MULTIPLE CRITERIADECISION ANALYSIS:STATE OF THE ART SURVEYS

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* A list of the early publications in the series is at the end of the book *

MULTIPLE CRITERIADECISION ANALYSIS:STATE OF THE ART SURVEYS

Edited by

JOSÉ FIGUEIRAUniversity of Coimbra

SALVATORE GRECOUniversity of Catania

MATTHIAS EHRGOTTUniversity of Auckland

Springer

eBook ISBN: 0-387-23081-5Print ISBN: 0-387-23067-X

Print ©2005 Springer Science + Business Media, Inc.

All rights reserved

No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,mechanical, recording, or otherwise, without written consent from the Publisher

Created in the United States of America

Boston

©2005 Springer Science + Business Media, Inc.

Visit Springer's eBookstore at: http://ebooks.kluweronline.comand the Springer Global Website Online at: http://www.springeronline.com

Contents

List of Figures

List of Tables

IntroductionJosé Figueira, Salvatore Greco, Matthias Ehrgott

Human Reflection about DecisionTechnical Reflection about Decision: MCDA Researchersbefore MCDAThe Reasons for this Collection of State-of-the-Art SurveysA Guided Tour of the BookAcknowledgment to the Referees

References

Part I An Overview of MCDA Techniques Today

Paradigms and ChallengesBernard Roy

What Are the Expectations that Multicriteria Decision Aiding(MCDA) Responds to?Three Basic ConceptsHow to Take Into Account Imperfect Knowledge?An Operational Point of ViewConclusion

References

Part II Foundations of MCDA

Preference ModellingMeltem Öztürk, Alexis Tsoukiàs, Philippe Vincke

IntroductionPurposeNature of InformationNotation and Basic DefinitionsLanguages

1.2.

3.4.5.

1

1.

2.3.4.5.

2

1.2.3.4.5.

xiii

xvii

xxi

xxi

xxiixxivxxv

xxxivxxxiv

3

47

12141718

27

2828303233

vi MULTIPLE CRITERIA DECISION ANALYSIS

Preference StructuresDomains and Numerical RepresentationsLogic of PreferencesConclusion

References

Conjoint measurement tools for MCDMDenis Bouyssou, Marc Pirlot

Introduction and MotivationDefinitions and NotationThe Additive Value Model in the “Rich” CaseThe Additive Value Model in the “Finite” CaseExtensions

References

Part III Outranking Methods

ELECTRE MethodsJoséFigueira, Vincent Mousseau, Bernard Roy

Introduction: A Brief HistoryMain Features of ELECTRE MethodsA Short Description of ELECTRE MethodsRecent Developments and Future IssuesSoftware and ApplicationsConclusion

References

PROMETHEE MethodsJean-Pierre Brans, Bertrand Mareschal

HistoryMulticriteria ProblemsThe PROMETHEE Preference Modelling InformationThe PROMETHEE I and II RankingsThe GAIA Visual Interactive ModuleThe PROMETHEE VI Sensitivity Tool (The “Human Brain”)PROMETHEE V: MCDA under ConstraintsThe PROMETHEE GDSS ProcedureThe DECISION LAB Software

References

Other Outranking ApproachesJean-Marc Martel, Benedetto Matarazzo

IntroductionOther Outranking Methods

6.7.8.9.

3

1.2.3.4.5.

4

1.2.3.4.5.6.

5

1.2.3.4.5.6.7.8.9.

6

1.2.

3948565960

73

748992

102112119

133

134136139149151153153

163

164164168171175181182183186189

197

198198

Contents

Pairwise Criterion Comparison ApproachOne Outranking Method for Stochastic DataConclusions

References

Part IV Multiattribute Utility and Value Theories

MAUT – Multiattribute Utility TheoryJames S. Dyer

IntroductionPreference Representations Under Certainty and Under RiskOrdinal Multiattribute Preference Functions for the Case ofCertaintyCardinal Multiattribute Preference Functions for the Case of RiskMeasurable Multiattribute Preference Functions for the Case ofCertaintyThe Relationships Among the Multiattribute Preference FunctionsConcluding Remarks

References

UTA MethodsYannis Siskos, Evangelos Grigoroudis, Nikolaos F. Matsatsinis

IntroductionThe UTA MethodVariants of the UTA MethodApplications and UTA-based DSSConcluding Remarks and Future Research

References

The Analytic Hierarchy and Analytic Network Processes for theMeasurement of Intangible Criteria and for Decision-Making

Thomas L. SaatyIntroductionPairwise Comparisons; Inconsistency and the Principal EigenvectorStimulus Response and the Fundamental ScaleHospice DecisionRating Alternatives One at a Time in the AHP – AbsoluteMeasurementPaired Comparisons Imply DependenceWhen is a Positive Reciprocal Matrix Consistent?In the Analytic Hierarchy Process Additive Composition is NecessaryBenefits, Opportunities, Costs and RisksOn the Admission of China to the World Trade Organization (WTO)The Analytic Network Process (ANP)

3.4.5.

7

1.2.3.

4.5.

6.7.

8

1.2.3.4.5.

9

1.2.3.4.5.

6.7.8.9.10.11.

vii

221254259260

265

266267

273278

281290292294

297

298302313328334335

345

346348354359

369372373375377378382

viii MULTIPLE CRITERIA DECISION ANALYSIS

Two Examples of Estimating Market Share – The ANP with a SingleBenefits Control CriterionOutline of the Steps of the ANPComplex Decisions with Dependence and FeedbackConclusions

References

On the Mathematical Foundation of MACBETHCarlos A. Bana e Costa, Jean-Marie De Corte, Jean-Claude Vansnick

IntroductionPrevious Research and Software EvolutionTypes of Preferential InformationNumerical Representation of the Preferential InformationConsistency – InconsistencyConsistency Test for Preferential InformationDealing with InconsistencyThe MACBETH ScaleDiscussion About a ScaleMACBETH and MCDA

References

Part V Non-Classical MCDA Approaches

Dealing with Uncertainties in MCDATheodor J Stewart

What is Uncertainty?Probabilistic Models and Expected UtilityPairwise ComparisonsRisk Measures as Surrogate CriteriaScenario Planning and MCDAImplications for Practice

References

Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision AidPatrick Meyer, Marc Roubens

IntroductionThe Data SetValued Preference Relation and Outranking RelationAggregation ProceduresThe Sorting ProblemThe TOMASO MethodThe Choice ProblemConclusion

References

12.

13.14.15.

10

1.2.3.4.5.6.7.8.9.10.

11

1.2.3.4.5.6.

12

1.2.3.4.5.6.7.8.

389400403405406

409

410412414415416417420432435437438

445

446450454457460466467

471

472474475478482483502503504

Contents ix

Decision Rule ApproachSalvatore Greco, Benedetto Matarazzo,

IntroductionDominance-based Rough Set Approach (DRSA) to Multiple-criteriaClassificationVariable-Consistency Dominance-Based Rough Set Approach (VC-DRSA)Induction of Decision Rules from Rough Approximations of Upwardand Downward Unions of Decision ClassesExtensions of DRSADRSA for Multiple-criteria Choice and RankingConclusions

References

Fuzzy Measures and Integrals in MCDAMichel Grabisch, Christophe Labreuche

IntroductionMeasurement Theoretic FoundationsUnipolar ScalesBipolar ScalesOrdinal ScalesConcluding Remarks

References

Verbal Decision AnalysisHelen Moshkovich, Alexander Mechitov, David Olson

Features of Unstructured Decision ProblemsMain Principles of Verbal Decision AnalysisDecision Methods for Multicriteria Alternatives RankingDecision Methods for Multicriteria Alternatives’ ClassificationPlace of Verbal Decision Analysis in MCDAConclusion

References

Part VI Multiobjective Mathematical Programming

Interactive MethodsPekka Korhonen

IntroductionBasic Definitions and Some TheoryPrinciples for Implementing Interactive MethodsGenerating Nondominated SolutionsSolving Multiple Objective ProblemsFinal SolutionExamples of Software Systems: VIG and VIMDA

13

1.2.

3.

4.

5.6.7.

14

1.2.3.4.5.6.

15

1.2.3.4.5.6.

16

1.2.3.4.5.6.7.

507

508

511

525

527536544555557

563

564566570583595604604

609

610610615625628633634

641

642643645649652656657

x MULTIPLE CRITERIA DECISION ANALYSIS

Concluding RemarksReferences

Multiobjective ProgrammingMatthias Ehrgott, Margaret M. Wiecek

IntroductionProblem Formulation and Solution ConceptsProperties of the Solution SetsConditions for EfficiencyGeneration of the Solution SetsApproximation of the Pareto SetSpecially Structured ProblemsCurrent and Future Research DirectionsConclusions

References

Multiple Objective Linear Programming with Fuzzy CoefficientsMasahiro Inuiguchi

IntroductionProblem Statement and ApproachesModality Constrained Programming ApproachModality Goal ProgrammingModal Efficiency ApproachConcluding Remarks

References

MCDM Location ProblemsStefan Nickel, Justo Puerto, Antonio M. Rodríguez-Chía

IntroductionLocation ProblemsContinuous Multicriteria Location ProblemsMulticriteria Network Location ProblemsMulticriteria Discrete Location ProblemsConclusions

References

Part VII Applications

Multicriteria Decision Aid/Analysis in FinanceJaap Spronk, Ralph E. Steuer, Constantin Zopounidis

IntroductionFinancial Decision MakingMCDA in Portfolio Decision-Making TheoryMCDA in Discrete Financial Decision-Making Problems

8.

17

1.2.3.4.5.6.7.8.9.

18

1.2.3.4.5.6.

19

1.2.3.4.5.6.

20

1.2.3.4.

661662

667

668669673675676692696707708708

723

724725731749754757757

761

762764767776783787787

799

800801819835

Contents xi

Conclusions and Future PerspectivesReferences

MCDA and Energy PlanningDanae Diakoulaki, Carlos Henggeler Antunes, António Gomes Martins

IntroductionMultiobjective Programming Models for Energy PlanningEnergy Planning Decisions with Discrete AlternativesConclusions

References

Multicriteria Analysis in Telecommunication Network Planning andDesign – Problems and Issues

João Clímaco, José CraveirinhaMotivationOverview of Current Evolutions in Telecommunication Networks andServicesMulticriteria Analysis in Telecommunication Network Planning andDesignReview and Discussion of Applications of MA to TelecommunicationNetwork PlanningFuture Trends

References

Multiple Criteria Decision Analysis and Sustainable DevelopmentGiuseppe Munda

The Concept of Sustainable DevelopmentMeasuring Sustainability: The Issue of Sustainability AssessmentIndexesA Defensible Axiomatic Setting for Sustainability Composite Indi-catorsWarning! 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 ofSustainability PoliciesConclusion

References

Part VIII MCDM Software

Multiple Criteria Decision Support SoftwareH. Roland Weistroffer, Charles H. Smith, Subhash C. Narula

IntroductionSoftware OverviewConcluding Remarks

5.

21

1.2.3.4.

22

1.2.

3.

4.

5.

23

1.2.

3.

4.5.6.

7.

24

1.2.3.

848849

859

860863874890891

899

900

900

908

912941944

953

954

958

963966971

976980981

989

990990

1009

xii MULTIPLE CRITERIA DECISION ANALYSIS

References

Contributing Authors

Index

1011

1019

1035

List of Figures

Graphical representation of R.Matrix representation of R.Graphical representation of the semiorder.Comparing the length of two rods.Comparing the length of composite rods.Using standard sequences.Building a standard sequence onBuilding a standard sequence onThe grid.The entire grid.The Thomsen condition.Restricted solvability onValue function when is discrete.Value function when is continuous.Inferring parameter values for ELECTRE TRI.Preference function.Valued outranking graph.The PROMETHEE outranking flows.Profile of an alternative.Projection on the GAIA plane.Alternatives and criteria in the GAIA plane.PROMETHEE II ranking. PROMETHEE decision axisand stick.Piloting the PROMETHEE decision stick.“Human Brain”.Two types of decision problems.Conflict between DM’s.Overview PROMETHEE GDSS procedure.Main window.

2.12.22.33.13.23.33.43.53.63.73.83.93.103.114.15.15.25.35.45.55.65.7

5.85.95.105.115.125.13

3434557879819495969799

100106107151169172173175176177

179180181182186186187

xiv MULTIPLE CRITERIA DECISION ANALYSIS

PROMETHEE rankings, action profiles, GAIA plane.Walking weights.Set of feasible weights.ORESTE flow chart.Outranking graph.Geometrical interpretation of preferences indices.Indifference areas.Indifference areas: rectangular.Indifference areas: rhomboidal.Indifference areas: elliptical.Aggregated semiorder structure.Aggregated pseudo-order structure.Partial profile of actionPartial profiles and partial broken lines ofPartial frequencies ofDetermination of a relation between the two alternatives

on the basis of the values of global indices.Partial preorder.Choice between two lotteries.Additive Independence Criterion for Risk.Piecewise linear approximation ofPiecewise linear approximation ofThe aggregation and disaggregation paradigms in MCDA [44].The disaggregation-aggregation approach [96].The normalized marginal value function.Post-optimality analysis [43].Ordinal regression curve (ranking versus global value).Normalized marginal value functions.A non-monotonic partial utility function [18].Distributional evaluation and marginal value function.Distribution of the actions and on [43].Simplified decision support process based on disaggre-gation approach [44].Methodological flowchart of MARKEX [63].Comparisons according to volume.To choose the best hospice plan, one constructs a hierar-chy modeling the benefits to the patient, to the institution,and to society. This is the benefits hierarchy of two sep-arate hierarchies.

5.145.156.16.26.36.46.56.66.76.86.96.106.116.126.136.14

6.157.17.27.37.48.18.28.38.48.58.68.78.88.98.10

8.119.19.2

188188202210215228232233234234236236241242243

254259279280289289300301303306307313316319321

329332359

361

List of Figures xv

To choose the best hospice plan, one constructs a hierar-chy modeling the community, institutional, and societalcosts. This is the costs hierarchy of two separate hierarchies.Employee evaluation hierarchy.Hierarchies for rating benefits, costs, opportunities, and risks.Prioritizing the strategic criteria to be used in rating the BOCR.How a hierarchy compares to a network.The supermatrix of a network and detail of a componentin it.The supermatrix of a hierarchy with the resulting limitmatrix corresponding to hierarchical composition.School choice hierarchy composition.Supermatrix of school choice hierarchy gives same re-sults as hierarchic composition.The clusters and nodes of a model to estimate the relativemarket share of Walmart, Kmart and Target.The clusters and nodes of a model to estimate the relativemarket share of footware.Hierarchy for rating benefits, opportunities, costs and risks.Example of sub-type b inconsistency.Example of incompatibility between (*) and (**).Procedure for all cases of inconsistency.Suggestion of change to resolve inconsistency.Matrix of judgements and basic MACBETH scale.Representations of the MACBETH scale.“Greatest” closed intervals included in the free and de-pendent intervals.Comparing two fuzzy intervals.Interpretation of the discriminant functions.Representation of the students problem.Classes forClasses forVisual representation of the classes,Results for the neighbour algorithm,

Decision tree representing knowledge included from Table 13.1.The hierarchy of attributes and criteria for a car classifi-cation problem.Different cases of interaction.Ternary alternatives for

9.3

9.49.59.69.79.8

9.9

9.10a9.10b

9.11

9.12

9.1310.110.210.310.410.510.610.7

12.112.212.312.412.512.612.7

13.113.2

14.114.2

362371380381384

385

385388

388

391

398405417424431433434435

437476493495496497499

501535

544578593

xvi MULTIPLE CRITERIA DECISION ANALYSIS

Illustrating the projection of a feasible and an infeasibleaspiration level point onto the nondominated surface.An example of the Pareto Race screen.The screen of the computer-graphics interface in VIMDA.Fuzzy inequality and equality relations.L-R fuzzy numberPossibility and necessity measures.Differences among six extended fuzzy relations.Relations among VWF, WF1, WF2, MF1, MF2, SF1,SF2 and VSF.Relations among VWF, MF1, MF2 and VSF.

Fuzzy maxSymmetric triangular fuzzy number defined byandTwo differences between fuzzy numbers andThe neo-classical view on the objective of the firm.Situations leading to MCDA in the firm.A bird’s-eye view of the framework.Feasible regions Z of (MC-Unrestr) and (MC-Bounds)for the same eight securities.Continuous, bullet-shaped, and unbounded feasible re-gion Z created by securities A, B and C.Nondominated frontiers as a function of changes in thevalue of upper bound parameterAn ellipsoidal feasible region projected onto two dimen-sional risk-return spaceTypical hierarchical structure of criteria used in energyplanning.MCDA methods in energy planning applications.State transition diagram.Example of priority regions.A systemic vision of sustainability issues.Impact matrix for the 4 chosen cities according to theselected indicators.The ideal problem structuring in SMCE.

16.1

16.216.318.118.218.318.418.5

18.618.718.818.9

18.1020.120.220.320.4

20.5

20.6

20.7

21.1

21.222.122.223.123.2

23.3

651660661726728731736

739740746746

748751811812817

826

827

830

834

882888914930956

967975

List of Tables

Principal t-norms and t-conorms.Various withEvaluation of the 5 offices on the 5 attributes.Evaluation table.Weights of relative importance.Types of generalised criteria Preference function).Single criterion net flows.Rank evaluation of alternatives (impact matrix).The concordance/discordance indices.Concordance matrix.Rank evaluation of alternatives (impact matrix).Regime matrix.Position-matrix.City-block.Preference matrix for a criterion with ordinal evaluation.Preference matrix for a criterion (Max) with evaluationon a ratio scale.Preference importance table forCombined preferences with weights variable.Evaluation of alternatives*.Criteria and (ordinal scales).Criterion (ordinal scale).Criterion (ratio scale MIN).Preference structure of weights.Pairwise comparison between andAxiomatic system of MAPPAC basic indices.Preference indices.Table of observed stochastic dominances.Explicable concordances indices.

2.12.23.15.15.25.35.46.16.26.36.46.56.66.76.86.9

6.106.116.126.136.146.156.166.176.186.196.206.21

375584

165168170176201201203204204208208211

211212212213213214214214214227228258259

xviii MULTIPLE CRITERIA DECISION ANALYSIS

Criteria values and ranking of the DM.Marginal value functions (initial solution).Linear programming formulation (post-optimality analysis).Post-optimality analysis and final solution.Marginal value functions (final solution).LP size of UTA models.Indicative applications of the UTA methods.The fundamental scale of absolute numbers.Which drink is consumed more in the U.S.? An exampleof estimation using judgments.The entries in this matrix respond to the question: Whichcriterion is more important with respect to choosing thebest hospice alternative and how strongly?The entries in this matrix respond to the question: Whichsubcriterion yields the greater benefit with respect to in-stitutional benefits and how strongly?The entries in this matrix respond to the question: Whichmodel yields the greater benefit with respect to direct careand how strongly?The entries in this matrix respond to the question: Whichcriterion is a greater determinant of cost with respect tothe care method and how strongly?The entries in this matrix respond to the question: Whichcriterion incurs greater institutional costs and how strongly?The entries in this matrix respond to the question: Whichmodel incurs greater cost with respect to institutionalcosts for recruiting staff and how strongly?Synthesis (P=Priorities, M=Model).(continued)Ranking intensities.Ranking alternatives.Random index.Calculating returns arithmetically.Normalized criteria weights and normalized alternativeweights from measurements in the same scale (additivesynthesis).Priority Ratings for the Merits: Benefits, Costs, Oppor-tunities, and Risks. Intensities: Very High (0.42), High(0.26), Medium (0.16), Low (0.1), Very Low (0.06).Four methods of synthesizing BOCR using the ideal mode.

8.18.28.38.48.58.68.79.19.2

9.3

9.4

9.5

9.6

9.7

9.8

9.99.99.109.119.129.139.14

9.15

9.16

309311312312313317335356

358

364

365

365

365

366

366367368371372374376

377

381382

List of Tables xix

The supermatrix.The limit supermatrix.The unweighted supermatrix.(continued)

The cluster matrix.The weighted supermatrix.(continued)The synthesized results for the alternatives.Footwear actual statistics and model results along withthe compatibility index.Priority ratings for the merits: Benefits, opportunities,costs and risks.Overall syntheses of the alternatives.Number of alternatives per evaluation level.Score of each of the evaluation levels.Profiles of the students.Importance indexes for the students problem.Global accuracy.Per class accuracy: Precise assignments.Assignments of the elements to intervals of classes.Importance indexes.Global and weighted accuracy in %.Data table presenting examples of comprehensive evalu-ations of students.Quality of classification and Shapley value for classifi-cation Cl and set of criteria P.Evaluations of new students.Evaluations of new students.Information table of the illustrative example.Students with interval evaluations.Example of missing values in the evaluation of students.Substitution of missing values in the evaluation of students.Decision table with reference objects.A fragment ofRanking of warehouses for sale by decision rules and theNet Flow Score procedure.Criteria for applicant evaluation.Comparison of hypothetical alternatives.An Example of a joint ordinal scale.

9.179.189.199.199.209.219.219.229.23

9.24

9.2512.112.212.312.412.512.612.712.812.913.1

13.2

13.313.413.513.613.713.813.913.1013.11

15.115.215.3

389389392393394395396397

401

405406485485495498498499499500501

511

522532533536538541542551552

554616618619

xx MULTIPLE CRITERIA DECISION ANALYSIS

Effectiveness of STEP-ZAPROS.Summary of references.Applications of MCDA approaches in bankruptcy andcredit risk assessment.Applications of MCDA approaches in portfolio selectionand management.Applications of MCDA approaches in the assessment ofcorporate performance.Applications of MCDA approaches in investment appraisal.Applications of MCDA approaches in other financialdecision-making problems.Broad categories of planning problems in power systems.Key aspects in problem structuring in papers of Group A.Key aspects in problem structuring in papers of Group B.Key aspects in problem structuring in papers of Group C.Key aspects in problem structuring in papers of Group D.Example of composite indicators. (Source: OECD; JRC,2002, cited in [72, p. 4])Normalised impact matrix.Outranking matrix of the 4 cities according to the 9 indicators.Possible ranking.Weighted outranking matrix.Possible ranking with new scores.Software by problem type.

15.419.120.1

20.2

20.3

20.420.5

21.121.221.321.421.523.1

23.223.323.423.523.624.1

624766

845

846

847848

848864880880880881

962968968968969970992

Introduction

José Figueira, Salvatore Greco, Matthias Ehrgott

1. Human Reflection about DecisionDecision has inspired reflection of many thinkers since the ancient times. Thegreat philosophers Aristotle, Plato, and Thomas Aquinas, to mention only afew names, discussed the capacity of humans to decide and in some mannersclaimed that this possibility is what distinguishes humans from animals. Toillustrate some important aspects of decision, let us briefly quote two importantthinkers: Ignatius of Loyola (1491-1556) and Benjamin Franklin (1706-1790).

To consider, reckoning up, how many advantages and utilities follow for me fromholding the proposed office or benefice [...] , and, to consider likewise, on thecontrary, the disadvantages and dangers which there are in having it. Doing thesame in the second part, that is, looking at the advantages and utilities there arein not having it, and likewise, on the contrary, the disadvantages and dangers innot having the same. [...] After I have thus discussed and reckoned up on all sidesabout the thing proposed, to look where reason more inclines: and so, accordingto the greater inclination of reason, [...], deliberation should be made on the thingproposed.

This fragment from the “Spiritual Exercises” of St. Ignatius of Loyola [14]has been taken from a paper by Fortemps and [12].

London, Sept 19, 1772

Dear Sir,

In the affair of so much importance to you, wherein you ask my advice, I cannot,for want of sufficient premises, advise you what to determine, but if you please Iwill tell you how. [...], my way is to divide half a sheet of paper by a line into twocolumns; writing over the one Pro, and over the other Con. [...] When I have thusgot them all together in one view, I endeavor to estimate their respective weights;and where I find two, one on each side, that seem equal, I strike them both out. IfI find a reason pro equal to some two reasons con, I strike out the three. If I judgesome two reasons con, equal to three reasons pro, I strike out the five; and thusproceeding I find at length where the balance lies; and if, after a day or two of

xxii MULTIPLE CRITERIA DECISION ANALYSIS

further consideration, nothing new that is of importance occurs on either side, Icome to a determination accordingly. [...] I have found great advantage from thiskind of equation, and what might be called moral or prudential algebra. Wishingsincerely that you may determine for the best, I am ever, my dear friend, yoursmost affectionately.

B. Franklin

This letter from Benjamin Franklin to Joseph Prestly has been taken from apaper by MacCrimmon [17].

What is interesting in the above two quotations is the fact that decision isstrongly related to the comparison of different points of view, some in favourand some against a certain decision. This means that decision is intrinsicallyrelated to a plurality of points of view, which can roughly be defined as criteria.Contrary to this very natural observation, for many years the only way to state adecision problem was considered to be the definition of a single criterion, whichamalgamates the multidimensional aspects of the decision situation into a singlescale of measure. For example, even today the textbooks of Operations Researchsuggest to deal with a decision problem as follows: to first define an objectivefunction, i.e., a single point of view like a comprehensive profit index (or acomprehensive cost index) representing the preferability (or dis-preferability)of the considered actions and then to maximize (minimize) this objective. Thisis a very reductive, and in some sense also unnatural, way to look at a decisionproblem. Thus, for at least thirty years, a new way to look at decision problemshas more and more gained the attention of researchers and practitioners. This isthe approach considered by Loyola and Franklin, i.e., the approach of explicitlytaking into account the pros and the cons of a plurality of points of view, in otherwords the domain of Multiple Criteria Decision Analysis (MCDA). Therefore,MCDA intuition is closely related to the way humans have always been makingdecisions. Consequently, despite the diversity of MCDA approaches, methodsand techniques, the basic ingredients of MCDA are very simple: a finite orinfinite set of actions (alternatives, solutions, courses of action, ...), at least twocriteria, and, obviously, at least one decision-maker (DM). Given these basicelements, MCDA is an activity which helps making decisions mainly in termsof choosing, ranking or sorting the actions.

2. Technical Reflection about Decision: MCDAResearchers before MCDA

Of course, not only philosophers reasoned about decision-making. Many im-portant technical aspects of MCDA are linked to classic works in economics, inparticular, welfare economics, utility theory and voting oriented social choicetheory (see [28]). Aggregating the opinion or the preferences of voters or indi-viduals of a community into collective or social preferences is quite similar a

Introduction xxiii

problem to devising comprehensive preferences of a decision-maker from a setof conflicting criteria in MCDA [7].

Despite the importance of Ramon Llull’s (1232-1316) and Nicolaus Cu-sanus’s (1401-1464) concerns about and interests in this very topic, the originsof voting systems are often attributed to Le Chevalier Jean-Charles de Borda(1733-1799) and Marie Jean Antoine Nicolas de Caritat (1743-1794), Le Mar-quis de Condorcet. However, Ramon Llull introduced the pairwise comparisonconcept before Condorcet [13], while Nicolaus Cusanus introduced the scor-ing method about three and a half centuries before Borda [27]. Furthermore, itshould be noted that a letter from Pliny the Younger AD 105) to Titus Aristoshows that he introduced the ternary approval voting strategy and was interestedin voting systems a long time before Ramon Llull and Nicolaus Cusanus [18,Chapter 2]. Anyway, Borda’s scoring method [4] has some similarities withcurrent utility and value theories as has Condorcet’s method [10] with the out-ranking approach of MCDA. In the same line of concerns, i.e., the aggregationof individual preferences into collective ones, Jeremy Bentham (1748-1832)introduced the utilitarian calculus to derive the total utility for the society fromthe aggregation of the personal interests of the individuals of a community[3]. Inspired by Bentham’s works, Francis Ysidro Edgeworth (1845-1926), autilitarian economist, was mainly concerned with the maximization of the util-ity of the different competing agents in economy. Edgeworth tried to find thecompetitive equilibrium points for the different agents. He proposed to drawindifference curves (lines of equal utility) for each agent and then derive thecontract curve, a curve that corresponds to the notion of the Pareto or efficientset [21]. Not long afterwards, Vilfredo Federico Damaso Pareto (1848-1923)gave the following definition of ophelimity [utility] for the whole community[22]:

We will say that the members of a collectivity enjoy maximum ophelimity in acertain position when it is impossible to find a way of moving from that posi-tion very slightly in such a manner that the ophelimity enjoyed by each of theindividuals of that collectivity increases or decreases. That is to say, any smalldisplacement in departing from that position necessarily has the effect of increas-ing the ophelimity which certain individuals enjoy, of being agreeable to some,and disagreeable to others.

From this definition it is easy to derive the concept of dominance, whichtoday is one of the fundamental concepts in MCDA.

MCDA also benefits from the birth and development of game theory. FélixEdouard Justin Emile Borel (1871-1956) and John von Neumann (1903-1957)are considered the founders of game theory [5, 6, 20, 19]. Many concepts fromthis discipline had a strong impact on the development of MCDA.

The concept of efficient point was first introduced in 1951 by Tjalling Koop-mans (1910-1985) in his paper “Analysis of production as an efficient combi-nation of activities” [15]:

xxiv MULTIPLE CRITERIA DECISION ANALYSIS

A possible point in the commodity space is called efficient whenever an increasein one of its coordinates (the net output of one good) can be achieved only at thecost of a decrease in some other coordinate (the net output of a good).

In the same year (1951) Harold William Kuhn (born 1925) and Albert WilliamTucker (1905-1995) introduced the concept of vector maximum problem [16].In the sixties, basic MCDA concepts were explicitly considered for the firsttime. As two examples we mention Charnes’ and Cooper’s works on goal pro-gramming [8] and the proposition of ELECTRE methods by Roy [23]. Theseventies saw what is conventionally considered the “official” starting point ofMCDA, the conference on “Multiple Criteria Decision Making” organised in1972 by Cochrane and Zeleny at Columbia University in South Carolina [9].Since then MCDA has seen a tremendous growth which continues today.

3. The Reasons for this Collection of State-of-the-ArtSurveys

The idea of MCDA is so natural and attractive that thousands of articles anddozens of books have been devoted to the subject, with many scientific journalsregularly publishing articles about MCDA. To propose a new collection of state-of-the-art surveys of MCDA in so rich a context may seem a rash enterprise.Indeed, some objections come to mind. There are many and good handbooksand reviews on the subject (to give an idea consider [1,11, 25, 26, 29]). The mainideas are well established for some years and one may question the contributionsthis volume can provide. Moreover, the field is so large and comprises devel-opments so heterogeneous that it is almost hopeless to think that an exhaustivevision of the research and practice of MCDA can be given.

We must confess that at the end of the work of editing this volume we agreewith the above remarks. However, we believe that a new and comprehensivecollection of state-of-the-art surveys on MCDA can be very useful. The mainreasons which, despite our original resistance, brought us to propose this bookare the following:

Many of the existing handbooks and reviews are not too recent. SinceMCDA is a field which is developing very quickly this is an importantreason.

Even though the field of research and application of MCDA is so large,there are some main central themes around which MCDA research andapplications have been developed. Therefore our approach was to try topresent the – at least in our opinion – most important of these ideas.

1

2

With reference to the first point, we can say that we observed many theoreticaldevelopments which changed MCDA over the last ten years. We tried to consider

Introduction xxv

these changes as much as possible and in this perspective strong points of thebook are the following:

It presents the most up-to-date discussions on well established method-ologies and theories such as outranking based methods and MAUT.

The book also contains surveys of new, recently emerged fields such asconjoint measurement, fuzzy preferences, fuzzy integrals, rough sets andothers.

1

2

Following these points we drafted a list of topics and asked well knownresearchers to present them. We encouraged the authors to cooperate with theaim to present different perspectives if topics had some overlap. We asked theauthors to present a comprehensive presentation of the most important aspectsof the field covered by their chapters, a simple yet concise style of exposition,and considerable space devoted to bibliography and survey of relevant literature.We also requested a sufficiently didactic presentation and a text that is useful forresearchers in MCDA as well as for people interested in real life applications.

The importance of these requirements is related also to the specific waythe MCDA community looks at its research field. It can be summarized in theobservation that there is a very strong and vital link between theoretical andmethodological developments on the one hand and real applications on theother hand. Thus, the validity of theoretical and methodological developmentscan only be measured in terms of the progress given to real world practice.Moreover, interest of MCDA to deal with concrete problems is related to theconsideration of a sound theoretical basis which ensures the correct applicationof the methodologies taken into account.

In fact, not only the chapters of our book but rather all MCDA contributionsshould satisfy the requirements stated out above, because they should be not too“esoteric” and therefore understandable for students, theoretically well founded,and applicable to some advantage in reality.

4. A Guided Tour of the Book

Of course, this book can be read from the first to the last page. However, we thinkthat this is not the only possibility and it may not even be the most interestingpossibility. In the following we propose a guided tour of the book suggestingsome reference points that are hopefully useful for the reader.

4.1 Part I: An Overview of MCDA Techniques TodayThis part is important because MCDA is not just a collection of theories, method-ologies, and techniques, but a specific perspective to deal with decision prob-lems. Losing this perspective, even the most rigorous theoretical developmentsand applications of the most refined methodologies are at risk of being meaning-

xxvi MULTIPLE CRITERIA DECISION ANALYSIS

less, because they miss an adequate consideration of the aims and of the role ofMCDA. We share this conviction with most MCDA researchers. Bernard Roydiscusses these “pre-theoretical” assumptions of MCDA and gives an overviewof the field. Bernard Roy, besides giving many important theoretical contribu-tions, engaged himself in thorough reflections on the meaning and the value ofMCDA, proposing some basic key concepts that are accepted throughout theMCDA community.

4.2 Part II: Foundations of MCDAThis part of the book is related to a fundamental problem of MCDA, the repre-sentation of preferences. Classically, for example in economics, it is supposedthat preference can be represented by a utility function assigning a numeri-cal value to each action such that the more preferable an action, the larger itsnumerical value. Moreover, it is very often assumed that the comprehensiveevaluation of an action can be seen as the sum of its numerical values for theconsidered criteria. Let us call this the classical model. It is very simple but nottoo realistic. Indeed, there is a lot of research studying under which conditionsthe classical model holds. These conditions are very often quite strict and it isnot reasonable to assume that they are satisfied in all real world situations. Thus,other models relaxing the conditions underlying the classical model have beenproposed. This is a very rich field of research, which is first of all importantfor those interested in the theoretical aspects of MCDA. However, it is also ofinterest to readers engaged in applications of MCDA. In fact, when we adopt aformal model it is necessary to know what conditions are supposed to be sat-isfied by the preferences of the DM. In the two chapters of this part problemsrelated to the representations of preferences are discussed.

Meltem Öztürk, Alexis Tsoukiàs, and Philippe Vincke present a very exhaus-tive review of preference modelling, starting from classical results but arrivingat the frontier of some challenging issues of scientific activity related to fuzzylogic and non-classical logic.

Denis Bouyssou and Marc Pirlot discuss the axiomatic basis of the differentmodels to aggregate multiple criteria preferences. We believe that this chapteris very important for the future of MCDA. Initially, the emphasis of MCDAresearch was on proposal of new methods. But gradually the necessity to un-derstand the basic conditions underlying each method and its specific axioma-tization became more and more apparent. This is the first book on MCDA withso much space dedicated to the subject of foundations of MCDA.

4.3 Part III: Outranking Methods

In this part of the book the class of outranking based multiple criteria decisionmethods is presented. Given what is known about the decision-maker’s prefer-

Introduction xxvii

ences and given the quality of the performances of the actions and the natureof the problem, an outranking relation is a binary relation S defined on the setof potential actions A such that if there are enough arguments to decidethat is at least as good as whereas there is no essential argument to refutethat statement [24]. Methods which strictly apply this definition of outrankingrelation are the ELECTRE methods. They are very important in many respects,not least historically, since ELECTRE I was the first outranking method [2].

However, within the class of outranking methods we generally consider allmethods which are based on pairwise comparison of actions. Thus, anotherclass of very well known multiple criteria methods, PROMETHEE methods,are considered in this part of the book. Besides ELECTRE and PROMETHEEmethods, many other interesting MCDA methods are based on the pairwisecom-parison of actions. José Figueira, Vincent Mousseau and Bernard Roy presentthe ELECTRE methods; Jean-Pierre Brans and Bertrand Mareschal presentthe PROMETHEE methods and Jean-Marc Martel and Benedetto Matarazzoreview the rich literature of other outranking methods.

4.4 Part IV: Multiattribute Utility and Value Theories

In this part of the book we consider multiple attribute utility theory (MAUT).This MCDA approach tries to assign a utility value to each action. This utility isa real number representing the preferability of the considered action. Very oftenthe utility is the sum of the marginal utilities that each criterion assigns to theconsidered action. Thus, this approach very often coincides with what we calledthe classical approach before. As we noted in commenting Part I, this approachis very simple at first glance. It is often applied in real life, e.g., every timewe aggregate some indices by means of a weighted sum we are applying thisapproach. Despite its simplicity the approach presents some technical problems.The first are related to the axiomatic basis and to the construction of marginalutility functions (i.e., the utility functions relative to each single criterion),both in case of decision under certainty and uncertainty. These problems areconsidered by James Dyer in a comprehensive chapter about the fundamentalsof this approach.

Yannis Siskos, Vangelis Grigoroudis and Nikolaos Matsatsinis present thevery well known UTA methods, which on the basis of the philosophy of theaggregation-disaggregation approach and using linear programming, build aMAUT model that is as consistent as possible with the DM’s preferences ex-pressed in actual previous decisions or on a “training sample”. The philosophyof aggregation-disaggregation can be summarized as follows: How is it possi-ble to assess the decision-maker’s preference model leading to exactly the samedecision as the actual one or at least the most “similar” decision?

xxviii MULTIPLE CRITERIA DECISION ANALYSIS

Thomas Saaty presents a very well known methodology to build utility func-tions, the AHP (Analytic Hierarchy Process) and its more recent extension,the ANP (Analytic Network Process). AHP is a theory of measurement thatuses pairwise comparisons along with expert judgments to deal with the mea-surement of qualitative or intangible criteria. The ANP is a general theory ofrelative measurement used to derive composite priority ratio scales from in-dividual ratio scales that represent relative measurements of the influence ofelements that interact with respect to control criteria. The ANP captures theoutcome of dependence and feedback within and between clusters of elements.Therefore AHP with its dependence assumptions on clusters and elements is aspecial case of the ANP.

Carlos Bana e Costa, Jean-Claude Vansnick, and Jean-Marie De Corte presentanother MCDA methodology based on the additive utility model. This method-ology is MACBETH (Measuring Attractiveness by a Categorical Based Evalu-ation Technique). It is an MCDA approach that requires only qualitative judge-ments about differences of values of attractiveness of one action over anotheraction to help an individual or a group to quantify the relative preferability ofdifferent actions. In simple words, the MACBETH approach tries to answer thefollowing questions: How can we build an interval scale of preferences on a setof actions without forcing evaluators to produce direct numerical representa-tions of their preferences? How can we coherently aggregate these qualitativeevaluations using an additive utility model?

4.5 Part V: Non-Classical MCDA Approaches

Many approaches have been proposed in MCDA besides outranking methodsand multiattribute utility theory. In this part of the book we try to collect in-formation about some of the most interesting proposals. First, the question ofuncertainty in MCDA is considered. Theo Stewart discusses risk and uncertaintyin MCDA. It is necessary to distinguish between internal uncertainties (relatedto decision-maker values and judgements) and external uncertainties (relatedto imperfect knowledge concerning consequences of actions). The latter, cor-responding to the most accepted interpretation of uncertainty in the specializedliterature, has been considered in the chapter. Four broad approaches for deal-ing with external uncertainties are discussed. These are multiattribute utilitytheory and some extensions; stochastic dominance concepts, primarily in thecontext of pairwise comparisons of alternatives; the use of surrogate risk mea-sures such as additional decision criteria; and the integration of MCDA andscenario planning.

The second consideration is the fuzzy set approach to MCDA. Most realworld decision problems take place in a complex environment where conflict-ing systems of logic, uncertain and imprecise knowledge, and possibly vague

Introduction xxix

preferences have to be considered. To face such complexity, preference model-ing requires the use of specific tools, techniques, and concepts which allow theavailable information to be represented with the appropriate granularity. In thisperspective, fuzzy set theory has received a lot of attention in MCDA for a longtime. Patrick Meyer and Marc Roubens present the fuzzy set approach to MCDAfor choice, ranking, and sorting problems. In this chapter, several MCDA ap-proaches based on fuzzy evaluations are reviewed. The authors give details ona sorting procedure for the assignment of alternatives to graded classes whenthe available information is given by interacting points of view and a subsetof prototypic alternatives whose assignment is given beforehand. A softwarededicated to that approach (TOMASO) is briefly presented. Finally they recallthe concepts of good and bad choices based on dominant and absorbent kernelsin the valued digraph that corresponds to an ordinal valued outranking relation.

Salvatore Greco, Benedetto Matarazzo and present thedecision rule approach to MCDA. This approach represents the preferences interms of “if ..., then ...” decision rules such as, for example, “if the maximumspeed of car is at least 175 km/h and its price is at most $12000, then car

is comprehensively at least medium”. This approach is related to rough settheory and to artificial intelligence. Its main advantages are the following. TheDM gives information in the form of examples of decisions, which requiresrelatively low cognitive effort and which is quite natural. The decision model isalso expressed in a very natural way by decision rules. This permits an absolutetransparency of the methodology for the DM. Another interesting feature ofthe decision rule approach is its flexibility, since any decision model can beexpressed in terms of decision rules and, even better, the decision rule modelcan be much more general than all other existing decision models used inMCDA.

Michel Grabisch and Christophe Labreuche present the fuzzy integral ap-proach that is known in MCDA for the last two decades. In very simple wordsthis methodology permits a flexible modeling of the importance of criteria. In-deed, fuzzy integrals are based on a capacity which assigns an importance toeach subset of criteria and not only to each single criterion. Thus, the importanceof a given set of criteria is not necessarily equal to the sum of the importanceof the criteria from the considered subset. Consequently, if the importance ofthe whole subset of criteria is smaller than the sum of the importances of itsindividual criteria, then we observe a redundancy between criteria, which insome way represents overlapping points of view. On the other hand, if the im-portance of the whole subset of criteria is larger than the sum of the importancesof its members, then we observe a synergy between criteria, the evaluations ofwhich reinforce one another. On the basis of the importance of criteria measuredby means of a capacity, the criteria are aggregated by means of specific fuzzy

xxx MULTIPLE CRITERIA DECISION ANALYSIS

integrals, the most important of which are the Choquet integral (for cardinalevaluations) and the Sugeno integral (for ordinal evaluations).

Finally, Helen Moshkovich, Alexander Mechitov and David Olson presentthe verbal decision methods MCDA. This is a class of methods originated fromthe work of one of the MCDA pioneers, the late Oleg Larichev. The idea ofverbal decision analysis is to build a decision model using mostly qualitativeinformation expressed in terms of a language that is natural for the DM. More-over, measurement of criteria and preference elicitation should be psycholog-ically valid. The methods, besides being mathematically sound, should checkthe DM’s consistency and provide transparent recommendations.

4.6 Part VI: Multiobjective Mathematical Programming

The classical formulation of an Operations Research model is based on the max-imization or minimization of an objective function subject to some constraints.A very rich and powerful arsenal of methodologies and techniques has beendeveloped and continues to be developed within Operations Research. How-ever, it is very difficult to summarize all the points of view related to the desiredresults of the decision at hand in only one objective function. Thus, it seemsnatural to consider a very general formulation of decision problems where a setof objective functions representing different criteria have to be “optimized”. Todeal with these types of problems requires not only to generalize the method-ologies developed for classical single objective optimization problems, but alsoto introduce new methodologies and techniques permitting to compare differentobjectives according to the preferences of the DM. In this part of the book wetried to give adequate space to these two sides of multiobjective programmingproblems.

Emphasis on the side of gathering information from the decision-maker andconsequent preference representation is given in the first chapter of this part, inwhich Pekka Korhonen introduces the main concepts and basic ideas of inter-active methods dealing with multiobjective programming problems. The basicobservation is that, since the DM tries to “maximize” a set of criteria in con-flict with each other and an increment of one criterion can only be reached byaccepting a decrement of at one or more other criteria, we need to compare theadvantages coming from increments with respect to some criteria with the dis-advantages coming from corresponding decrements of other criteria. A utilityor value function representing DM preferences would seem the most appro-priate for this aim, but the key assumption in multiple objective programmingis that this utility function is unknown. Therefore many methodologies havebeen proposed with the aim of developing a fruitful dialogue with the DM per-mitting, on the one hand, to provide the DM with relevant information aboutnon-dominated solutions and, on the other hand, to obtain useful information

Introduction xxxi

about the preferences of the DM. This dialogue is generally assisted by spe-cific software, very often employing graphical representations of the results. Itpermits to define a solution which the DM can accept as a good compromise.

In the next chapter, Matthias Ehrgott and Margaret Wiecek introduce math-ematical methods to solve multiobjective programming (MOP) problems. Intheir survey, they present solution concepts of MOP, properties of efficient andnondominated sets, optimality conditions, solution techniques, approximationof efficient and nondominated sets, and specially-structured problems includinglinear and discrete MOPs as well as selected nonlinear MOPs. The contents ofthe chapter have been selected on the idea that the primary (although not nec-essarily the ultimate) goal of multiobjective programming is to seek solutionsof MOPs and therefore a special attention was paid to methods suitable forfinding these solutions. Since the ultimate goal of MOP problem is selection ofa preferred solution, for which an adequate representation of DM preferencesis necessary, this chapter is well complemented by the previous one.

Masahiro Inuiguchi deals with multiple objective programming problemswith fuzzy coefficients. The introduction of fuzziness in multiple objectiveprogramming is due to the observation that in real world problems imprecisespecifications of parameters fluctuating in certain ranges are very usual. Forexample, let us consider an activity for which the acceptable expense is 100million dollars. However, the DM may accept the expense of 100.1 million dol-lars if the objective functions take much better values by this small violation ofthe constraint. Due to their specific nature, fuzzy multiobjective programmingproblems need an interpretation which leads to specific approaches to the prob-lem. Since fuzzy programming has a relatively long history, many approachesrelated to different interpretations of the fuzzy MOP have been proposed. In thischapter the approach based on necessity and possibility is considered, as manyof the approaches proposed in the specialized literature are of this type. Thedifference to other approaches often lies solely in the measures employed forthe evaluation of a fuzzy event. Thus, describing the approaches based on pos-sibility and necessity measures would be sufficient to acknowledge the essenceof multiple objective programming problems with fuzzy coefficients.

Finally, this part is concluded by a chapter that deals with an area of Op-erations Research in which multiobjective programming has been used quitefrequently. Stefan Nickel, Justo Puerto and Antonio Rodríguez-Chía presentthe multiple criteria approach to locational analysis. An important characteris-tic of location models is their intrinsic multiple criteria nature. In this contextdifferent criteria are related to one or several new facilities and depend on thedistances of these facilities to the set of fixed or demand facilities. There are atleast two natural ways of deriving the different criteria. First, a decision about anew facility to be located is typically a group decision and each decision makerwill have his own preferences, which may be expressed by a corresponding

xxxii MULTIPLE CRITERIA DECISION ANALYSIS

criterion. Secondly, the functions may represent different evaluation criteriafor the new facility to be located, like cost, reachability, risk, etc. The chapterprovides a broad overview of the most representative multiple criteria locationproblems which have been divided into the three classes of continuous, network,and discrete problems.

4.7 Part VII: Applications

It is apparent that the validity and success of all the developments of MCDAresearch are measured by the number and quality of the decisions supported byMCDA methodologies. Applications in this case discriminate between resultsthat are really interesting for MCDA and results that, even though beautifuland interesting for economics, mathematics, psychology, or other scientificfields, are not interesting for MCDA. The applications of MCDA in real worldproblems are very numerous and in very different fields. Therefore, it was clearfrom the outset that it would be impossible to cover all the fields of applicationof MCDA. We decided to select some of the most significant areas.

Jaap Spronk, Ralph Steuer and Constantin Zopounidis discuss the contribu-tions of MCDA in finance. A very valuable feature of their chapter is the focuson justification of the multidimensional character of financial decisions and theuse of different MCDA methodologies to support them. The presentation ofthe contributions of MCDA in finance permits to structure complex evaluationproblems in a scientific context and in a transparent and flexible way, with theintroduction of both quantitative (i.e., financial ratios) and qualitative criteriain the evaluation process.

Danae Diakoulaki, Carlos Henggeler Antunes and António Gomes Martinspresent applications of MCDA in energy planning problems. In modern tech-nologically developed societies, decisions concerning energy planning must bemade in complex and sometimes ill-structured contexts, characterized by tech-nological evolution, changes in market structures, and new societal concerns.Decisions to be made by different agents (at utility companies, regulatory bod-ies, and governments) must take into account several aspects of evaluation suchas technical, socio-economic, and environmental ones, at various levels of de-cision making (ranging from the operational to the strategic level) and withdifferent time frames. Thus, energy planning problems inherently involve mul-tiple, conflicting and incommensurate axes of evaluation. The chapter aims atexamining to which extent the use of MCDA in energy planning applicationshas been influenced by those changes currently underway in the energy sector,in the overall socio-economic context, and in particular to which extent it isadapted to the new needs and structuring and modelling requirements.

João Clímaco and José Craveirinha present multiple criteria decision analysisin telecommunication network planning and design. Decision making processes

Introduction xxxiii

in this field take place in an increasingly complex and turbulent environmentinvolving multiple and potentially conflicting options. Telecommunication net-works is an area where different socio-economic decisions involving commu-nication issues have to be made, but it is also an area where technologicalissues are of paramount importance. This interaction between a complex socio-economic environment and the extremely fast development of new telecommu-nication technologies and services justifies the interest in using multiple criteriaevaluation in decision making processes. The chapter presents a review of con-tributions in these areas, with particular emphasis on network modernisationplanning and routing problems and outlines an agenda of current and futureresearch trends and issues for MCDA in this area.

Finally, Giuseppe Munda addresses applications of MCDA in problems con-cerning sustainable development. Sustainable development is strongly relatedto environmental questions, i.e., sustainable development generalizes environ-mental management taking into account not only an ecological but also socio-economic, technical and ethical perspectives. Ecological problems were amongthe first to be dealt with by MCDA. Therefore, there is a strong tradition in thisfield and many interesting stimuli for MCDA research came from there. Theextensive perspective of sustainable development is very significant because itimproves the quality of decisions concerning the environment taking into ac-count other criteria, which are not strictly environmental but which stronglyinteract with it. In making sustainability policies operational, basic questionsto be answered are sustainability of what and whom? As a consequence, sus-tainability issues are characterised by a high degree of conflict. Therefore, inthis context MCDA appears as an adequate approach.

4.8 Part VIII: MCDM SoftwareApplication of an MCDA method requires such a considerable amount of com-putation that even the development of many MCDA methodologies withoutthe use of a specialized software is hardly imaginable. While software is aneven more important element in the application of MCDA methodologies, thisdoes not mean that to have a good software is sufficient to apply an MCDAmethodology correctly. Clearly, software is a tool and it should be used as atool. Before using a software, it is necessary to have a sound knowledge of theadopted methodology and of the decision problem at hand.

After these remarks about cautious use of software, the problem is: Whatsoftware is available for MCDA? Heinz Roland Weistroffer, Subhash Narulaand Charles H. Smith present well known MCDA software packages. Whilethere is certainly some MCDA software available that is not present in thechapter, it can help the reader. She may get suggestions of well known software,

xxxiv MULTIPLE CRITERIA DECISION ANALYSIS

but also information about aspects to be taken into account when evaluating asoftware for adoption in an application.

5. Acknowledgment to the Referees

The editors are very grateful to Euro Beinat, Nabil Belacel, Denis Bouys-sou, John Buchanan, João Clímaco, Danae Diakoulaki, Luís Dias, MichaelDoumpos, Ernest Forman, Philippe Fortemps, Lorraine Gardiner, ChristopheGonzales, Michel Grabisch, Winfried Hallerbach, Raimo P. Hämäläinen, Car-los Henggeler Antunes, Masahiro Inuiguchi, Robin Keller, Pekka Korhonen,Masahiro Inuiguchi, Christophe Labreuche, RistoLahdelma, Thierry Marchant,Benedetto Matarazzo, Manuel Matos, Nikolaos Matsatsinis, Kaisa Miettinen,Maria Franca Norese, Wlodzimierz Ogryczak, Patrice Perny, Jacques Pictet,Marc Pirlot, Jean-Charles Pomerol, Justo Puerto, Marc Roubens,

Jerzy Stefanowsky, Ralph Steuer, Theo Stewart, Christianne Tammer,Jean-Claude Vansnick, Luis Vargas, Philippe Vincke, Peter Wakker, MargaretWiecek, Szymon Wilk who served as referees for this volume.

The editors would also like to express their gratitude to people who supportedthem with very valuable advice along all the preparation of the book: BernardRoy, Denis Bouyssou, Benedetto Matarazzo, Gary Folvenand Frederick S. Hillier.

Acknowledgments

José Figueira was supported by the grant SFRH/BDP/6800/2001 (Fundaçãopara a Ciência e Tecnologia, Portugal) and gratefully acknowledges DIMACSResearch Center at Rutgers University and LAMSADE at University Paris-Dauphine for the welcome during his sabbatical leave and the short visits tothe Catania University, Auckland University and London School of Economics.His research has partially benefited also from MONET research grant (POCTI/GES/37707) and the luso-french scientifique collaborations ICCTI/Embassyof France in Lisbon (500B4) and Program Pessoa 2004. Matthias Ehrgott waspartially supported by University of Auckland grant 3602178/9275 and by theDeutsche Forschungsgemeinschaft grant Ka 477/27-1.

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