Approaches;776
10.2.5.1.11;18.5.1.11 Gauge-Based Approaches;778
10.2.5.1.12;18.5.1.12 Composite and Other Approaches;779
10.2.5.2;18.5.2 Approaches Based on Non-Pareto Optimality;779
10.2.5.2.1;18.5.2.1 The Lexicographic Approach;779
10.2.5.2.2;18.5.2.2 The Max-Ordering Approach;780
10.2.5.2.3;18.5.2.3 The Lexicographic Max-Ordering Approach;781
10.2.5.2.4;18.5.2.4 The Equitability Approach;782
10.2.5.3;18.5.3 Descent Methods;783
10.2.5.4;18.5.4 Set-Oriented Methods;783
10.2.5.4.1;18.5.4.1 The Balance and Level Set Approaches;784
10.2.5.4.2;18.5.4.2 The ?-Efficiency Approach;785
10.2.5.4.3;18.5.4.3 Continuation Methods;785
10.2.5.4.4;18.5.4.4 Covering Methods;786
10.2.6;18.6 Approximation of the Pareto Set;787
10.2.6.1;18.6.1 Quality Measures for Representations;788
10.2.6.1.1;18.6.1.1 Measures of Cardinality;788
10.2.6.1.2;18.6.1.2 Measures of Coverage;788
10.2.6.1.3;18.6.1.3 Measures of Spacing;789
10.2.6.1.4;18.6.1.4 Hybrid Measures;790
10.2.6.2;18.6.2 Representation and Approximation Approaches;791
10.2.6.2.1;18.6.2.1 Representation for BOPs;791
10.2.6.2.2;18.6.2.2 Representation for MOPs;792
10.2.6.2.3;18.6.2.3 Polyhedral Approximation;794
10.2.6.2.4;18.6.2.4 Nonlinear Approximation;795
10.2.7;18.7 Specially Structured Problems;796
10.2.7.1;18.7.1 Multiobjective Linear Programming;796
10.2.7.1.1;18.7.1.1 Multicriteria Simplex Methods;798
10.2.7.1.2;18.7.1.2 Interior Point Methods;800
10.2.7.1.3;18.7.1.3 Objective Space Methods;801
10.2.7.2;18.7.2 Nonlinear MOPs;803
10.2.7.2.1;18.7.2.1 MOPs with Piecewise Linear Objectives;804
10.2.7.2.2;18.7.2.2 Quadratic MOPs;804
10.2.7.2.3;18.7.2.3 Polynomial MOPs;805
10.2.7.2.4;18.7.2.4 Fractional MOPs;805
10.2.7.3;18.7.3 Parametric Multiobjective Programming;806
10.2.7.3.1;18.7.3.1 Parametric MOPs;806
10.2.7.3.2;18.7.3.2 Parametrization of the Scalarized MOP;807
10.2.7.4;18.7.4 Bilevel Multiobjective Programming;808
10.2.7.4.1;18.7.4.1 Relationships between Bilevel Single Objective and Multiobjective Programming;808
10.2.7.4.2;18.7.4.2 Theory of Bilevel Multiobjective Programming;809
10.2.7.4.3;18.7.4.3 Methodology for Bilevel Multiobjective Programming;811
10.2.8;18.8 Current and Future Research Directions;812
10.2.8.1;18.8.1 Research on Set-Oriented Methods;813
10.2.8.2;18.8.2 Theoretical and Methodological Studies Motivated by Mathematical and Real-Life Applications;813
10.2.8.3;18.8.3 Applications in New Areas;814
10.2.8.4;18.8.4 Integration of Multiobjective Programming with Multicriteria Decision Analysis (MCDA);814
10.2.9;18.9 Conclusion;814
10.2.10;References;815
10.3;19 Exact Methods for Multi-Objective CombinatorialOptimisation;833
10.3.1;19.1 Introduction;833
10.3.1.1;19.1.1 Definitions;834
10.3.1.2;19.1.2 Computational Complexity;838
10.3.1.3;19.1.3 Connectedness of Efficient Solutions;840
10.3.1.4;19.1.4 Bounds and Bound Sets;840
10.3.1.5;19.1.5 Outlook;842
10.3.2;19.2 Extending Single Objective Algorithms;843
10.3.2.1;19.2.1 Labelling Algorithms;843
10.3.2.2;19.2.2 Greedy Algorithms;844
10.3.3;19.3 Scalarisation;845
10.3.3.1;19.3.1 Scalarisation Algorithms from the Literature;850
10.3.4;19.4 The Two-Phase Method;850
10.3.4.1;19.4.1 The Two Phase Method for Two Objectives;851
10.3.4.2;19.4.2 The Two Phase Method for Three Objectives;855
10.3.4.3;19.4.3 Two-Phase Algorithms from the Literature;856
10.3.5;19.5 Multi-Objective Branch and Bound;857
10.3.5.1;19.5.1 Branching and Node Selection;857
10.3.5.2;19.5.2 Bounding and Fathoming Nodes;858
10.3.5.3;19.5.3 Multi-Objective Branch and Bound Algorithms from the Literature;860
10.3.6;19.6 Conclusion;860
10.3.7;References;862
10.4;20 Fuzzy Multi-Criteria Optimization: Possibilistic and Fuzzy/Stochastic Approaches;867
10.4.1;20.1 Introduction;868
10.4.2;20.2 Problem Statement and Preliminaries;869
10.4.3;20.3 Single Objective Function Case;873
10.4.3.1;20.3.1 Optimization of Upper and Lower Bounds;873
10.4.3.2;20.3.2 Possibly and Necessarily Optimal Solutions;876
10.4.3.3;20.3.3 Minimax Regret Solutions and the Related Solution Concepts;881
10.4.4;20.4 Multiple Objective Function Case;884
10.4.4.1;20.4.1 Possibly and Necessarily Efficient Solutions;884
10.4.4.2;20.4.2 Efficiency Test and Possible Efficiency Test;891
10.4.4.3;20.4.3 Necessary Efficiency Test;893
10.4.4.3.1;Implicit Enumeration Algorithm Bitran;895
10.4.5;20.5 Interactive Fuzzy Stochastic Multiple Objective Programming;898
10.4.5.1;20.5.1 Fuzzy Random Variable;899
10.4.5.2;20.5.2 Brief Survey of Fuzzy Random Multiple Objective Programming;901
10.4.5.3;20.5.3 Problem Formulation;901
10.4.5.4;20.5.4 Possibilistic Expectation Model;905
10.4.5.4.1;20.5.4.1 Interactive Satisficing Method for the Possibilistic Expectation Model;907
10.4.5.5;20.5.5 Possibilistic Variance Model;908
10.4.5.5.1;20.5.5.1 Extended Dinkelbach-Type Algorithm for Solving (20.114);912
10.4.5.5.2;20.5.5.2 Interactive Satisficing Method for the Possibilistic Variance Model;913
10.4.5.6;20.5.6 Recent Topics: Random Fuzzy Multiple Objective Programming;913
10.4.6;References;914
10.5;21 A Review of Goal Programming;919
10.5.1;21.1 Introduction;919
10.5.2;21.2 Goal Programming Variants;920
10.5.2.1;21.2.1 Lexicographic Goal Programming;920
10.5.2.2;21.2.2 Weighted Goal Programming;921
10.5.2.3;21.2.3 Chebyshev Goal Programming;922
10.5.2.4;21.2.4 Extended Goal Programming;923
10.5.2.5;21.2.5 Meta Goal Programming;924
10.5.2.6;21.2.6 Multi-Choice Goal Programming;924
10.5.2.7;21.2.7 Fuzzy Goal Programming;925
10.5.2.8;21.2.8 Goal Programming with Non-standard Preferences;925
10.5.2.9;21.2.9 Integer and Binary Goal Programming;926
10.5.2.10;21.2.10 Non-linear and Fractional Goal Programming;926
10.5.3;21.3 Goal Programming as Part of a Mixed-Modelling Framework;927
10.5.3.1;21.3.1 Goal Programming as a Statistical Tool;927
10.5.3.2;21.3.2 Goal Programming and Other Distance-Metric Based Approaches;928
10.5.3.3;21.3.3 Goal Programming and Pairwise Comparison Techniques;930
10.5.3.3.1;21.3.3.1 Using the AHP to Determine Goal Programming Preferential Weights;930
10.5.3.3.2;21.3.3.2 Using Goal Programming as a Technique to Derive the Weighting Vector in AHP;930
10.5.3.4;21.3.4 Goal Programming and Other Multi-Criteria Decision Analysis Techniques;931
10.5.3.4.1;21.3.4.1 Goal Programming and Interactive Methods;931
10.5.3.4.2;21.3.4.2 Goal Programming and A Posteriori Techniques;931
10.5.3.4.3;21.3.4.3 Goal Programming and Discrete Choice/Outranking Methods;932
10.5.3.5;21.3.5 Goal Programming and Computing/Artificial Intelligence Techniques;932
10.5.3.5.1;21.3.5.1 Goal Programming and Pattern Recognition;932
10.5.3.5.2;21.3.5.2 Goal Programming and Fuzzy Logic;933
10.5.3.5.3;21.3.5.3 Goal Programming and Meta Heuristic Methods;933
10.5.3.6;21.3.6 Goal Programming and Data Envelopment Analysis;934
10.5.4;21.4 Application of Goal Programming;935
10.5.5;21.5 Conclusions;936
10.5.6;References;936
10.6;22 Interactive Nonlinear Multiobjective Optimization Methods;943
10.6.1;22.1 Introduction;943
10.6.2;22.2 Concepts;945
10.6.3;22.3 Introduction to Interactive Methods;947
10.6.4;22.4 Methods Using Aspiration Levels;950
10.6.4.1;22.4.1 Reference Point Method;950
10.6.4.2;22.4.2 GUESS Method;952
10.6.4.3;22.4.3 Light Beam Search;953
10.6.4.4;22.4.4 Other Methods Using Aspiration Levels;955
10.6.5;22.5 Methods Using Classification;955
10.6.5.1;22.5.1 Step Method;955
10.6.5.2;22.5.2 Satisficing Trade-Off Method;957
10.6.5.3;22.5.3 Reference Direction Method;959
10.6.5.4;22.5.4 NIMBUS Method;960
10.6.5.5;22.5.5 Other Methods Using Classification;963
10.6.6;22.6 Methods Where Solutions Are Compared;964
10.6.6.1;22.6.1 Chebyshev Method;964
10.6.6.2;22.6.2 NAUTILUS Method;965
10.6.6.3;22.6.3 Other Methods Where Solutions Are Compared;969
10.6.7;22.7 Methods Using Marginal Rates of Substitution;969
10.6.7.1;22.7.1 Interactive Surrogate Worth Trade-Off Method;970
10.6.7.2;22.7.2 Geoffrion-Dyer-Feinberg Method;971
10.6.7.3;22.7.3 Other Methods Using Marginal Rates of Substitution;973
10.6.8;22.8 Navigation Methods;973
10.6.8.1;22.8.1 Reference Direction Approach;973
10.6.8.2;22.8.2 Pareto Navigator Method;975
10.6.8.3;22.8.3 Pareto Navigation Method;977
10.6.8.4;22.8.4 Other Navigation Methods;978
10.6.9;22.9 Other Interactive Methods;978
10.6.10;22.10 Comparing the Methods;979
10.6.11;22.11 Conclusions;979
10.6.12;References;980
10.7;23 MCDA and Multiobjective Evolutionary Algorithms;993
10.7.1;23.1 Introduction;993
10.7.2;23.2 Multiobjective Evolutionary Algorithms;994
10.7.2.1;23.2.1 Non-dominated Sorting Genetic Algorithm (NSGA-II);996
10.7.2.2;23.2.2 Indicator-Based MOEAs;997
10.7.2.3;23.2.3 Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D);998
10.7.2.4;23.2.4 Interactive Evolutionary Algorithms;999
10.7.3;23.3 MCDM to Support the Selection from a Set of Solutions Generated by an MOEA;999
10.7.4;23.4 Integrating User Preferences in MOEA;999
10.7.4.1;23.4.1 Scaling;1001
10.7.4.2;23.4.2 Constraints;1002
10.7.4.3;23.4.3 Providing a Reference Point;1003
10.7.4.4;23.4.4 Limiting Possible Trade-Offs;1007
10.7.4.5;23.4.5 Weighting the Objective Space;1009
10.7.4.6;23.4.6 Specifying a Distribution over Utility Functions;1009
10.7.4.7;23.4.7 Approaches Based on Outranking Relations;1011
10.7.4.8;23.4.8 Approaches Based on Solution Comparison;1011
10.7.4.8.1;23.4.8.1 Determining a Representative Value Function;1012
10.7.4.8.2;23.4.8.2 Determining a Set of Compatible Value Functions;1015
10.7.4.8.3;23.4.8.3 Other Algorithmic Principles;1017
10.7.5;23.5 Summary and Open Research Questions;1019
10.7.6;References;1020
11;Part VII Applications;1025
11.1;24 Multicriteria Decision Aid/Analysis in Finance;1026
11.1.1;24.1 Introduction;1026
11.1.2;24.2 Financial Decision Making;1028
11.1.2.1;24.2.1 Issues, Concepts, and Principles;1028
11.1.2.2;24.2.2 Focus of Financial Research;1030
11.1.2.3;24.2.3 Descriptive vs. Conditional-Normative Modelling;1032
11.1.2.4;24.2.4 Decision Support for Financial Decisions;1035
11.1.2.5;24.2.5 Relevance of MCDA for Financial Decisions;1036
11.1.2.6;24.2.6 A Multicriteria Framework for Financial Decisions;1039
11.1.2.6.1;24.2.6.1 Principles;1040
11.1.2.6.2;24.2.6.2 Allocation Decisions;1041
11.1.2.6.3;24.2.6.3 Uncertainty and Risk;1041
11.1.2.6.4;24.2.6.4 A Bird's-Eye View of the Framework;1042
11.1.2.6.5;24.2.6.5 The Framework and Modern Financial Theory;1044
11.1.3;24.3 MCDA in Portfolio Decision-Making Theory;1044
11.1.3.1;24.3.1 Portfolio Selection Problem;1045
11.1.3.2;24.3.2 Background on Multicriteria Optimization;1047
11.1.3.3;24.3.3 Two Model Variants;1048
11.1.3.4;24.3.4 Bullet-Shaped Feasible Regions;1049
11.1.3.5;24.3.5 Assumptions and Nondominated Sensitivities;1052
11.1.3.6;24.3.6 Expanded Formulations and New Assumptions;1055
11.1.3.7;24.3.7 Nondominated Surfaces;1056
11.1.3.8;24.3.8 Idea of a Projection;1057
11.1.3.9;24.3.9 Further Research in MCDA in Portfolio Analysis;1058
11.1.4;24.4 MCDA in Discrete Financial Decision-Making Problems;1059
11.1.4.1;24.4.1 Outranking Relations;1060
11.1.4.2;24.4.2 Utility Functions-Based Approaches;1062
11.1.4.3;24.4.3 Decision Rule Models: Rough Set Theory;1065
11.1.4.4;24.4.4 Applications in Financial Decisions;1066
11.1.5;24.5 Conclusions and Future Perspectives;1071
11.1.6;References;1071
11.2;25 Multi-Objective Optimization and Multi-Criteria Analysis Models and Methods for Problems in the Energy Sector;1081
11.2.1;25.1 Introduction;1082
11.2.2;25.2 Multi-Objective Optimization Models and Methods for Energy Planning;1085
11.2.2.1;25.2.1 Power Generation Expansion Planning and Operation Planning;1086
11.2.2.2;25.2.2 Transmission and Distribution Network Planning;1093
11.2.2.3;25.2.3 Reactive Power Planning and Voltage Regulation;1102
11.2.2.4;25.2.4 Unit Commitment and Dispatch Problems;1105
11.2.2.5;25.2.5 Load Management;1110
11.2.2.6;25.2.6 Energy-Economy Planning Models;1113
11.2.2.7;25.2.7 Energy Markets;1115
11.2.3;25.3 Energy Planning Decisions with Discrete Alternatives;1117
11.2.3.1;25.3.1 Comparison of Power Generation Technologies;1119
11.2.3.2;25.3.2 Energy Plans and Policies;1119
11.2.3.3;25.3.3 Selection of Energy Projects;1135
11.2.3.4;25.3.4 Siting Decisions;1135
11.2.3.5;25.3.5 Energy Efficiency;1135
11.2.3.6;25.3.6 Miscellaneous;1135
11.2.3.7;25.3.7 The Choice of Criteria;1135
11.2.3.8;25.3.8 Technical Criteria;1145
11.2.3.9;25.3.9 Economic Criteria;1149
11.2.3.9.1;25.3.9.1 Costs;1149
11.2.3.9.2;25.3.9.2 Economic Performance;1151
11.2.3.10;25.3.10 Environmental Criteria;1153
11.2.3.10.1;25.3.10.1 Local Impacts;1153
11.2.3.10.2;25.3.10.2 Global Impacts;1155
11.2.3.11;25.3.11 Social Criteria;1155
11.2.3.11.1;25.3.11.1 Health Impacts;1155
11.2.3.11.2;25.3.11.2 Risks;1156
11.2.3.11.3;25.3.11.3 Development;1157
11.2.3.11.4;25.3.11.4 Acceptability;1157
11.2.3.12;25.3.12 MCDA Methods;1159
11.2.3.13;25.3.13 Uncertainty Treatment;1162
11.2.4;25.4 Conclusions;1164
11.2.5;References;1165
11.3;26 Multicriteria Analysis in Telecommunication Network Planning and Design: A Survey;1180
11.3.1;26.1 Motivation;1180
11.3.2;26.2 Overview of Current Evolutions in Telecommunication Networks and Services;1181
11.3.2.1;26.2.1 Major Technological Evolutions;1181
11.3.2.2;26.2.2 Increasing Relevance of QoS Issues in the New Technological Platforms;1185
11.3.3;26.3 Multicriteria Analysis in Telecommunication Network Planning and Design;1186
11.3.4;26.4 Review and Discussion of Applications of MA to Telecommunication Network Planning;1191
11.3.4.1;26.4.1 Routing Models;1191
11.3.4.1.1;26.4.1.1 Background Concepts;1191
11.3.4.1.2;26.4.1.2 Review of Multiple Criteria Routing Approaches;1192
11.3.4.2;26.4.2 Network Planning and Design;1217
11.3.4.3;26.4.3 Models Studying Interactions Between Telecommunication Evolution and Socio-Economic Issues;1224
11.3.5;26.5 Future Trends;1226
11.3.5.1;26.5.1 Routing Models;1227
11.3.5.2;26.5.2 Network Planning and Design and Models Studying Interactions Between Telecommunication Evolution and Socio-Economic Issues;1230
11.3.6;References;1231
11.4;27 Multiple Criteria Decision Analysis and SustainableDevelopment;1247
11.4.1;27.1 The Concept of Sustainable Development and the Incommensurability Principle;1247
11.4.2;27.2 Measuring Sustainability: The Issue of Sustainability Assessment Indexes;1253
11.4.3;27.3 A Defensible Setting for Sustainability Composite Indicators;1257
11.4.4;27.4 Warning! Not Always Rankings Have to Be Trusted …;1261
11.4.5;27.5 The Issue of the “Quality of the Social Decision Processes”;1265
11.4.6;27.6 The Issue of Consistency in Multi-Criteria Evaluation of Sustainability Policies;1270
11.4.7;27.7 Conclusion;1273
11.4.8;References;1274
11.5;28 Multicriteria Portfolio Decision Analysis for Project Selection;1280
11.5.1;28.1 Introduction;1280
11.5.2;28.2 A Formal Framework for MCPDA;1282
11.5.3;28.3 Modelling Challenges;1285
11.5.3.1;28.3.1 Structuring;1285
11.5.3.2;28.3.2 Exploring;1288
11.5.4;28.4 Application Domains;1291
11.5.4.1;28.4.1 R&D Project Selection;1291
11.5.4.2;28.4.2 Military Planning and Procurement;1294
11.5.4.3;28.4.3 Commissioning Health Services;1296
11.5.4.4;28.4.4 Environment and Energy Planning;1297
11.5.5;28.5 Conclusion and Directions for Future Research;1300
11.5.6;References;1301
12;Part VIII MCDM Software;1310
12.1;29 Multiple Criteria Decision Analysis Software;1311
12.1.1;29.1 Introduction;1311
12.1.2;29.2 General Overview of Available MCDA Software;1312
12.1.2.1;29.2.1 MADA Versus MOO Software;1312
12.1.2.2;29.2.2 MCDA Methods Implemented;1313
12.1.2.3;29.2.3 Group Decision Support;1318
12.1.2.4;29.2.4 Platform Supported;1318
12.1.3;29.3 Software Review;1319
12.1.3.1;29.3.1 1000Minds;1319
12.1.3.2;29.3.2 4eMka2/jMAF;1322
12.1.3.3;29.3.3 ACADEA;1322
12.1.3.4;29.3.4 Accord;1322
12.1.3.5;29.3.5 Analytica Optimizer;1323
12.1.3.6;29.3.6 APOGEE;1323
12.1.3.7;29.3.7 BENSOLVE;1324
12.1.3.8;29.3.8 Criterium Decision Plus (CDP);1324
12.1.3.9;29.3.9 DecideIT;1324
12.1.3.10;29.3.10 Decision Explorer®;1325
12.1.3.11;29.3.11 Decision Desktop Software (d2)/Diviz;1325
12.1.3.12;29.3.12 Decision Lab 2000/Visual PROMETHEE;1326
12.1.3.13;29.3.13 DPL 8;1326
12.1.3.14;29.3.14 D-Sight;1327
12.1.3.15;29.3.15 ELECTRE III-IV;1327
12.1.3.16;29.3.16 ELECTRE IS;1328
12.1.3.17;29.3.17 ELECTRE TRI;1328
12.1.3.18;29.3.18 Equity3;1328
12.1.3.19;29.3.19 ESY;1329
12.1.3.20;29.3.20 Expert Choice;1329
12.1.3.21;29.3.21 FGM;1329
12.1.3.22;29.3.22 FuzzME;1330
12.1.3.23;29.3.23 GeNIe & SMILE;1330
12.1.3.24;29.3.24 GUIMOO;1330
12.1.3.25;29.3.25 HIPRE 3+;1331
12.1.3.26;29.3.26 HiPriority;1331
12.1.3.27;29.3.27 HIVIEW3;1331
12.1.3.28;29.3.28 IDS Multicriteria Assessor (IDS Version 2.1);1332
12.1.3.29;29.3.29 IND-NIMBUS;1332
12.1.3.30;29.3.30 INPRE and ComPAIRS;1333
12.1.3.31;29.3.31 IRIS;1333
12.1.3.32;29.3.32 iMOLPe;1334
12.1.3.33;29.3.33 interalg;1334
12.1.3.34;29.3.34 iSight;1334
12.1.3.35;29.3.35 JAMM;1335
12.1.3.36;29.3.36 Logical Decisions;1335
12.1.3.37;29.3.37 MakeItRational;1335
12.1.3.38;29.3.38 Markex (Market Expert);1336
12.1.3.39;29.3.39 MindDecider;1336
12.1.3.40;29.3.40 MINORA;1336
12.1.3.41;29.3.41 M-MACBETH and WISED;1337
12.1.3.42;29.3.42 modeFrontier;1337
12.1.3.43;29.3.43 MOIRA and MOIRA Plus;1338
12.1.3.44;29.3.44 NAIADE;1338
12.1.3.45;29.3.45 OnBalance;1338
12.1.3.46;29.3.46 Optimus;1339
12.1.3.47;29.3.47 ParadisEO-MOEO;1339
12.1.3.48;29.3.48 Pareto Front Viewer;1339
12.1.3.49;29.3.49 Prime Decisions;1340
12.1.3.50;29.3.50 Priority Mapper;1340
12.1.3.51;29.3.51 Prism's Group Decision Support System;1340
12.1.3.52;29.3.52 PROBE;1341
12.1.3.53;29.3.53 RGDB;1341
12.1.3.54;29.3.54 RICH Decisions;1342
12.1.3.55;29.3.55 Rubis (Plug-in);1342
12.1.3.56;29.3.56 SANNA 2009;1342
12.1.3.57;29.3.57 MC-SDSS for ArcGIS;1343
12.1.3.58;29.3.58 SOLVEX;1343
12.1.3.59;29.3.59 TransparentChoice;1343
12.1.3.60;29.3.60 Triptych;1343
12.1.3.61;29.3.61 TRIMAP;1344
12.1.3.62;29.3.62 UTA Plus;1344
12.1.3.63;29.3.63 Very Good Choice;1344
12.1.3.64;29.3.64 VIP Analysis;1345
12.1.3.65;29.3.65 Visual Market/2;1345
12.1.3.66;29.3.66 VISA;1345
12.1.3.67;29.3.67 VisualUTA;1346
12.1.3.68;29.3.68 WINGDSS;1346
12.1.3.69;29.3.69 WINPRE;1346
12.1.4;29.4 Concluding Remarks;1347
12.1.5;References;1348
13;Index;1352
Introduction.- History of MCDA.- Paradigms and Challenges.- Preference Modelling.- Conjoint Measurement Tools for MCDM.- ELECTRE Methods.- PROMETHEE Methods.- Other Outranking Approaches.- MAUT - Multiattribute Utility Theory.- UTA Methods.- The Analytic Hierarchy and Analytic Network Processes for the Measurement of Intangible Criteria and for Decision-Making.- On the Mathematical Foundation of MACBETH.- Dealing with Uncertainties in MCDA.- Decision Rule Approach.- Fuzzy Measures and Integrals in MCDA.- Verbal Decision Analysis.- A Review of Fuzzy Sets in Decision Sciences: Achievements, Limitations and Perspectives.- Vector and Set Valued Optimization.- Multiobjective Continuous Optimization.- Multiobjective Combinatorial Optimization.- Fuzzy Multiple Objective Programming.- Goal Programming.- Interactive Methods.- MCDA and Evolutionary Multiobjective Optimization.- Multicriteria Decision Aid/Analysis in Finance.- MVDA and Energy Planning.- Multicriteria Analysis in Telecommunication Network Planning and Design - Problems and Issues.- Multiple Criteria Decision Analysis and Sustainable Development.- MCDA and Portfolio/Project Analysis.- Multiple Vriteria Decision Support Software.
