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 |  موضوع: كتاب Multiple Criteria Decision Analysis - State of the Art Surveys الثلاثاء 07 سبتمبر 2021, 2:14 am | |
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أحضرت لكم كتاب
Multiple Criteria Decision Analysis - State of the Art Surveys
Edited by
JOSÉ FIGUEIRA
University of Coimbra
SALVATORE GRECO
University of Catania
MATTHIAS EHRGOTT
University of Auckland
و المحتوى كما يلي :
Contents
List of Figures
List of Tables
Introduction
José Figueira, Salvatore Greco, Matthias Ehrgott
Human Reflection about Decision
Technical Reflection about Decision: MCDA Researchers
before MCDA
The Reasons for this Collection of State-of-the-Art Surveys
A Guided Tour of the Book
Acknowledgment to the Referees
References
Part I An Overview of MCDA Techniques Today
Paradigms and Challenges
Bernard Roy
What Are the Expectations that Multicriteria Decision Aiding
(MCDA) Responds to?
Three Basic Concepts
How to Take Into Account Imperfect Knowledge?
An Operational Point of View
Conclusion
References
Part II Foundations of MCDA
Preference Modelling
Meltem Öztürk, Alexis Tsoukiàs, Philippe Vincke
Introduction
Purpose
Nature of Information
Notation and Basic Definitions
Languages
33vi MULTIPLE CRITERIA DECISION ANALYSIS
Preference Structures
Domains and Numerical Representations
Logic of Preferences
Conclusion
References
Conjoint measurement tools for MCDM
Denis Bouyssou, Marc Pirlot
Introduction and Motivation
Definitions and Notation
The Additive Value Model in the “Rich” Case
The Additive Value Model in the “Finite” Case
Extensions
References
Part III Outranking Methods
ELECTRE Methods
JoséFigueira, Vincent Mousseau, Bernard Roy
Introduction: A Brief History
Main Features of ELECTRE Methods
A Short Description of ELECTRE Methods
Recent Developments and Future Issues
Software and Applications
Conclusion
References
PROMETHEE Methods
Jean-Pierre Brans, Bertrand Mareschal
History
Multicriteria Problems
The PROMETHEE Preference Modelling Information
The PROMETHEE I and II Rankings
The GAIA Visual Interactive Module
The PROMETHEE VI Sensitivity Tool (The “Human Brain”)
PROMETHEE V: MCDA under Constraints
The PROMETHEE GDSS Procedure
The DECISION LAB Software
References
Other Outranking Approaches
Jean-Marc Martel, Benedetto Matarazzo
Introduction
Other Outranking Methods
198Contents
Pairwise Criterion Comparison Approach
One Outranking Method for Stochastic Data
Conclusions
References
Part IV Multiattribute Utility and Value Theories
MAUT – Multiattribute Utility Theory
James S. Dyer
Introduction
Preference Representations Under Certainty and Under Risk
Ordinal Multiattribute Preference Functions for the Case of
Certainty
Cardinal Multiattribute Preference Functions for the Case of Risk
Measurable Multiattribute Preference Functions for the Case of
Certainty
The Relationships Among the Multiattribute Preference Functions
Concluding Remarks
References
UTA Methods
Yannis Siskos, Evangelos Grigoroudis, Nikolaos F. Matsatsinis
Introduction
The UTA Method
Variants of the UTA Method
Applications and UTA-based DSS
Concluding Remarks and Future Research
References
The Analytic Hierarchy and Analytic Network Processes for the
Measurement of Intangible Criteria and for Decision-Making
Thomas L. Saaty
Introduction
Pairwise Comparisons; Inconsistency and the Principal Eigenvector
Stimulus Response and the Fundamental Scale
Hospice Decision
Rating Alternatives One at a Time in the AHP – Absolute
Measurement
Paired Comparisons Imply Dependence
When is a Positive Reciprocal Matrix Consistent?
In the Analytic Hierarchy Process Additive Composition is Necessary
Benefits, Opportunities, Costs and Risks
On the Admission of China to the World Trade Organization (WTO)
The Analytic Network Process (ANP)
382viii MULTIPLE CRITERIA DECISION ANALYSIS
Two Examples of Estimating Market Share – The ANP with a Single
Benefits Control Criterion
Outline of the Steps of the ANP
Complex Decisions with Dependence and Feedback
Conclusions
References
On the Mathematical Foundation of MACBETH
Carlos A. Bana e Costa, Jean-Marie De Corte, Jean-Claude Vansnick
Introduction
Previous Research and Software Evolution
Types of Preferential Information
Numerical Representation of the Preferential Information
Consistency – Inconsistency
Consistency Test for Preferential Information
Dealing with Inconsistency
The MACBETH Scale
Discussion About a Scale
MACBETH and MCDA
References
Part V Non-Classical MCDA Approaches
Dealing with Uncertainties in MCDA
Theodor J Stewart
What is Uncertainty?
Probabilistic Models and Expected Utility
Pairwise Comparisons
Risk Measures as Surrogate Criteria
Scenario Planning and MCDA
Implications for Practice
References
Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid
Patrick Meyer, Marc Roubens
Introduction
The Data Set
Valued Preference Relation and Outranking Relation
Aggregation Procedures
The Sorting Problem
The TOMASO Method
The Choice Problem
Conclusion
References
504Contents ix
Decision Rule Approach
Salvatore Greco, Benedetto Matarazzo,
Introduction
Dominance-based Rough Set Approach (DRSA) to Multiple-criteria
Classification
Variable-Consistency Dominance-Based Rough Set Approach (VCDRSA)
Induction of Decision Rules from Rough Approximations of Upward
and Downward Unions of Decision Classes
Extensions of DRSA
DRSA for Multiple-criteria Choice and Ranking
Conclusions
References
Fuzzy Measures and Integrals in MCDA
Michel Grabisch, Christophe Labreuche
Introduction
Measurement Theoretic Foundations
Unipolar Scales
Bipolar Scales
Ordinal Scales
Concluding Remarks
References
Verbal Decision Analysis
Helen Moshkovich, Alexander Mechitov, David Olson
Features of Unstructured Decision Problems
Main Principles of Verbal Decision Analysis
Decision Methods for Multicriteria Alternatives Ranking
Decision Methods for Multicriteria Alternatives’ Classification
Place of Verbal Decision Analysis in MCDA
Conclusion
References
Part VI Multiobjective Mathematical Programming
Interactive Methods
Pekka Korhonen
Introduction
Basic Definitions and Some Theory
Principles for Implementing Interactive Methods
Generating Nondominated Solutions
Solving Multiple Objective Problems
Final Solution
Examples of Software Systems: VIG and VIMDA
657x MULTIPLE CRITERIA DECISION ANALYSIS
Concluding Remarks
References
Multiobjective Programming
Matthias Ehrgott, Margaret M. Wiecek
Introduction
Problem Formulation and Solution Concepts
Properties of the Solution Sets
Conditions for Efficiency
Generation of the Solution Sets
Approximation of the Pareto Set
Specially Structured Problems
Current and Future Research Directions
Conclusions
References
Multiple Objective Linear Programming with Fuzzy Coefficients
Masahiro Inuiguchi
Introduction
Problem Statement and Approaches
Modality Constrained Programming Approach
Modality Goal Programming
Modal Efficiency Approach
Concluding Remarks
References
MCDM Location Problems
Stefan Nickel, Justo Puerto, Antonio M. Rodríguez-Chía
Introduction
Location Problems
Continuous Multicriteria Location Problems
Multicriteria Network Location Problems
Multicriteria Discrete Location Problems
Conclusions
References
Part VII Applications
Multicriteria Decision Aid/Analysis in Finance
Jaap Spronk, Ralph E. Steuer, Constantin Zopounidis
Introduction
Financial Decision Making
MCDA in Portfolio Decision-Making Theory
MCDA in Discrete Financial Decision-Making Problems
835Contents xi
Conclusions and Future Perspectives
References
MCDA and Energy Planning
Danae Diakoulaki, Carlos Henggeler Antunes, António Gomes Martins
Introduction
Multiobjective Programming Models for Energy Planning
Energy Planning Decisions with Discrete Alternatives
Conclusions
References
Multicriteria Analysis in Telecommunication Network Planning and
Design – Problems and Issues
João Clímaco, José Craveirinha
Motivation
Overview ofCurrent Evolutions in Telecommunication Networks and
Services
Multicriteria Analysis in Telecommunication Network Planning and
Design
Review and Discussion ofApplications of MA to Telecommunication
Network Planning
Future Trends
References
Multiple Criteria Decision Analysis and Sustainable Development
Giuseppe Munda
The Concept of Sustainable Development
Measuring Sustainability: The Issue of Sustainability Assessment
Indexes
A Defensible Axiomatic Setting for Sustainability Composite Indicators
Warning! Not Always Rankings Have to Be Trusted ...
The Issue of the “Quality of the Social Decision Processes”
The Issue of Consistency in Multi-Criteria Evaluation of
Sustainability Policies
Conclusion
References
Part VIII MCDM Software
Multiple Criteria Decision Support Software
H. Roland Weistroffer, Charles H. Smith, Subhash C. Narula
Introduction
Software Overview
Concluding Remarks
1009xii MULTIPLE CRITERIA DECISION ANALYSIS
References
Contributing Authors
Index
solution, 676
approach, 696
bi-capacity, 598
bi-capacity, 598
additive, 590
conjugate, 590
decomposable bi-capacity, 598
identification of bi-capacity, 598
symmetric, 590
Bicriteria problems, 775, 782, 791
Binary alternative, 578
Binary preference relation, 270
Binary relation, 32, 89, 673–674
asymmetry, 33, 38
complete, 271
completeness, 89
dominance, 118
equivalence, 89
interval order, 114
irreflexivity, 33, 38
numerical representation, 74
properties, 89
reflexive, 270
reflexivity, 33, 38
approach, 683
preference structure, 40
preference structures, 43
ACADEA, 1010, 996
Achievement function, 686
Achievement function approach, 686
Achievement function
increasing, 686
strictly increasing, 686
strongly increasing, 686
Achievement scalarizing function, 654
Action, 8
ADBASE, 1004, 653, 996
Additive difference model, 116
Additive independence, 456
Additive nontransitive model, 116
Additive value function, 304–305
Additive value functions, 304
Admissible transformation, 571
AGAP, 1008, 996
AgentAllocator, 1010, 996
Aggregated index, 225
Aggregated preference index, 170, 172
Aggregation, 440, 482
Aggregation function, 568
Aggregation procedures, 14
AHP, 269, 288, 294, 650, 892
Alternative, 8
Ambiguity, 520, 529
Ambiguous assignment, 493
Analytic Hierarchy Process, 347, 349, 377, 385,
650, 999
Analytic Network Process, 347, 349, 379, 385
Applications, 440
ARGOS, 1008–1009, 996
ARGUS, 210
Arrow K.J., 968
Aspiration level, 653–654
Attribute
essential, 99
importance, 97
AutoMan, 1010, 996
Axiom
Archimedean, 94, 99
restricted solvability, 99
Thomsen, 98
Axiomatic characterization, 776–777
Balance criterion, 786
Balance number, 695
apportioned, 695
Balance point, 694
Balance set approach, 694
BANKADVISOR, 1010, 996
Bankruptcy risk, 848
Banville C., 976
Barbier E.B., 958
Basic index, 226
Behavioral convergence, 660
Benefits, 347, 350, 362, 365–366, 368, 379–381,
383, 391, 402, 404
Benson approach, 684
Bi-capacity, 5901036 MULTIPLE CRITERIA DECISION ANALYSIS
semiorder, 114
symmetry, 33, 38
trace, 118
transitive, 270
transitivity, 33, 38, 41, 89
weak order, 89
Bisection, 102
Blumenthal A., 350–351
Boolean polynomial, 599
Bordley R., 292
Boundary, 524
C-K-Y-L ranking procedure, 968
Camerer C., 274
Capacity, 576
Capacity expansion, 868
Capacity
583
584
2-additive capacity, 584
additive, 576
bipolar capacity, 590
conjugate, 576
identification of capacity, 584
symmetric, 576
Capital budgeting, 806
Cardinal scale, 10
CASTART, 1011,996
Causal mapping, 995
CAUSE, 883
Cent-dian problem, 769, 776, 779, 782–784, 786,
789
Center problem, 768–769, 775, 777, 779, 782–783,
766
Cesaro sum, 354
Cesaro summability, 354, 388, 392
CGX, 1011,996
Characteristic relation, 39
Charnes A., 289–290
China, 380–381, 384, 405, 408
Choice problem, 476, 483
Choice problematic, 11, 140
Choquet integral, 485, 576, 584, 591
asymmetric, 589
symmetric, 588
Classification, 29
Clustering, 359
Co-evolutionary paradigm, 959
Coalition of criteria, 576
Commensurateness, 569, 574
Comonotonic additivity, 577
Comonotonicity, 577
Compact polyhedron, 701
Comparisons, 349, 360, 365, 371, 374, 401, 404
pairwise, 347, 349–350, 356, 385
redundant, 365
Compensability analysis, 252
Complementary criteria, 581
Complex decision, 405, 407
Complexity, 616, 632, 634, 637, 775, 778, 784, 787
Composite indicators, 964
Composition, 387–388
additive, 377
hierarchic, 386, 389
Concatenation operation, 79
Concordance, 137
Concordance condition, 218
Conditional problems, 791
Conditions for efficiency, 679
Condorcet Marquis de, 967
Cone, 673–674
polyhedral, 675
Conflict analysis, 237
Connectedness, 678
Consistency, 418
Continuous multiple criteria problem, 647
Convex hull, 771–774, 778
Convex MOP, 678
Cooper W.W., 289–290
Core, 525
Corporate financing, 806
Cost-benefit analysis, 614, 635, 976
Costs, 347, 350, 362, 379, 381, 383, 402, 404
Country risk assessment, 852
Credit risk, 848
Criterion space, 647, 825
Criterion vector, 825
Criterium Decision Plus, 996–997
Critical regime, 204
CTLite, 1009, 996
Cumulative prospect theory, 589
ordinal, 603
Customer satisfaction, 328
Cycle, 385, 404
CYCLE, 632
DAM, 996–997
Data mining, 335
Data table, 515
DEA, 790
Debreu G., 272, 276
Decision-aid, 300
Decision-making, 348–349, 355, 384, 387
Decision aiding, 28–29, 45, 52
Decision analysis, 74, 615, 617, 621, 635
Decision axis, 179–181, 186, 188
Decision Explorer, 995–996
Decision Lab, 996–997
Decision problematics, 839
Decision rules, 531, 518, 552
Decision space, 673, 825
Decision stick, 179–181
Decision support, 330
Decision support systems, 330
Decision trees, 538
Decision under uncertainty, 75–76, 546Index 1037
Decision variables, 648
Decomposable model, 570
Decomposable nontransitive model, 117
Deconvolution, 754
DEFINITE, 207
Degeneracy, 701
Degree of assignment, 493
Degrees, 9
Deontic logic, 56
Dependence, 347, 349, 368, 374, 379, 384–386,
403, 405
Description problematic, 11
DIDASN++, 1011, 996
Difference of attractiveness, 412
DIMITRA, 1011, 996
Direct rating, 102
Disaggregation-aggregation approach, 301–302
Discrete alternatives, 878
Discrete MOP, 707
Discrete multiple criteria problem, 647
Discriminant analysis, 304, 322
Discrimination thresholds, 139
Dispatch, 873
Dispatching, 882
Distance function, 685
Distribution network planning, 871
Distributive mode, 368, 370–371, 379
Diversification, 807
Dominance-based Rough Set Approach (DRSA),
514
Dominance, 351, 353–355, 357, 365, 388, 391, 531,
540, 617, 621–623, 627, 630–633, 673
Dominance principle, 514, 517
Duality, 780, 784
Dyer J.S., 273, 275, 288, 293
Dynamic routing, 935
Ecological distribution, 959
Edwards W., 273–274, 286
Efficient, 649
Efficient basis, 702
Efficient extreme point, 702–703
Efficient face, 701
maximal, 701, 706
Efficient frontier, 649
Efficient nonbasic variable, 702
test for, 703
Efficient pivot, 703
Efficient set, 678, 826
connectedness, 678
Efficient solution, 674–675, 729
approximately, 676
condition for, 679
existence, 677
geometric characterization, 695
properly, 676, 679
strictly, 675
weakly, 675
Efficient solutions, 825
Eigenvalue, 352–356, 376
Eigenvector, 354, 377, 382, 385, 388
principal, 350–351, 354–355, 375
Ekeland’s variational principle, 780
Elastic constraint approach, 683
ELECCALC, 996, 998
ELECTRE, 1002, 1007–1008, 1013, 633, 996, 998
ELECTRE I, 140
ELECTRE II, 144
ELECTRE III, 145, 893
ELECTRE IS, 142
ELECTRE Iv, 142
ELECTRE IV, 147
ELECTRE methods, 841
history, 134
ELECTRE TRI, 148, 893
Electrical Power Districting, 1011
Elicitation, 150
Ellsberg D., 275
Employees, 372
Energy, 864
Energy planning, 865
Energy plans, 881
Energy projects, 881
Enumeration procedures, 789
Equitability approach, 693
Equity, 996, 998
Equivalence relation, 33, 38
ESY, 1011, 996
EVAMIX, 215
Even swaps, 83
Evolutionary algorithm, 940
Evolutions in telecommunications, 904
Expected utility, 455
Expert Choice, 996, 999
Expert system, 1011–1012
Exploitation procedure, 16
Extended peer-communities, 976
Extension principle, 732
Extensive facility, 784
External uncertainties, 889
Family of criteria, 10
Farquhar P.H., 273, 282
Feasibility degree, 741
Feasible Goals Method, 1004, 1013, 996
Feasible region, 647
Feasible set, 648
Feasible set in criterion space, 1004
Feedback, 347, 349, 384–385, 403, 405
Feinberg A., 275
Ferguson R.O., 289
Finance, 806
Financial decision making, 805
Financial investment, 807
Financial management, 335
FINCLAS, 1011, 9961038 MULTIPLE CRITERIA DECISION ANALYSIS
FINEVA, 1012, 996
Finite dominating set, 783
Fishburn P.C., 271, 273–274,289
Flexible programming problem, 730
Four-valued outranking, 554
Fractile optimization model, 744
Free search, 659
Fritz-John necessary conditions, 679
Future trends, 945
Fuzzy dominance, 542
Fuzzy equality relation, 730
Fuzzy inequality relation, 730
Fuzzy integral
Choquet, 114
Sugeno, 114
Fuzzy integral, 330
Fuzzy interval, 478
Fuzzy linear function, 732
Fuzzy max, 749
Fuzzy measure, 576
fuzzy measure, 583
fuzzy measure, 584
2-additive fuzzy measure, 584
decomposable fuzzy measure, 583
non-monotonic fuzzy measure, 576
Fuzzy multiobjective programming, 463
Fuzzy number, 731
Fuzzy orders, 45
fuzzy interval order, 45
fuzzy partial order, 45
fuzzy partial preorder, 46
fuzzy semi-order, 45
fuzzy total order, 45
fuzzy weak order, 45
Fuzzy ordinal value, 478
Fuzzy preferences, 558
Fuzzy sets, 35, 451, 453, 888
De Morgan triplets, 37–38, 46
t-conorm, 36, 45
t-norm, 36, 45
Fuzzy unceratinty, 982
GAIA, 997
GAIA plane, 176–181, 185–186, 188
Game, 576
bi-cooperative game, 590
ternary voting game, 589
Gauge-based approach, 690
inner, 690
outer, 690
Gauge, 771, 773, 778-779
GDF-method, 651
Generalised criterion-preference function, 170, 176,
185
Generalized center problem, 782
Genetic algorithm, 1005–1006, 1011
Geoffrion A., 275, 292
Geometrical descriptions, 774, 776–777, 779, 789
Global frequency, 244
Global preference, 302, 315, 318, 332
Global preference index, 229
Global value function, 305
GMCR, 1009, 996
Goal-attainment approach, 688
Goal, 350, 353, 369, 381, 384, 386, 389
Goal programming, 289, 463, 650, 687, 788
Archimedean, 650
Gorman W.M., 276
Gradient method, 377
Graphical representation, 33, 54
Greedy algorithm, 699
Green accounting, 963
Guddat et al. approach, 682
R.P., 273
R.P., 288
Hadamard product, 392, 399
Hard constraint, 729
Harker P., 377
Heuristics, 698, 700
Hierarchical decision problem, 547
Hierarchy, 359, 362, 366–367, 371, 379, 382,
384–386, 388–389, 404
HiPriority, 1008, 996
HIVIEW, 996, 999
Homogeneous elements, 350, 359
Hospice decision, 361
Human judgment, 614–616
Ideal mode, 368, 370–371, 373, 382
Ideal point, 676
Identification of capacities, 606
IDRA, 248
Ignizio J.P., 289
Ijiri J., 289
Imperfect knowledge, 12
Implicit value function, 651
Importance, 527
Importance index, 580, 596
Shapley, 581
Imprecision, 451
Incomparability, 29, 42–44, 46, 165–167, 174
Incompatibility, 426
Inconsistency, 350–351, 354–355, 365–366, 377,
415, 418, 426
Independence, 90
weak, 90, 113
Indifference, 29, 31, 40, 45–46, 49, 165, 170, 174
Indifference area, 233
Indifference
nontransitive, 114
Indiscernibility, 540
Indiscernibility principle, 513
Indiscernibility relation, 847
Induction, 512, 535
Inequality measures, 76Index 1039
Information, 28, 30, 38, 43–44, 59
Intangible, 347, 349–350, 362, 370
Integer programming, 787
Intelligent agents, 334
Intensity, 351, 353, 372, 384
Intensity level, 352
Interaction, 527
Interaction between criteria, 575, 569, 581–582,
596
Interaction index, 582, 596
Interaction transform, 583
Interactive, 656
Interactive algorithms, 788
Interactive multicriteria, 920
Interior point methods, 705
Internal uncertainties, 887
Intertemporal decision, 76
Interval criterion weights, 651
Interval orders, 542
Interval scale, 10
Intervals, 414, 438
Investment appraisal, 851
INVEX, 1012, 996
IRIS, 1007, 996
Jia J., 275
Joint Gains, 1009, 996
Joint Ordinal Scale (JOS), 619, 622–625, 627–628,
637
Judgement
reciprocal, 350
Judgement, 414
Judgment, 347, 349, 351, 353, 356–357, 365, 372,
375, 377, 382, 384, 389, 402, 405
absolute, 350–351
comparative, 350–351
inconsistent, 355, 365
relative, 351
Judgment, 353
K-shortest path, 931
Kahneman D., 274
Kamenetzky R.D., 273, 288
Keeney R.L., 268–269, 274, 277, 280, 282, 286,
288, 295
Keller L.R., 273, 275
Kemeny J., 967
Kendall’s 316
Kenney R.L., 277
Kirkwood C.W., 273, 282, 286, 292
Knowledge, 517
certain, 533
doubtful, 533
possible, 533
Krantz D.H., 280
Kreps D.M., 271
Krzysztofowicz R., 275
Kuhn-Tucker constraint qualification, 679–680
Kuhn-Tucker necessary conditions, 679
Kuhn-Tucker sufficient conditions, 680
L-good choice, 506
L-R fuzzy number, 732
LBS, 652
Least squares, 355
logarithmic, 355
Level curve, 695
Level set, 695
Level set approach, 694
Level set
strict, 695
Levenglick A., 967
Lexicographic approach, 691
Lexicographic max-ordering approach, 693
Lexicographic order, 289
Lexicographical, 617
Light beam search, 652
Limit supermatrix, 388–389, 391–392, 399
Limits, 438
Linear programming, 917
Load management, 875
Local search, 699
Location problems, 791, 765, 768–769, 780
continuous, 771
discrete, 787–788
network, 781
networks, 787
Logarithmic response, 356
Logic of preferences, 56
Logical Decisions, 996, 999
Logics, 33
classical logic, 34
four-valued logics, 39
fuzzy sets, 35, 45
multivalued logics, 31, 46, 39
nonclassical logics, 31, 39
Lottery, 273
Lower approximation, 521–522, 551
Luce R.D., 276
M&P, 1000
MACBETH, 1000, 413, 440, 573, 650, 996, 999
MACBETH method, 110
MACBETH scale, 435
MACBETH software, 414
MacModel, 1000, 996
MAPPAC, 226
Marginal analysis, 371
Marginal value functions, 306
Market portfolio, 837
Market share, 391–392, 396, 399, 402, 405–406
MARKEX, 1012, 996
Martel and Zaras’ method, 256
Martinez-Alier J., 959
Matrix representation, 33
MAUT, 633–636, 650
Max-ordering approach, 692–6931040 MULTIPLE CRITERIA DECISION ANALYSIS
MCDM, 75
Measuarble multiattribute value function, 283
Measurable multiattribute preference function
additive, 284
multiplicative, 284
Measurable multiattribute value function
difference consistent, 283
weak difference independence, 283
Measureable multiattribute preference function
difference independence, 285
Measureable multiattribute value function
assessment, 286
Measurement, 347–349, 379, 570
absolute, 371
conjoint, 73
difference measurement, 571
extensive, 82
inequality, 76
interval scale, 97, 101
length, 77
ordinal, 79
ordinal measurement, 570
relative, 349, 359, 375
scale of, 370
uniqueness, 76
Medi-center problem, 782
Median problem, 766, 768, 772–773, 776–779,
782, 786, 789
MEDIATOR, 1009–1010, 996
MEDICS, 1012, 996
MELCHIOR, 220
Mergers and acquisitions, 852
Merits, 350, 379, 384,404–406
Metaheuristics, 699–700
local-search-based, 699
population-based, 700
Method
outranking, 118
MHDIS method, 846
Michnik J., 289
MICROQUALIFLEX, 201
MIIDAS, 1000, 996
MINORA, 1000, 996
Missing values, 545
Modality constrained programming, 735
Modality goal programming, 753
Modality optimization model, 746
Modernization planning, 916
Modified Pascoletti and Serafini approach, 689
Modulus, 389
MOFP, 710
MOIP, 708
MOIRA, 1012, 996
MOLP, 649
MOMHLib++, 1005, 996
Monotonicity, 576
Monotonicity constraints, 309
Monotonicity of preferences, 307, 317
MOP, 673
convex, 678
discrete, 707
fractional, 710
linear, 700
piecewise linear, 710
quadratic, 710
stability, 677
Morgenstern O., 269, 273
Most preferred solution, 649
MOZOP, 708
MPS, 649
Multiattribute, 944
Multiattribute preference function, 275
conjoint measurement, 277
mutual preference independence, 276
ordinal additive value function, 277
assessment, 277
preference independence, 276
additive ordinal multiattribute value function, 276
Multiattribute utility function
additive, 281
additive independence, 282
assessment, 282
multplicative, 281
utility independence, 280
Multiattribute utility theory, 455, 843
Multicriteria analysis, 912
Multicriteria decision support systems, 853
Multicriteria routing, 926
Multicriteria Simplex methods, 702–703
Multifacility, 766, 773, 776, 791
MultiGen, 1005, 996
Multigraded dominance, 550
Multiobjective linear programming, 649, 700
Multiobjective optimization, 326
Multiobjective programming, 672, 867
Multiple-criteria choice, 548
Multiple-criteria classification, 515, 545
Multiple attribute utility theory, 650
Multiple Criteria Decision Making, 646
Multiple Criteria Decision Making Support
Systems (MCDSS), 646
Multiple criteria design problem, 647
Multiple criteria evaluation problem, 647
Multiple criteria optimization, 825
Multiple objective linear programming, 729
Multistat Optimizer, 1005, 996
Musgrave A., 980
MUSTARD, 1000, 996
Nadir point, 677
NAIADE, 1001, 996
National missile defense, 405
Nearness, 29–30
Necessarily efficient solution, 759
Negative outranking flow, 173–175Index 1041
Negative transitivity, 270
Net outranking flow, 174
Net outranking flows, 179
Network, 349, 384–386, 388, 391–393, 396, 403,
405–406
Neurath O., 962
Neurons, 351, 356
Neutral level, 572
NIMBUS, 1006
No stable value function, 652
Non-additive utility functions, 330
Non-discordance, 137
Non-monotonic preferences, 317
Nonconvex problems, 791
Nondominated, 648
Nondominated criterion vector, 825
Nondominated frontier, 649
Nondominated outcome, 674
Nondominated point
existence, 677
Nondominated set, 674, 678, 826
connectedness, 678
properties of, 675
Nondominated surfaces, 837
Nonscalarizing methods, 680, 691, 696
approach, 696
balance set approach, 694
equitability approach, 693
level set approach, 694
lexicographic approach, 691
lexicographic max-ordering approach, 693
max-ordering approach, 692
Norgaard R.B., 958
Norm, 685
monotonically increasing, 685
strictly monotonically increasing, 685
Normal boundary intersection approach, 690
Normalization, 378
Numerical representation, 30, 48, 53, 568, 570
Numerical scale, 9
O’Connor M., 959
Objective function
vector-valued, 673
Objective function, 648
Objective space, 673
Objective space methods, 705
OnBalance, 1001, 996
Operational planning, 942
Opportunities, 347, 350, 379, 381, 383, 402, 404
Option pricing theory, 811
ORCLASS, 629
Ordered median problem, 779
Ordered sets, 40
complete order, 48
complete preorder, 53
quasi-order, 44
total order, 40
complete order, 40, 53
complete preorder, 41, 49, 53
double threshold orders, 43, 51
interval order, 28, 31, 35, 42, 50, 55
linear order, 40, 48, 53
partial order, 44, 52
partial preorder, 44
partial weak order, 52
PQI interval order, 51
pseudo-orders, 43–45, 51
quasi-order, 44
semi-order, 41
semiorder, 54
simple order, 40, 48, 53
total order, 48, 53
total preorder, 41, 49, 53
weak order, 41, 49, 53
Ordered sorting, 476
Ordering problem, 476, 484
Ordinal classification, 619, 629–631, 637
Ordinal judgments, 616–619, 621, 634
Ordinal scale, 9
ORESTE, 207
Outcome set-based algorithm, 707
Outranking, 460, 893
Outranking method, 166
Outranking methods, 16
Outranking relation, 137, 479
Outranking relations, 840
PACMAN, 251
Pairwise comparison, 166–167,169–170
Pairwise comparison table (PCT), 549
Pairwise comparisons, 315, 458
Pairwise Criterion Comparison Approach (PCCA),
222
Parameter space investigation, 698
Parametric analysis, 772
Pareto condition
strong Pareto condition, 601
weak Pareto condition, 601
Pareto face
maximal, 706
Pareto preference, 675
Pareto Principle, 617
Pareto Race, 662
Pareto relation, 675
Pareto set
approximation, 696
exact approximation, 696
heuristic approaches, 698
heuristic methods, 700
nonlinear approximation, 698
piece-wise linear approximation, 697
point-wise approaximation, 697
Partial frequency, 242
Partial order, 52, 674
Partial profile, 521,5311042 MULTIPLE CRITERIA DECISION ANALYSIS
Participative multi-criteria evaluation, 976
Pascoletti and Serafini approach, 688
Performance, 9
Perron eigenvalue, 377
Perron theory, 354
Perturbation, 353–354, 377
Piecewise linear objective, 710
Point-objective location problem, 766, 771, 789
Policies, 881
Portfolio selection, 849
Portfolio theory, 823
Positive outranking flow, 173, 175
Positive reciprocal matrix, 375–377
Possibly efficient solution, 759
Post-optimality analysis, 307
Posterior articulation of preferences, 653
Potential action, 7
Potential index, 226
Power generation, 865, 880
PRAGMA, 240
Pratt J.W., 274
Pre-aggregation, 482
Pre-scoring, 484
PREFCALC, 1001, 996, 998
PREFDIS, 1007, 996
Preference, 165, 170, 172, 174, 673, 675
Preference asymmetry, 270
Preference difference, 102
Preference differences, 75
Preference disaggregation, 300, 844
Preference elicitation, 615–617, 621–622, 624,
630–631, 633
Preference function, 169–171, 175, 186, 188
Preference model, 300–301, 306, 327, 330, 332,
336
Preference modelling, 52
Preference relation
monotonicity, 601
symmetric, 270
Preference structure, 29, 39, 44, 48
Preference
Pareto, 675
independence, 274
indifference, 270
interval, 88
nontransitive, 115
ratio, 273
strict, 270
weak, 271
weak order, 270
Preferences, 412
Preferential independence, 617–618, 622, 624
Preferential independence, 628
Preferential independence, 633, 636
Preferential information, 416, 512, 549
Preference
preference difference, 271
PRIAM, 1001, 996
PRIME Decisions, 1001, 1004, 996
Priorities, 347, 349–352, 354–355, 357, 362, 366,
368–369, 372, 375, 377, 379, 381–382, 385,
388–389, 392, 396, 399, 402, 405–406
global, 368, 402
local, 368
PROAFTN, 1007, 996
Probability distribution, 75
Problem formulation, 90
Problem statement, 300–301
Problem structure, 614, 618, 627, 629, 634,
636–637
Problem structuring, 883
Problematic, 11
Product set, 75, 90
Profiles of alternatives, 175–176, 185–186, 188
PROMETHEE, 1011–1012, 1014, 633, 893, 997
Promethee GDSS
group decision support system, 183
PROMETHEE I partial ranking, 173
PROMETHEE II complete ranking, 174–175, 188
PROMETHEE methods, 842
PROMETHEE V, 182–183
PROMETHEE VI, 181
Properly efficient solution, 676
Psychological validity, 615
QoS issues, 910
QoS routing, 926
Quadratic function, 710
QUALIFLEX, 199
Qualitative judgements, 414
Qualitative scales, 888
Quality of approximation, 525, 552
Quantitative scale, 9
Questioning procedure, 416
Raiffa H., 277, 268–269, 274, 277, 280, 282, 286,
288, 295
Ranking, 548
Ranking problematic, 12, 143
Ratings, 372–373, 405–406
Ratio scale, 10, 357, 372, 399
Raynaud H., 968
Reactive power compensation, 872
Reciprocal matrix, 355
Reduced cost matrix, 702
Reduct, 525
Reducts, 848
Redundancy, 496
Reference point|688 reference actions, 302
Reference actions, 302, 306, 309, 320, 322
Reference direction approach, 689
Reference direction method, 661
Reference direction vector, 661
Reference level, 653
Reference point, 654, 684
Reference point approach, 788Index 1043
Reference set, 845
Reference set approach, 688
REGIME, 202
Regime matrix, 203
Relative importance of criteria, 138
REMBRANDT, 1002, 996
Reservation level, 653
RGDB, 1002, 996
Risk-return trade-off, 807
Risk, 450
Risk aversion, 807
Risk measures, 461
Risks, 347, 350, 379, 381, 383, 402, 404
Robust programming, 749
Robustness, 779
Robustness concerns, 149
Rough approximations, 519
Rough set theory, 847
Rough sets, 451, 453
Routing models, 925
Roy approach, 688
Roy B., 976
Salary raises, 372
Salo A.A., 273, 288
SANEX, 1012, 996
SANNA, 1002, 996
Sarin R.A., 293
Sarin R.K., 275, 288
Satisfactory level, 573
Satisficing bounded rationality, 573
Savage L.J., 274
Scalarization, 680, 691
approach, 683
achievement function approach, 686
Benson approach, 684
direction-based approaches, 688
distance function, 684
elastic constraint approach, 683
gauge-based approach, 690
goal-attainment approach, 688
Guddat et al. approach, 682
modified Pascoletti and Serafini approach, 689
normal boundary intersection approach, 690
Pascoletti and Serafini approach, 688
reference direction approach, 689
reference point approaches, 684
reference set approach, 688
Roy aproach, 688
weighted-sum approach, 681
weighted power approach, 681
weighted geometric mean approach, 687
weighted quadratic approach, 682
Scalarizing function, 653
Scale, 9, 360, 418, 435,570
absolute, 347, 349, 371, 399
bipolar scale, 572, 587
bounded scale, 573
fundamental, 347, 349, 356–357, 367, 372
interval, 351, 356
interval scale, 571
ordinal, 75, 351
ordinal scale, 571, 599
ratio scale, 571
relative, 349
unidimensional, 350
unipolar scale, 572, 574
Scaling, 888
SCDAS, 1010, 996
Scenario planning, 464
Scenarios, 887, 889
Scores, 9
Scott D., 272
Search algorithms, 943
Second-order conditions, 680
Selection problem, 647
Semi-obnoxious, 777, 782, 787
Sensitivity
walking weights, 188–189
Separability
weak, 113
Set of actions, 28
Set of alternatives, 28
Shapley importance index, 596
Shapley value, 494, 528, 581
Similarity, 29, 46, 540
Simpson decisions, 775
Simulated annealing, 1005, 699
Single facility, 766, 773, 784, 786
Sink node, 385
Šipoš integral, 588
Siting, 882
Skills Evaluator, 1012, 996
Social choice, 76
Social incommensurability, 961
Social multi-criteria evaluation, 977
Socio-economic issues, 944
Soft constraint, 729
Software, 414
Software
Decision Lab, 168, 170, 181, 186, 188–189
Promcalc, 168, 170, 181, 183, 186
Solutions
efficient, 767
lexicographic, 767
max-ordering, 767
Pareto, 767
properly efficient, 767
strictly efficient, 767
weakly efficient, 767
SOLVEX, 1006, 996
Sorting, 29
Sorting problem, 476, 484, 486
Sorting problematic, 12, 147
Source node, 3851044 MULTIPLE CRITERIA DECISION ANALYSIS
Stability of MOP, 677
Stability
external, 677
Stakeholder multi-criteria decision aid, 976
Stakeholders, 889
Standard sequence, 81, 93, 98, 102
States of nature, 453
Steel Mill Scheduling, 996
Steps of ANP, 402
Stimulus, 350, 356
Stimulus response, 356
Stochastic, 888
Stochastic approaches, 889
Stochastic dominance, 459
Stochastic matrix, 389, 396
Stochastic programming, 463
Strength of preference, 271
Strength Pareto Evolutionary Algorithm, 1005
Strictly efficient solution, 675
Strong preference, 29, 45–46, 58
Strong sustainability, 981
Structuration of objectives, 90
Subdifferentials, 774, 778
Substitutability, 572
Substitutive criteria, 581
Sugeno integral, 599, 601
symmetric, 603
Suggestions, 415, 432
Supermatrix, 386, 388–390, 392, 396, 404
unweighted, 392, 396
weighted, 396, 399
Suppes P., 272
Support, 656
Sustainable development, 866, 957
Swing procedure, 617
Sylvester J.J., 388
Symmetric maximum, 602
Symmetric minimum, 602
Symmetrical importance, 965
Synergy, 496
Synthesis, 350, 360, 370–371, 377–379, 389, 404
Tabu search, 700
TACTIC, 218
Tchebycheff criterion, 319
Tchebychev norm, 771, 783
Technical incommensurability, 961
Technological evolutions, 907
TELOS, 1013, 996
Ternary alternative, 590, 594
Threshold, 43, 47, 49–50
Thresholds, 166, 170, 186
Tolerant decision maker, 569
TOMASO, 1008, 487, 996
TOMMIX, 1006, 996
Topological properties, 774, 780
TOPSIS, 1002, 996
Tradeoff, 83, 349, 380
Transitivity, 355
Transitivity of preferences, 618, 622, 624, 626
Transitivity of preferences, 628
Transitivity of preferences, 633
Transmission, 871
Trapezoidal number, 478
Tree networks, 783–784, 786
TRIMAP, 1006, 996
Trzaskalik T., 289
Tukey J.W., 276
Tversky A., 274
Uncapacitated facility location, 790
Uncertainty, 30, 35, 42–43, 45, 450, 887
external, 451
internal, 451
Unfuzzy non dominated solution, 484
Unit commitment, 873
Upper approximation, 521–522, 551
UTA method, 108,844
UTA Plus, 1001–1002, 996
UTADIS method, 845
Utility function, 270, 320, 568, 648
Utility independence, 456
Utility theory, 273
continuity, 274
independence, 273
Utility
expected, 75
Utopia point, 676, 685
V.I.S.A, 1003
Validation, 359
Value, 438
Value and utility theory, 891
Value function, 74, 270, 648
additive, 76, 100
finite case, 102
Linear Programming, 106
rich case, 92
cardinal, 272
decomposable, 112
interval scale, 272
measurable, 271
multiplicative, 77
ordinal, 271
pseudoconcave, 661
Value space, 648
Valued preference relation, 479
Valued relation, 37, 45
Valued structures, 45
Variable-consistency dominance-based rough set
approach (VC-DRSA), 529
Variable space, 648
Vector-maximum approach, 651
Vector of ordered outcomes, 694
Vectorial best approximation, 779
Venture capital, 852Index 1045
Verbal scale, 9
Verification, 624
Veto criterion, 569
VIG, 1006, 659, 661, 996
VIMDA, 1003, 661, 996
VIP Analysis, 1003, 996
Von Neumann J., 269, 273
Von Winterfeldt D., 273–274, 286
Voting theory, 775
Wakker P., 274
Water Quality Plan, 996
Weak comparability, 960
Weak order, 306
Weak preference, 29, 43, 58
Weak separability, 572
directional weak separability, 600
Weak sustainability, 981
Weakly efficient, 649
Weakly efficient solution, 674–675
Weakly nondominated, 648
Weakly nondominated outcome, 674
Weber-Fechner law, 356
WebHIPRE, 996
Weight space decomposition, 702
Weighted-sum approach, 681
Weighted power aproach, 681
Weighted geometric mean approach, 687
Weighted quadratic approach, 682
Weighting, 888
Weights, 167–168, 170, 175–176, 179–181,
185–186, 188
WINGDSS, 1010, 996
WINPRE, 1004, 996
World Trade Organization, 380
WWW-NIMBUS, 1006, 996
Young H.P., 967
Zadeh L.A., 982
ZAPROS-STEP, 625
ZAPROS, 619, 622, 624–630, 636–637
ZAPROS III, 625–627
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