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MULTIPLE CRITERIADECISION ANALYSIS:STATE OF THE ART SURVEYS
Edited by
JOSE FIGUEIRAUniversity of Coimbra
SALVATORE GRECOUniversity of Catania
MATTHIAS EHRGOTTUniversity of Auckland
Kluwer Academic PublishersBoston/Dordrecht/London
Contents
List of Figures ix
List of Tables xvi
Introduction xvii
Jose Figueira, Salvatore Greco, Matthias Ehrgott
1. Human Reflection about Decision xvii
2. Technical Reflection about Decision: MCDA Researchersbefore MCDA xviii
3. The Reasons for this Collection of State-of-the-Art Surveys xx
4. A Guided Tour of the Book xxi
5. Acknowledgment to the Referees xxx
References xxx
Part I An Overview of MCDA Techniques Today
1
Paradigms and Challenges 3Bernard Roy
1. What Are the Expectations that Multicriteria Decision Aiding(MCDA) Responds to? 4
2. Three Basic Concepts 7
3. How to Take Into Account Imperfect Knowledge? 12
4. An Operational Point of View 14
5. Conclusion 17
References 18
Part II Foundations of MCDA
2
Preference Modelling 27
MeltemOzturk, Alexis Tsoukias, Philippe Vincke
1. Introduction 28
2. Purpose 28
3. Nature of Information 30
4. Notation and Basic Definitions 32
5. Languages 33
6. Preference Structures 39
7. Domains and Numerical Representations 48
8. Logic of Preferences 56
9. Conclusion 59
References 60
3
Conjoint measurement tools for MCDM 73Denis Bouyssou, Marc Pirlot
1. Introduction and Motivation 74
2. Definitions and Notation 89
3. The Additive Value Model in the “Rich” Case 92
4. The Additive Value Model in the “Finite” Case 102
5. Extensions 112
References 119
Part III Outranking Methods
4
ELECTRE Methods 133Jose Figueira, Vincent Mousseau, Bernard Roy
1. Introduction: A Brief History 134
2. Main Features of ELECTRE Methods 136
3. A Short Description of ELECTRE Methods 139
4. Recent Developments and Future Issues 149
5. Software and Applications 151
6. Conclusion 153
References 153
5
PROMETHEE Methods 163Jean-Pierre Brans, Bertrand Mareschal
1. History 164
2. Multicriteria Problems 164
3. The PROMETHEE Preference Modelling Information 168
4. The PROMETHEE I and II Rankings 171
5. The GAIA Visual Interactive Module 175
6. The PROMETHEE VI Sensitivity Tool (The “Human Brain”)181
7. PROMETHEE V: MCDA under Constraints 182
8. The PROMETHEE GDSS Procedure 183
9. The DECISION LAB Software 186
References 189
6
Other Outranking Approaches 197Jean-Marc Martel, Benedetto Matarazzo
1. Introduction 198
2. Other Outranking Methods 198
3. Pairwise Criterion Comparison Approach 221
4. One Outranking Method for Stochastic Data 254
5. Conclusions 259
References 260
Part IV Multiattribute Utility and Value Theories
7
MAUT – Multiattribute Utility Theory 265James S. Dyer
1. Introduction 266
2. Preference Representations Under Certainty and Under Risk 267
3. Ordinal Multiattribute Preference Functions for the Case ofCertainty 273
4. Cardinal Multiattribute Preference Functions for the Case ofRisk 278
5. Measurable Multiattribute Preference Functions for theCaseofCertainty 281
6. The Relationships Among the Multiattribute Preference Func-tions 290
7. Concluding Remarks 292
References 294
8
UTA Methods 297Yannis Siskos, Evangelos Grigoroudis, Nikolaos F. Matsatsinis
1. Introduction 298
2. The UTA Method 302
3. Variants of the UTA Method 313
4. Applications and UTA-based DSS 328
5. Concluding Remarks and Future Research 334
References 335
9
The Analytic Hierarchy and Analytic Network Processes for theMeasurement of Intangible Criteria and for Decision-Making
345
Thomas L. Saaty
1. Introduction 346
2. Pairwise Comparisons; Inconsistencyand the Principal Eigen-vector 348
3. Stimulus Response and the Fundamental Scale 354
4. Hospice Decision 359
5. Rating Alternatives One at a Time in the AHP – AbsoluteMeasurement 369
6. Paired Comparisons Imply Dependence 372
7. When is a Positive Reciprocal Matrix Consistent? 373
8. In the Analytic Hierarchy Process Additive Composition isNecessary 375
9. Benefits, Opportunities, Costs and Risks 377
10. On the Admission of China to the World Trade Organization(WTO) 378
11. The Analytic Network Process (ANP) 382
12. Two Examples of Estimating Market Share – The ANP witha Single Benefits Control Criterion 389
13. Outline of the Steps of the ANP 400
14. Complex Decisions with Dependence and Feedback 403
15. Conclusions 405
References 406
10
On the Mathematical Foundation of MACBETH 409Carlos A. Bana e Costa, Jean-Marie De Corte, Jean-Claude Vansnick
1. Introduction 410
2. Previous Research and Software Evolution 412
3. Types of Preferential Information 414
4. Numerical Representation of the Preferential Information 415
5. Consistency – Inconsistency 416
6. Consistency Test for Preferential Information 417
7. Dealing with Inconsistency 420
8. The MACBETH Scale 432
9. Discussion About a Scale 435
10. MACBETH and MCDA 437
References 438
Part V Non-Classical MCDA Approaches
11
Dealing with Uncertainties in MCDA 445Theodor J Stewart
1. What is Uncertainty? 446
2. Probabilistic Models and Expected Utility 450
3. Pairwise Comparisons 454
4. Risk Measures as Surrogate Criteria 457
5. Scenario Planning and MCDA 460
6. Implications for Practice 466
References 467
12
Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid 471Patrick Meyer, Marc Roubens
1. Introduction 472
2. The Data Set 474
3. Valued Preference Relation and Outranking Relation 475
4. Aggregation Procedures 478
5. The Sorting Problem 482
6. TheTomaso Method 483
7. The Choice Problem 502
8. Conclusion 503
References 504
13
Decision Rule Approach 507Salvatore Greco, Benedetto Matarazzo, Roman Słowinxski
1. Introduction 508
2. Dominance-based Rough Set Approach (DRSA) to Multiple-criteria Classification 511
3. Variable-ConsistencyDominance-Based Rough Set Approach(VC-DRSA) 525
4. Induction of Decision Rules from Rough Approximations ofUpward and Downward Unions of Decision Classes 527
5. Extensions of DRSA 536
6. DRSA for Multiple-criteria Choice and Ranking 544
7. Conclusions 555
References 557
14
Fuzzy Measures and Integrals in MCDA 563Michel Grabisch, Christophe Labreuche
1. Introduction 564
2. Measurement Theoretic Foundations 566
3. Unipolar Scales 570
4. Bipolar Scales 583
5. Ordinal Scales 595
6. Concluding Remarks 604
References 604
15
Verbal Decision Analysis 609Helen Moshkovich, Alexander Mechitov, David Olson
1. Features of Unstructured Decision Problems 610
2. Main Principles of Verbal Decision Analysis 610
3. Decision Methods for Multicriteria Alternatives Ranking 615
4. Decision Methods for Multicriteria Alternatives’ Classifica-tion 625
5. Place of Verbal Decision Analysis in MCDA 628
6. Conclusion 633
References 634
Part VI Multiobjective Mathematical Programming
16
Interactive Methods 641Pekka Korhonen
1. Introduction 642
2. Basic Definitions and Some Theory 643
3. Principles for Implementing Interactive Methods 645
4. Generating Nondominated Solutions 649
5. Solving Multiple Objective Problems 652
6. Final Solution 656
7. Examples of Software Systems: VIG and VIMDA 657
8. Concluding Remarks 661
References 662
17
Multiobjective Programming 667Matthias Ehrgott, Margaret M. Wiecek
1. Introduction 668
2. Problem Formulation and Solution Concepts 669
3. Properties of the Solution Sets 673
4. Conditions for Efficiency 675
5. Generation of the Solution Sets 676
6. Approximation of the Pareto Set 692
7. Specially Structured Problems 696
8. Current and Future Research Directions 707
9. Conclusions 708
References 708
18
Multiple Objective Linear Programming with Fuzzy Coefficients 723Masahiro Inuiguchi
1. Introduction 724
2. Problem Statement and Approaches 725
3. Modality Constrained Programming Approach 731
4. Modality Goal Programming 749
5. Modal Efficiency Approach 754
6. Concluding Remarks 757
References 757
19
MCDM Location Problems 761Stefan Nickel, Justo Puerto, Antonio M. Rodrıguez-Chıa
1. Introduction 762
2. Location Problems 764
3. Continuous Multicriteria Location Problems 767
4. Multicriteria Network Location Problems 776
5. Multicriteria Discrete Location Problems 783
6. Conclusions 787
References 787
Part VII Applications
20
Multicriteria Decision Aid/Analysis in Finance 799Jaap Spronk, Ralph E. Steuer, Constantin Zopounidis
1. Introduction 800
2. Financial Decision Making 801
3. MCDA in Portfolio Decision-Making Theory 819
4. MCDA in Discrete Financial Decision-Making Problems 835
5. Conclusions and Future Perspectives 848
References 849
21
MCDA and Energy Planning 859Danae Diakoulaki, Carlos Henggeler Antunes, Antonio Gomes Martins
1. Introduction 860
2. Multiobjective Programming Models for Energy Planning 863
3. Energy Planning Decisions with Discrete Alternatives 874
4. Conclusions 890
References 891
22
Multicriteria Analysis in Telecommunication Network Planning andDesign – Problems and Issues
899
Joao Clımaco, Jose Craveirinha
1. Motivation 900
2. Overview of Current Evolutions in Telecommunication Net-works and Services 900
3. Multicriteria Analysis in Telecommunication Network Plan-ning and Design 908
4. Review and Discussion of Applications of MA to Telecom-munication Network Planning 912
5. Future Trends 941
References 944
23
Multiple Criteria Decision Analysis and Sustainable Development 953Giuseppe Munda
1. The Concept of Sustainable Development 954
2. Measuring Sustainability: The Issue of Sustainability Assess-ment Indexes 958
3. A Defensible Axiomatic Setting for Sustainability CompositeIndicators 963
4. Warning! Not Always Rankings Have to Be Trusted ... 966
5. The Issue of the “Quality of the Social Decision Processes” 971
6. The Issue of Consistency in Multi-Criteria Evaluation ofSustainability Policies 976
7. Conclusion 980
References 981
Part VIII MCDM Software
24
Multiple Criteria Decision Support Software 989H. Roland Weistroffer, Charles H. Smith, Subhash C. Narula
1. Introduction 990
2. Software Overview 990
3. Concluding Remarks 1009
References 1011
Contributing Authors 1019
Index 1035
Introduction
Jose Figueira, Salvatore Greco, Matthias Ehrgott
1. Human Reflection about Decision
Decision 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 humansfrom 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 Słowinski [12].
London, Sept 19, l772
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 strikethem 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 outthe five; and thusproceeding I find at length where the balance lies; and if, after a day or two of
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 bedefined 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
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 NicolausCusanus [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. Edgeworthtried to find thecompetitive equilibrium points for the different agents. He proposed to drawindifference curves (lines of equal utility) for each agentand then derive thecontract curve, a curve that corresponds to the notion of thePareto 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. FelixEdouard 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]:
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 ofa good).
In the same year (1951) HaroldWilliam Kuhn (born1925) andAlbert 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 workson 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 continuestoday.
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 rashenterprise.Indeed, some objections come to mind. There are many and goodhandbooksand 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 thinkthat 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 usto propose this bookare the following:
1 Many of the existing handbooks and reviews are not too recent. SinceMCDA is a field which is developing very quickly this is an importantreason.
2 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 theseideas.
With reference to the first point, we can say that we observed many theoreticaldevelopments whichchanged MCDA over the last ten years. We tried toconsider
these changes as much as possible and in this perspective strong points of thebook are the following:
1 It presents the most up-to-date discussions on well established method-ologies and theories such as outranking based methods and MAUT.
2 The book also contains surveys of new, recently emerged fields such asconjoint measurement, fuzzy preferences, fuzzy integrals, rough sets andothers.
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 mostimportant 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 atext 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 isrelated 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, theoreticallywell 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 themost interestingpossibility. In the following we propose a guided tour of thebook suggestingsome reference points that are hopefully useful for the reader.
4.1 Part I: An Overview of MCDA Techniques Today
This 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-
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 andgives 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 MCDA
This 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 thecomprehensiveevaluation of an action can be seen as the sum of its numericalvalues 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 thispart problemsrelated to the representations of preferences are discussed.
MeltemOzturk, Alexis Tsoukias, 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 bookon 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-
ences and given the quality of the performances of the actions and the natureof the problem, an outranking relation is a binary relationS defined on the setof potential actionsA such thataSb if there are enough arguments to decidethata is at least as good asb, 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 inmany 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, manyother interesting MCDA methods are based on the pairwise com-parison of actions. Jose 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 toeach 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?
Thomas Saaty presents a very well known methodology to buildutility 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 ageneral 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, andJean-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 aggregatethese 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 ofsurrogate 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 environmentwhere conflict-ing systems of logic, uncertain and imprecise knowledge, and possibly vague
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 ofview 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 Roman Słowinski 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 carx is at least 175 km/h and its price is at most $12000, then carx 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 fuzzyintegral 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 otherhand, 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
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 naturalfor 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 subjectto 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 basicideas of inter-active methods dealing with multiobjective programming problems. The basicobservation is that, since the DM tries to “maximize” a set ofcriteria 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 dialoguewith 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
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 programmingis to seek solutionsof MOPs and therefore a special attention was paid to methodssuitable forfinding these solutions. Since the ultimate goal of MOP problem is selection ofa preferred solution, for which an adequate representationof 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 hasbeen used quitefrequently. Stefan Nickel, Justo Puerto and Antonio Rodrıguez-Chıa presentthe multiple criteria approach to locational analysis. An important characteris-tic of location models is their intrinsic multiple criterianature. 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
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 Antonio 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 newsocietal 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 towhich extent it isadapted to the new needs and structuring and modelling requirements.
Joao Clımaco and Jose Craveirinha present multiple criteria decision analysisin telecommunication network planning and design. Decision making processes
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 ofnew 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. Ecologicalproblems were amongthe first to be dealt with by MCDA. Therefore, there is a strongtradition 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 environmentalbut 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 Software
Application 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 soundknowledge 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,
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, Joao Clımaco, Danae Diakoulaki, Luıs Dias, MichaelDoumpos, Ernest Forman, Philippe Fortemps, Lorraine Gardiner, ChristopheGonzales, Michel Grabisch, Winfried Hallerbach, Raimo P. Hamalainen, Car-los Henggeler Antunes, Masahiro Inuiguchi, Robin Keller, Pekka Korhonen,Masahiro Inuiguchi, Christophe Labreuche, Risto Lahdelma, 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, Roman Sło-winski, Jerzy Stefanowsky, Ralph Steuer, Theo Stewart, Christianne Tammer,Jean-Claude Vansnick, Luis Vargas, Philippe Vincke, PeterWakker, 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, Roman Słowinski, Gary Folvenand Frederick S. Hillier.
Acknowledgments
Jose Figueira was supported by the grant SFRH/BDP/6800/2001 (Fundacaopara a Ciencia e Tecnologia, Portugal) and gratefully acknowledgesDIMACSResearch Center at Rutgers University and LAMSADE at University Paris-Dauphine for the welcome during his sabbatical leave and theshort 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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[23] B. Roy. Classement et choix en presence de point de vue multiples: Le methode ELECTRE.Revue Francaise d’Informatique et de Recherche Operationnelle, 8:57–75, 1968.
[24] B. Roy. Criteres multiple et modelisation des pref’erence: L’apport des relations desurclassement.Revue d’Economie Politique, 1:1–44, 1974.
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I
AN OVERVIEW OF MCDATECHNIQUES TODAY
Chapter 1
PARADIGMS AND CHALLENGES
Bernard RoyLAMSADEUniversite Paris-DauphinePlace du Marechal De Lattre de Tassigny, 75775 Paris Cedex 16France
Abstract The purpose of this introductory part is to present an overall view of what MCDAis today. In Section 1, I will attempt to bring answers to questions such as: whatis it reasonable to expect from MCDA? Why decision aiding is more often multi-criteria than monocriterion? What are the main limitationsto objectivity? Section2 will be devoted to a presentation of the conceptual architecture that constitutesthe main keys for analyzing and structuring problem situations. Decision aidingcannot and must not be envisaged jointly with a hypothesis ofperfect knowledge.Different ways for apprehending the various sources of imperfect knowledge willbe introduced in Section 3. A robustness analysis is necessary in most cases. Thecrucial question of how can we take into account all criteriacomprehensively inorder to compare potential actions to one another will be tackled in Section 4. Inthis introductory part, I will only present a general framework for positioning themain operational approaches that exist today. In Section 5,I will discuss somemore philosophical aspects of MCDA. For providing some aid in a decision con-text, we have to choose among different paths which one seemsto be the mostappropriate, or how to combine some of them: the path of realism which leadsto the quest for a discussion for discovering, the axiomaticpath which is oftenassociated with the quest of norms for prescribing, or the path of constructivismwhich goes hand in hand with the quest of working hypothesis for recommending.
Keywords: Multiple criteria decision aiding, imperfect knowledge, aggregation procedures.
II
FOUNDATIONS OF MCDA
Chapter 2
PREFERENCE MODELLING
MeltemOzturk, Alexis TsoukiasLAMSADE-CNRS, Universite Paris Dauphine,75775 Paris Cedex 16,France
{ozturk,tsoukias}@lamsade.dauphine.fr
Philippe VinckeUniversite Libre de BruxellesCP 210/1, Bld. du Triomphe, 1050 Bruxelles,Belgium
Abstract This chapter provides the reader with a presentation of preference modellingfundamental notions as well as some recent results in this field. Preference mod-elling is an inevitable step in a variety of fields: economy, sociology, psychology,mathematical programming, even medicine, archaeology, and obviously decisionanalysis. Our notation and some basic definitions, such as those of binary rela-tion, properties and ordered sets, are presented at the beginning of the chapter. Westart by discussing different reasons for constructing a model or preference. Wethen go through a number of issues that influence the construction of preferencemodels. Different formalisations besides classical logicsuch as fuzzy sets andnon-classical logics become necessary. We then present different types of pref-erence structures reflecting the behavior of a decision-maker: classical, extendedand valued ones. It is relevant to have a numerical representation of preferences:functional representations, value functions. The concepts of thresholds and min-imal representation are also introduced in this section. InSection 8, we brieflyexplore the concept of deontic logic (logic of preference) and other formalismsassociated with “compact representation of preferences” introduced for specialpurposes. We end the chapter with some concluding remarks.
Keywords: Preference modelling, decision aiding, uncertainty, fuzzy sets, non classical logic,ordered relations, binary relations.
Chapter 3
CONJOINT MEASUREMENT TOOLS FOR MCDM
A Brief Introduction
Denis BouyssouCNRSLAMSADE, Universite Paris DauphineF-75775 Paris Cedex 16France
Marc PirlotFaculte Polytechnique de Mons9, rue de HoudainB-7000 MonsBelgium
Abstract This paper offers a brief and nontechnical introduction to the use of conjointmeasurement in multiple criteria decision making. The emphasis is on the, central,additive value function model. We outline its axiomatic foundations and presentvarious possible assessment techniques to implement it. Some extensions of thismodel, e.g. nonadditive models or models tolerating intransitive preferences arethen briefly reviewed.
Keywords: Conjoint Measurement, additive value function, preference modelling.
III
OUTRANKING METHODS
Chapter 4
ELECTRE METHODS
Jose FigueiraFaculdade de Economia and INESC-CoimbraUniversidade de CoimbraAv. Dias da Silva, 165, 3004-512 CoimbraPortugal
Vincent Mousseau, Bernard RoyLAMSADEUniversite Paris-DauphinePlace du Marechal De Lattre de Tassigny, 75775 Paris Cedex 16France
{mousseau,roy}@lamsade.dauphine.fr
Abstract Over the last three decades a large body of research in the field of ELECTRE fam-ily methods appeared. This research has been conducted by several researchersmainly in Europe. The purpose of this chapter is to present a survey of the ELEC-TRE methods since their first appearance in mid-sixties, when ELECTRE I wasproposed by Bernard Roy and his colleagues at SEMA consultancy company.The chapter is organized in five sections. The first section presents a brief historyof ELECTRE methods. The second section is devoted to the mainfeatures ofELECTRE methods. The third section describes the differentELECTRE meth-ods existing in the literature according to the three main problematics: choosing,ranking and sorting. The fourth section presents the recentdevelopments andfuture issues on ELECTRE methods. Finally, the fifth sectionis devoted to thesoftware and applications. An extensive and up-to-date bibliography is also pro-vided in the end of this chapter.
Keywords: Multiple criteria decision aiding, Outranking approaches, ELECTRE methods.
Chapter 5
PROMETHEE METHODS
Jean-Pierre BransCentrum voor Statistiek en Operationeel OnderzoekVrije Universiteit BrusselPleinlaan 2, B-1050 BrusselsBelgium
Bertrand MareschalService de Mathematiques de la GestionUniversite Libre de BruxellesBoulevard du Triomphe CP 210-01, B-1050 BrusselsBelgium
Abstract This paper gives an overview of the PROMETHEE-GAIA methodology forMCDA. It starts with general comments on multicriteria problems, stressing thata multicriteria problem cannot be treated without additional information relatedto the preferences and the priorities of the decision-makers. The information re-quested by PROMETHEE and GAIA is particularly clear and easyto define forboth decision-makers and analysts. It consists in a preference function associ-ated to each criterion as well as weights describing their relative importance. ThePROMETHEE I, the PROMETHEE II complete ranking, as well as the GAIAvisual interactive module are then described and commented. The two next sec-tions are devoted to the PROMETHEE VI sensitivity analysis procedure (humanbrain) and to the PROMETHEE V procedure for multiple selection of alternativesunder constraints. An overview of the PROMETHEE GDSS procedure for groupdecision making is then given. Finally the DECISION LAB software implemen-tation of the PROMETHEE-GAIA methodology is described using a numericalexample.
Keywords: MCDA, outranking methods, PROMETHEE-GAIA, DECISION LAB.
Chapter 6
OTHER OUTRANKING APPROACHES
Jean-Marc MartelFacultes des Sciences de l’AdministrationUniversity of LavalCanada
Benedetto MatarazzoDepartment of Economics and Quantitative MethodsUniversity of CataniaCorso Italia, 55, CataniaItaly
Abstract In this chapter, we shortly describe some outranking methods other than ELEC-TRE and PROMETHEE. All these methods (QUALIFLEX, REGIME, ORESTE,ARGUS, EVAMIX, TACTIC and MELCHIOR) propose definitions andcompu-tations of particular binary relations, more or less linkedto the basic idea of theoriginal ELECTRE methods. Beside them, we will also describe other outrank-ing methods (MAPPAC, PRAGMA, IDRA and PACMAN) that have beendevel-oped in the framework of the Pairwise Criterion Comparison Approach (PCCA)methodology, whose peculiar feature is to split the binary relations constructionphase in two steps: in the first one, each pair of actions is compared with respectto two criteria a time; in the second step, all these partial preference indices areaggregated in order to obtain the final binary relations. Finally, one outrankingmethod for stochastic data (the Martel and Zaras’ method) ispresented, based onthe use of stochastic dominance relations between each pairof alternatives.
Keywords: Multiple criteria decision analysis, outranking methods,pairwise criteria com-parison approach.
IV
MULTIATTRIBUTE UTILITY ANDVALUE THEORIES
Chapter 7
MAUT – MULTIATTRIBUTE UTILITYTHEORY
James S. DyerDepartment of Management Science and Information SystemsThe Graduate School of BusinessUniversity of Texas at AustinAustin, TX 78712USA
Abstract In this chapter, we provide a review of multiattribute utility theory. We begin witha brief review of single-attribute preference theory, and we explore preferencerepresentations that measure a decision maker’s strength of preference and herpreferences for risky alternatives. We emphasize the distinction between thesetwo cases, and then explore the implications for multiattribute preference mod-els. We describe the multiattribute decision problem, and discuss the conditionsthat allow a multiattribute preference function to be decomposed into additiveand multiplicative forms under conditions of certainty andrisk. The relation-ships among these distinct types of multiattribute preference functions are thenexplored, and issues related to their assessment and applications are surveyed.
Keywords: Multiattribute utility theory, additive value functions,preference modeling.
Chapter 8
UTA METHODS
Yannis SiskosUniversity of PiraeusDepartment of Informatics80 Karaoli& Dimitriou Str.18534 Piraeus, Greece
Evangelos Grigoroudis, Nikolaos F. MatsatsinisTechnical University of CreteDecision Support Systems LaboratoryUniversity Campus, Kounoupidiana73100 Chania,– Greece
{vangelis,nikos}@ergasya.tuc.gr
Abstract UTA methods refer to the philosophy of assessing a set of value or utility func-tions, assuming the axiomatic basis of MAUT and adopting thepreference dis-aggregation principle. UTA methodology uses linear programming techniques inorder to optimally infer additive value/utility functions, so that these functions areas consistent as possible with the global decision-maker’spreferences (inferenceprinciple). The main objective of this chapter is to analytically present the UTAmethod and its variants and to summarize the progress made inthis field. Thehistorical background and the philosophy of the aggregation-disaggregation ap-proach are firstly given. The detailed presentation of the basic UTA algorithm ispresented, including discussion on the stability and sensitivity analyses. Severalvariants of the UTA method, which incorporate different forms of optimality crite-ria, are also discussed. The implementation of the UTA methods is illustrated by ageneral overview of UTA-based DSSs, as well as real-world decision-making ap-plications. Finally, several potential future research developments are discussed.
Keywords: UTA methods, preference disaggregation, ordinal regression, additive utility, mul-ticriteria analysis.
Chapter 9
THE ANALYTIC HIERARCHY ANDANALYTIC NETWORK PROCESSESFOR THE MEASUREMENT OFINTANGIBLE CRITERIA ANDFOR DECISION-MAKING
Thomas L. SaatyKatz Graduate School of BusinessUniversity of PittsburghUSA
Abstract The Analytic Hierarchy Process (AHP) and its generalization to dependence andfeedback, the Analytic Network Process (ANP), are theoriesof relative measure-ment of intangible criteria. With this approach to relativemeasurement, a scaleof priorities is derived from pairwise comparison measurements only after theelements to be measured are known. The ability to do pairwisecomparisons isour biological heritage and we need it to cope with a world where everythingis relative and constantly changing. In traditional measurement one has a scalethat one applies to measure any element that comes along thathas the propertythe scale is for, and elements are measured one by one, not by comparing themwith each other. In the AHP paired comparisons are made with judgments usingnumerical values taken from the AHP absolute fundamental scale of 1-9. A scaleof relative values is derived from all these paired comparisons and it also belongsto an absolute scale that is invariant under the identity transformation like thesystem of real numbers. The AHP/ANP is useful for making multicriteria deci-sions involving benefits, opportunities, costs and risks. The ideas are developedin stages and illustrated with examples of real life decisions. The subject is trans-parent and despite some mathematics, it is easy to understand why it is done theway it is along the lines discussed here.
Keywords: Analytic Hierarchy Process, decision-making, prioritization, negative priorities,rating, benefits, opportunities, costs, risks.
Chapter 10
ON THE MATHEMATICALFOUNDATIONS OF MACBETH
Carlos A. Bana e CostaCentre for Management Studies of Instituto Superior TecnicoTechnical University of LisbonAv. Rovisco Pais, 1049-001 Lisbon, PortugalandDepartment of Operational Research, London School of EconomicsHoughton Street, London WC2A 2AE, U.K.
[email protected],[email protected]
Jean-Marie De Corte, Jean-Claude VansnickCentre de Recherche Warocque, Universite de Mons-HainautPlace du Parc, 20, 7000 MonsBelgium
{Jean-Marie.DeCorte,Jean-Claude.Vansnick}@umh.ac.be
Abstract MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Tech-nique) is a multicriteria decision analysis approach that requires only qualitativejudgements about differences of value to help an individualor a group quantifythe relative attractiveness of options. This chapter presents an up-to-date sur-vey of the mathematical foundations of MACBETH. Reference is also made toreal-world applications and an extensive bibliography, spanning back to the early1990’s, is provided.
Keywords: MACBETH, questioning procedure, qualitative judgements,judgmental incon-sistency, cardinal value measurement, interaction.
V
NON-CLASSICAL MCDAAPPROACHES
Chapter 11
DEALING WITH UNCERTAINTIESIN MCDA
Theodor J StewartDepartment of Statistical SciencesUniversity of Cape TownRondebosch 7701South Africa
Abstract Many MCDA models are based on essentially deterministic evaluations of theconsequences of each action in terms of each criterion, possibly subjecting finalresults and recommendations to a degree of sensitivity analysis. In many situa-tions, such an approach may be justified when the primary source of complexityin decision making relates to the multicriteria nature of the problem rather thanto the stochastic nature of individual consequences. Nevertheless, situations doarise, especially in strategic planning problems, when risks and uncertainties areas critical as the issue of conflicting management goals. In such situations, moreformal modelling of these uncertainties become necessary.
In this paper, we start by reviewing the meaning and origin ofrisk and uncer-tainty. We recognize both internal uncertainties (relatedto decision maker valuesand judgements) and external uncertainties (related to imperfect knowledge con-cerning consequences of action), but for this paper focus onthe latter. Four broadapproaches to dealing with external uncertainties are discussed. These are mul-tiattribute utility theory and some extensions; stochastic dominance concepts,primarily in the context of pairwise comparisons of alternatives; the use of surro-gate risk measures as additional decision criteria; and theintegration of MCDAand scenario planning. To a large extent, the concepts carrythrough to all schoolsof MCDA. A number of potential areas for research are identified, while somesuggestions for practice are included in the final section.
Keywords: Multicriteria analysis, multiobjective programming, uncertainty, risk, utility the-ory.
Chapter 12
CHOICE, RANKING AND SORTINGIN FUZZY MULTIPLE CRITERIADECISION AID
Patrick Meyer, Marc RoubensDepartment of MathematicsUniversity of LiegeGrande Traverse, 124000 LiegeBelgium
[email protected], [email protected]
Abstract In this chapter we survey several approaches to derive a recommendation fromsome preference models for multiple criteria decision aid.Depending on thespecificities of the decision problem, the recommendation can be a selection ofthe best alternatives, a ranking of these alternatives or a sorting. We detail a sortingprocedure for the assignment of alternatives to graded classes when the availableinformation is given by interacting points of view and a subset of prototypicalternatives whose assignment is given beforehand. A software dedicated to thatapproach (Tomaso) is briefly presented. Finally we define the concepts of goodand bad choices based on dominant and absorbant kernels in the valued digraphthat corresponds to an ordinal valued outranking relation.
Keywords: Aggregation with fuzzy environment, fuzzy choice, ordinalordered sorting, cho-quet integral,Tomaso.
Chapter 13
DECISION RULE APPROACH
Salvatore Greco, Benedetto MatarazzoFaculty of Economics, University of CataniaCorso Italia 55, 95129 CataniaItaly
{salgreco,matarazzo}@unict.it
Roman SłowinskiInstitute of Computing Science, Poznan University of Technology, 60-965 Poznan andSystems Research Institute, Polish Academy of Sciences, 01-447 WarsawPoland
Abstract We present the methodology of Multiple-Criteria Decision Aiding (MCDA) basedon preference modelling in terms of “if. . . , then . . .” decision rules. The basicassumption of the decision rule approach is that the decision maker (DM) acceptsto give preferential information in terms of examples of decisions and looks forsimple rules justifying her decisions. An important advantage of this approachis the possibility of handling inconsistencies in the preferential information, re-sulting from hesitations of the DM. The proposed methodology is based on theelementary, natural and rational principle of dominance. It says that if actionxis at least as good as actiony on each criterion from a considered family, thenx is also comprehensively at least as good asy. The set of decision rules consti-tuting the preference model is induced from the preferential information using aknowledge discovery technique properly modified, so as to handle the dominanceprinciple. The mathematical basis of the decision rule approach to MCDA is theDominance-based Rough Set Approach (DRSA) developed by theauthors. Wepresent some basic applications of this approach, along with didactic exampleswhose aim is to show in an easy way how DRSA can be used in various contextsof MCDA.
Keywords: Dominance, rough sets, decision rules, multiple criteria classification, choice andranking.
Chapter 14
FUZZY MEASURES AND INTEGRALS IN MCDA
Michel GrabischUniversite Paris I – Pantheon-SorbonneLIP6, 8 rue du Capitaine Scott75015 Paris, France
Christophe LabreucheThales Research & TechnologyDomaine de Corbeville91404 Orsay Cedex, France
Abstract This chapter aims at a unified presentation of various methods of MCDA basedon fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem of multicriteriadecision making, and describes the various possible scalesof measurement (car-dinal unipolar and bipolar, and ordinal). Then a whole section is devoted to eachcase in detail: after introducing necessary concepts, the methodology is described,and the problem of the practical identification of fuzzy measures is given. Theimportant concept of interaction between criteria, central in this chapter, is ex-plained in detail. It is shown how it leads tok-additive fuzzy measures. The caseof bipolar scales leads to the general model based on bi-capacities, encompassingusual models based on capacities. A general definition of interaction for bipolarscales is introduced. The case of ordinal scales leads to theuse of Sugeno inte-gral, and its symmetrized version when one considers symmetric ordinal scales.A practical methodology for the identification of fuzzy measures in this contextis given.
Keywords: Choquet integral, fuzzy measure, interaction, bi-capacities.
Chapter 15
VERBAL DECISION ANALYSIS
Helen Moshkovich, Alexander MechitovCollege of BusinessThe University of MontevalloMontevallo, AL 35115USA
MoshHM,[email protected]
David OlsonDepartment of ManagementUniversity of Nebraska, LincolnLincoln, NE 68588-0491USA
Abstract Verbal Decision Analysis is a new methodological approach for the constructionof decisions methods with multiple criteria. The approach is based on cognitivepsychology, applied mathematics, and computer science. Problems of elicitingexact quantitative estimations from the decision makers may be overcome byusing preferential information from the decision makers inthe ordinal form (e.g.,“more preferable”, “less preferable”,...). This type of judgments is known to bemuch more stable and consistent. Ways of how to obtain and useordinal judg-ments for multicriteria alternatives’ evaluation are discussed. Decision methodsZAPROS, and ORCLASS based on the approach are briefly described.
Keywords: Decision analysis, multiple criteria, ordinal judgments,preference elicitation,ZAPROS, ORCLASS.
VI
MULTIOBJECTIVE MATHEMATICALPROGRAMMING
Chapter 16
INTERACTIVE METHODS
Pekka KorhonenHelsinki School of EconomicsDepartment of Economics and Management ScienceRuneberginkatu 14–16, 00100 HelsinkiFinland
Abstract We provide an introduction to the use of interactive methodsin multiple objectiveprogramming. We focus on discussing the principles to implement those methods.Our purpose is not to review existing procedures, but some examples are pickedto illustrate the main ideas behind those procedures. Furthermore, we discuss twoavailable software systems developed to implement interactive methods.
Keywords: Decision making, multiple objective, multiple criteria, interactive, behavioral.
Chapter 17
MULTIOBJECTIVE PROGRAMMING
Matthias EhrgottDepartment of Engineering ScienceThe University of AucklandPrivate Bag 92019, AucklandNew Zealand
[email protected], [email protected]
Margaret M. WiecekDepartment of Mathematical SciencesClemson UniversityClemson, SC 29634-0975USA
Abstract We present our view of the state of the art in multiobjective programming. Afteran introduction we formulate the multiobjective program (MOP) and define themost important solution concepts. We then summarize the properties of efficientand nondominated sets. In Section 4 optimality conditions are reviewed. The mainpart of the chapter consists of Sections 5 and 6 that deal withsolution techniquesfor MOPs and approximation of efficient and nondominated sets. In Section 7 wediscuss specially-structured problems including linear and discrete MOPs as wellas selected nonlinear MOPs. In Section 8 we present our perspective on futureresearch directions.
Keywords: Multiobjective programming, efficient solution, nondominated solution, scalar-ization, approximation.
Chapter 18
MULTIPLE OBJECTIVE LINEARPROGRAMMING WITH FUZZYCOEFFICIENTS
Masahiro InuiguchiDepartment of Systems InnovationGraduate School of Engineering Science, Osaka University1-3, Machikaneyama, Toyonaka, Osaka 560-8531Japan
Abstract In this paper, we treat multiple objective programming problems with fuzzy co-efficients. We introduce the approaches based on possibility and necessity mea-sures. Our aim in this paper is to describe the treatments of the problem ratherthan the solution method for the problem. We describe the modality constrainedprogramming approach, the modality goal programming approach and modalefficiency approach. In the first approach, we discuss treatments of fuzziness inthe programming problems. The extensions of a fuzzy relation to the relationbetween fuzzy numbers are developed in order to treat generalized constraints.In the second approach, we show that two kinds of differencesbetween a fuzzyobjective function value and a fuzzy target are conceivableunder the fuzziness.We describe the distinction of their applications in programming problems. In thethird approach, we describe how the efficiency can be extended to multiple ob-jective programming problems with fuzzy coefficients. Necessary and sufficientconditions for a feasible solution to satisfy the extended efficiency are discussed.Finally some concluding remarks are given.
Keywords: Multiple objective programming, fuzzy coefficient, fuzzy relation, possibilitymeasure, necessity measure.
Chapter 19
MCDM LOCATION PROBLEMS
Stefan NickelFakultat fur Rechts- und Wirtschaftswissenschaften, Universitat des Saarlands66041 Saarbrucken, GermanyandFraunhofer Insitute for Industrial Mathematics (ITWM)67663 Kaiserslautern, Germany
Justo PuertoFacultad de MatematicasUniversidad de Sevilla41012 Seville, Spain
Antonio M. Rodrıguez-ChıaFacultad de CienciasUniversidad de Cadiz11510 Puerto Real (Cadiz), Spain
Abstract In this chapter, we provide a broad overview of the most representative multi-criteria location problems as well as of the most relevant achievements in thisfield, indicating the relationship between them whenever possible. We consider alarge number of references which have been classified in three sections dependingon the type of decision space where the analyzed models are stated. Therefore,we distinguish between continuous, network, and discrete multicriteria locationproblems.
Keywords: Locational Analysis, multicriteria location problems, point-objective locationproblems, multiobjective location problems.
VII
APPLICATIONS
Chapter 20
MULTICRITERIA DECISION AID/ANALYSIS IN FINANCE
Jaap SpronkErasmus University Rotterdam, Department of Finance and InvestmentP.O.Box 1738, 3000 DR Rotterdam, The Netherlands
Ralph E. SteuerUniversity of Georgia, Department of Banking and Finance, Terry College of Business, Athens,Georgia 30602-6253USA
Constantin ZopounidisTechnical University of Crete, Department of Production Engineering and Management,Financial Engineering Laboratory, University Campus, 73100 Chania, Greece
Abstract Over the past decades the complexity of financial decisions has increased rapidly,thus highlighting the importance of developing and implementing sophisticatedand efficient quantitative analysis techniques for supporting and aiding financialdecision making. Multicriteria decision aid (MCDA), an advanced branch of op-erations research, provides financial decision makers and analysts with a widerange of methodologies well-suited for the complexity of modern financial deci-sion making. The aim of this chapter is to provide an in-depthpresentation of thecontributions of MCDA in finance focusing on the methods used, applications,computation, and directions for future research.
Keywords: Multicriteria decision aid, finance, portfolio theory, multiple criteria optimization,outranking relations, preference disaggregation analysis.
Chapter 21
MCDA AND ENERGY PLANNING
Danae DiakoulakiNational Technical University of AthensDepartment of Chemical EngineeringLabortaory of Industrial and Energy EconomicsZografou Campus, 15780 AthensGreece
Carlos Henggeler Antunes, Antonio Gomes MartinsUniversity of Coimbra and INESC CoimbraDepartment of Electrical Engineering and ComputersPolo II, Pinhal de Marrocos, 3030 CoimbraPortugal
cantunes,[email protected]
Abstract The growing environmental awareness and the apparent conflict between eco-nomic and environmental objectives was the main impetus that pushed energyplanners during the early eighties towards the use of MCDA methods. Thereafter,the rapid changes and the increasing complexity of the energy market gave rise tofurther methodological developments. Although the energymarket restructuringand ongoing liberalization seemed to restrict the purpose for centralized energydecisions, they added new dimensions in energy planning. Increasing competitionalong with the prerequisite for sustainability have broadened the energy appli-cation field by bringing out new challenges for the development of integratedmulticriteria and multi-stakeholders approaches also taking uncertainty into con-sideration. This paper aims at illustrating the evolution of MCDA approaches, inthe context of the emerging problems faced by energy planners and other stake-holders involved in energy-related decision situations, one of the most active andexciting areas of application of MCDA models and methods.
Keywords: Multicriteria, multiobjective, energy planning, electricity.
Chapter 22
MULTICRITERIA ANALYSIS INTELECOMMUNICATION NETWORKPLANNING AND DESIGN –PROBLEMS AND ISSUES
Joao ClımacoFaculty of EconomicsThe University of Coimbra and INESC – CoimbraPortugal
Jose CraveirinhaDepartment of Electrical Engineering Sience and ComputersFaculty of Science and TechnologyThe University of Coimbra and INESC – CoimbraPortugal
Abstract The interaction between a complex socio-economic environment and the ex-tremely fast pace of development of new telecommunication technologies andservices justifies the interest in using multicriteria evaluation in decision makingprocesses associated with several phases of network planning and design. Basedon an overview of current and foreseen evolutions in telecommunication networktechnologies and services we begin by identifying and discussing challenges andissues concerning the use of multicriteria analysis (M.A.)in telecommunicationnetwork planning and design problems. Next we present a review of contributionsin these areas, with particular emphasis on network modernisation planning androuting problems. We will also outline an agenda of current and future researchtrends and issues in this application area of multicriteriamodelling.
Keywords: Telecommunication planning and design, multicriteria analysis.
Chapter 23
MULTIPLE CRITERIA DECISIONANALYSIS AND SUSTAINABLEDEVELOPMENT
Giuseppe MundaUniversitat Autonoma de BarcelonaDepartment of Economics and Economic History, Edifici BandInstitute for Environmental Sciences and Technologies08193, Bellaterra, Barcelona, Spain
Abstract Sustainable development is a multidimensional concept, including socio-eco-nomic, ecological, technical and ethical perspectives. Inmaking sustainabilitypolicies operational, basic questions to be answered are sustainability of whatand whom? As a consequence, sustainability issues are characterised by a highdegree of conflict. The main objective of this Chapter is to show that multiple-criteria decision analysis is an adequate approach for dealing with sustainabilityconflicts at both micro and macro levels of analysis. To achieve this objective,lessons, learned from both theoretical arguments and empirical experience, arereviewed. Guidelines of “good practice” are suggested too.
Keywords: Sustainable development, economics, complex systems, incommensurability, so-cial choice, social multi-criteria evaluation.
VIII
MCDM SOFTWARE
Chapter 24
MULTIPLE CRITERIA DECISIONSUPPORT SOFTWARE
H. Roland Weistroffer, Charles H. Smith, Subhash C. NarulaSchool of BusinessVirginia Commonwealth UniversityBox 844000, Richmond, Virginia 23284-4000USA
{hrweistr,chsmith,snarula}@vcu.edu
Abstract We present an overview of the current state of multiple criteria decision-making(MCDM) decision support software. Many approaches have been proposed inthe literature to solve multiple criteria decision-makingproblems, and there is anabundance of software that implements these approaches. Much of the softwareis still quasi-experimental, developed by academic researchers to test specificalgorithms or to solve a specific problem on an ad hoc basis.
Keywords: DSS, MCDSS, software packages.
Contributing Authors
Carlos A. Bana e Costais Full Professor of Decision and Information at theTechnical University of Lisbon “Instituto Superior Tecnico” (IST), Departmentof Engineering and Management, Centennial Professor of Operational Researchat the London School of Economics and Political Science, andpresident of theCenter of Management Studies of IST. His primary interests are in the fieldsof management and decision sciences, namely multicriteriadecision analysisand decision conferencing, and he has published widely in these areas. He isco-author of the MACBETH approach. He is also a decision-aidconsultant ofmany private and public organizations in Portugal, Brazil and other countries,following the socio-technical facilitation perspective shared by the members ofthe International Decision Conferencing Forum.
Denis Bouyssouholds a doctorate in Operations Research. He is presentlysenior researcher at the Centre National de Recherche Scientifique (CNRS).His research interests include decision theory, social choice theory, and multiplecriteria decision making.
Jean-Pierre Bransreceived his Ph.D. in Mathematics at the ULB/VUB Univer-sity of Brussels (1966). He has been Professor in these Universities since 1964and dean of the VUB-Solvay Business school (1975-78). He hasheld visitingprofessorships at the universities of Kinshasa, Constantine, Aix-en-Provence,ENSTA (Paris), AIT (Bangkok), KUL (Leuven), and Lulea (Sweden). He hastaught courses taught on statistical analysis, OR, MCDA, mathematical pro-gramming, and system dynamics. Dr. Brans has been presidentof the BelgianOR society (1975-78), president of EURO (1983-84), vice-president of IFORS(1977-80 and 1989-92), initiator of the EURO K Conferences and organisor ofthe first one in Brussels (1975), initiator of the EURO SummerInstitutes andorganisor of the two first ones, initiator of the MINI EURO Conferences andorganisor of the 1st, the 7th and the 12th ones. He has presented over 100 in-vited lectures all over the world and published over 100 papers in internationalscientific journals. He is the initiator of the PROMETHEE-GAIA Methodologyand has written one book on this subject with B. Mareschal. Hereceived theEURO Gold Medal 1994 and Doctor Honoris Causa from Copenhagen (2000)
and Fribourg (2002). He has been elected Professor of the Year by the studentsof the VUB Brussels (2002).
Joao C. N. Clımacois Full Professor at the School of Economics, University ofCoimbra, and researcher at the Systems Engineering and Computers InstituteINESC Coimbra. Currently he is president of the Scientific Committee of IN-ESC Coimbra. He obtained an M.Sc. in Control Systems from Imperial College,University of London, and the Diploma of Membership of the Imperial Collegeof Science and Technology (1978), a Ph.D. (1982) in Electrical Engineeringfrom the University of Coimbra, and the Aggregation (1989) from the Univer-sity of Coimbra. His current interests of research are in multicriteria decisionmaking, group decision and negotiation, decision support systems, and telecom-munication planning, design, and management. He is author (or co-author) ofmore than seventy papers published in refereed international scientific journalsand about thirty papers (or chapters) published in thematicscientific books. Hebelongs to the editorial board of the “Group Decision and Negotiation Journal”and of “Investigacao Operacional”. He was vice-president of APDIO and ofALIO. Currently he belongs to the international executive committee of theInternational Society on MCDM.
Jose Manuel F. Craveirinha is Full Professor in Telecommunications at theDepartment of Electrical Engineering Science of the Faculty of Sciences andTechnology of the University of Coimbra, Portugal, since 1997. He obtainedthe following degrees: Undergraduate Diploma in Electrical Engineering Sci-ence (E.E.S.) – Telecommunications & Electronics at IST, Lisbon TechnicalUniversity (1975); M.Sc. (1981) and Ph.D. (1984) in E.E.S. at the Universityof Essex (UK) and Doctor of Science in E.E.S – Telecommunications at theUniversity of Coimbra (1996). Previous positions were: Associate Professor,Assistant Professor, and Assistant Lecturer at FCUT, Coimbra University, andtelecommunications R&D engineer at CET-Portugal Telecom.He has coor-dinated a research group in teletraffic theory & network planning at INESC-Coimbra R&D institute since 1986 and was director of this institute 1994-99.He is author/co-author of more than 95 scientific and technical publicationsin modelling of teletraffic, reliability analysis and planning of telecommunica-tion networks. His main present interests are in traffic modelling and routing inInternet and multiple objective routing in multiservice networks.
Jean-Marie De Corteis Assistant Professor at the University of Mons-Hainautand member of the Warocque Research Center. He received his Ph.D. in Math-ematics in 2002. His current research interest is in the fieldof multiple criteriadecision aid, more specifically on development of algorithms for “minimal solv-ing” of inconsistencies and for several robustness analyses in the framework ofthe MACBETH approach. He is also the designer of the MACBETH software.His work has been published in international journals such as Omega.
Danae Diakoulakireceived her Ph.D. degree in Engineering (Operations Man-agement) at the National Technical University of Athens (NTUA) in 1988. Sheis currently an Associate Professor at the Chemical Engineering Departmentof NTUA and heads the area of energy and environmental management at theLaboratory of Industrial and Energy Economics. Her research activities con-cern mainly the use of MCDA methods in energy and environmental planningas well as the exploitation of energy externalities in energy policy making. Shehas participated in several national and European Commission research projectsand published numerous articles in refereed internationaljournals.
James S. Dyeroccupies the Fondren Centennial Chair in Business in the Col-lege of Business Administration, University of Texas at Austin. Dr. Dyer’sresearch and teaching interests include risk management and capital budgeting,and he has published extensively on these subjects in various journals, includ-ing Management Science and Operations Research. He is the former Chair ofthe Decision Analysis Society of the Operations Research Society of America(now INFORMS). He is the Area Editor for the field of decision analysis forthe journal Operations Research. In 2002 he received the Ramsey Award foroutstanding career achievements from the Decision Analysis Society. Dr. Dyerhas consulted with a number of companies regarding the application of deci-sion and risk analysis tools to a variety of practical problems, including Amoco,Texaco, Unocal, ENI, and the Department of Energy.
Matthias Ehrgott is Associate Professor of Operations Research in the De-partment of Engineering Science, The University of Auckland, New Zealand.He obtained his Diploma, Ph.D. and Dr. habil. degrees in Mathematics from theUniversity of Kaiserslautern, Germany, in 1992, 1997, and 2001, respectively.From 1997 to 2000 he was Assistant Professor at the University of Kaiser-slautern. He has been invited professor at Universite de Valenciennes, Copen-hagen University and Mercator Visiting Profesor at the University of Kaiser-slautern. Dr. Ehrgott is the author or editor of six books, and has written morethan 30 refereed articles on multiobjective and combinatorial optimization thathave been published in international journals or proceedings volumes. He is amember of the international executive committee of the MCDMSociety, mem-ber of the council of the Operations Research Society of New Zealand, editorof OR Spectrum and associate editor of Asia Pacific Journal ofOperationalResearch. He received the Wiley Prize for best applied paperin MCDA at theInternational Conference on MCDM in 2002.
Jose Figueira is an Associate Professor at the School of Economics of theUniversity of Coimbra, Portugal, and researcher at INESC-Coimbra and LAM-SADE, Paris-Dauphine University, France. He obtained his Ph.D. (1996) inOperations Research from the University of Paris-Dauphine. He has been in-vited researcher London School of Economics, Rutgers University, Auckland
University, University of Catania, University of Talca, Free University of Brus-sels, Clemson University, University of Georgia, University of Valenciennesand Carnegie Mellon University. His current research interests are in decisionanalysis, integer programming, network flows and multiple criteria decisionaiding. His works have been published in international journals such as Eu-ropean Journal of Operational Research, Computers & Operations Research,Journal of the Operational Research Society, Journal of Mathematical Mod-elling and Algorithms, European Business Review. He is the current editor ofthe newsletter of the European Working Group on MCDA.
Michel Grabisch received his Graduate Engineer Diploma in 1979 and hisPh.D. degree in signal processing in 1982, both from Ecole Nationale desIngenieurs Electriciens de Grenoble (ENSIEG). From 1984 to 1993 he workedat Thomson-Sintra Activites Sous-Marines and from 1993 to 2000 at CentralResearch Laboratory of Thomson-CSF. He spent two years from1989 to 1991 atTokyo Institute of Technology, Japan, and participated in the LIFE (Laboratoryfor International Fuzzy Engineering Research) project. From 2000 to 2002 hewas Associate Professor at Universite Pierre et Marie Curie, Paris. Since 2002,he is Professor of Computer Science at Universite Pantheon-Sorbonne, Paris.He is area editor of IEEE Transactions on Fuzzy Systems, Fuzzy Optimizationand Decision, and belongs to the editorial board of Fuzzy Sets and Systems.His interests are fuzzy measure and capacity theory, decision making, fuzzysets and possibility theory as well as discrete mathematics.
Salvatore Grecois Full Professor at the Faculty of Economics of Catania Uni-versity since 2001. His main research interests are in the field of multicriteriadecision aid, in the application of the rough set approach todecision analysis, inthe axiomatic foundation of multicriteria methodology andin the fuzzy integralapproach to MCDA. In these fields he cooperates with many researchers of dif-ferent countries. He received the Best Theoretical Paper Award by the DecisionSciences Institute (Athens, 1999). Together with Benedetto Matarazzo, he or-ganized the VIIth International Summer School on MCDA (Catania, 2000). Heis author of many articles published in international journals and specializedbooks. He has been invited professor at Poznan Technical University and atthe University of Paris Dauphine. He has been invited speaker in internationalconferences. He is referee of the most relevant journals in the field of decisionanalysis.
Evangelos Grigoroudisreceived his M.Sc. and Ph.D. degrees in Decision Sci-ences and Operations Research from the Technical University of Crete (Greece)in 1996 and 1999, respectively. He is Lecturer on Managementof Quality Pro-cesses at the Department of Production Engineering and Management, Tech-nical University of Crete. During 1999-2002 he was Adjunct Professor at theDepartment of Political Sciences, University of Crete. He is member of the In-
ternational Society on Multiple Criteria Decision Making,the EURO WorkingGroups on Multicriteria Aid for Decisions and Financial Modelling, the Amer-ican Society for Quality, the Hellenic Operational Research Society, and theHellenic Institute of Production and Operations Management. He is the authorof a book on the measurement of service quality and a large number of researchreports and papers in scientific journals and conference proceedings. His re-search interests include operational research, multicriteria decision analysis,and management and control of quality.
Carlos Henggeler-Antunesreceived his Ph.D. degree in Electrical Engineer-ing (Optimization and Systems Theory) from the University of Coimbra in1992. Presently, he is an Associate Professor at the Department of Electri-cal Engineering and Computers, University of Coimbra, and director of theR&D Institute INESC Coimbra. His research interests include multiple ob-jective programming, management of uncertainty in decision support models,energy-environment models, and energy policy and planning. He was secretary(1993-95) and vice-president (1995-99) of APDIO (Portuguese OR Society).He was chairman of the Programme Committee of the 9th Congress of APDIO(2000) and the 15th Mini EURO Conference on “Managing Uncertainty in De-cision Support Models” (2004). His most recent works have been publishedin the European Journal of Operational Research, Decision Support Systems,Energy, IEEE Transactions in Power Systems.
Masahiro Inuiguchi received a D.E. degree in Industrial Engineering at OsakaPrefecture University in 1991. He worked as a Research Associate at OsakaPrefecture University and an Associate Professor at Hiroshima University andlater at Osaka University. Presently, he is a Full Professorat the Departmentof Systems Innovation, Graduate School of Engineering Science, Osaka Uni-versity. He is an editor of two books and has written more than100 refereedjournal and proceedings articles. He is an area editor of Fuzzy Optimization andDecision Making and a member of editorial committee of FuzzySets and Sys-tems. He received the Best Paper Award by Japan Society for Fuzzy Theory andSystems in 1997. He is interested in possibility theory, fuzzy mathematical pro-gramming, rough sets, Dempster-Shafer’s theory of evidence, and approximatereasoning.
Pekka J. Korhonenhas been Professor of Statistics at the Helsinki School ofEconomics, Finland since 1988. He received a Ph.D. in Applied Mathematicsfrom the University of Helsinki. His research interests areMCDM, productiv-ity/efficiency analysis, and computational statistics. Over 60 refereed journalarticles have appeared in journals like Journal of the Operational Research So-ciety, Management Science, European Journal of Operational Research, NavalResearch Logistics, Operations Research, etc. He is memberof the editorialboards of the journals Theory and Decision, Group Decision and Negotiation,
and Journal of Productivity Analysis. He was the President of InternationalSociety on MCDM during 1996-2000, and is currently the member of the in-ternational executive committee. In the ISI Web of Science,there are about 750citations to his scientific work. The George Cantor-Prize was awarded to himby the International Society on MCDM in 1994. He is an honorary chairmanof the Finnish Operations Research Society.
Christophe Labreuche received a Graduate Engineer Diploma from EcoleCentrale de Lyon and a Master in Numerical Analysis, both in 1993. He re-ceived a Ph.D. degree in Applied Mathematics in 1997 from Universite de ParisIX Dauphine. His first publications were in the areas of partial differential equa-tions and more specifically scattering and inverse scattering. He was workingat University of Delaware (USA) during the 1995/1996 academic year. From1997 to 1998 he was working at the research lab of Thales in numerical analy-sis. Then he joined the advanced software department to workon multicriteriadecision aid. On top of conducting industrial applicationson MCDA and de-veloping a software on MCDA, he works in the areas of fuzzy logic as wellas fuzzy measure theory, fuzzy integrals and their application in MCDA. Hisfield of interest includes also the representation of uncertainty and vagueness,decision theory and the modeling of expert knowledge.
Bertrand Mareschal received his Ph.D. in Mathematics from the ULB FreeUniversity of Brussels (1989). He has been Professor at the ULB since 1993.He has been part-time professor at the UMH (Universite de Mons-Hainaut, Bel-gium), HEC-Liege (Belgium), EDHEC (Lille, France) and Universite de Lille-3(France) as well as visiting professor at Ecole des Mines de Nancy (France). Hetaught courses in statistics, operations research, decision aid, computer scienceand mathematics. He is chairman of IDM (Innovative Decisionfor Manage-ment – www.idm-belgium.com) and iitiator of the QED multicriteria decisionaid web project (www.qed-solutions.com).
Jean-Marc Martel received B.Sc. and M.Sc. degrees in Mathematics at LavalUniversity in 1963 and 1965 and a Ph.D. degree in Applied Economics (Quanti-tative Methods) at Leuven University in 1975. Since 1965 he has been workingat the Faculty of Business Adminstration of Laval University, from 1965 to 1976as Associate Professor and from 1976 to 2000 as Full Professor in the Depart-ment of Operations and Decision Systems. Since 2001 he is Emeritus Professorat Laval University and since 2002 member of Royal Society ofCanada He hasbeen invited professor at several universities and research centers. He has beenorganiser of FRANCORO III (Quebec, 2001), MOPGP’98, the 48th meeting ofthe European Working Group on MCDA and the Fourth International SummerSchool on MCDA (Quebec, 1991). His main research interests are multi-criteriadecision aid under uncertainty, Bayesian analysis, information value, group de-cision and participative processes.
Antonio Gomes Martins received his Ph.D. degree in Electrical Engineeringfrom the University of Coimbra in 1985. He is presently Full Professor at theDepartment of Electrical Engineering at this University, where he is respon-sible for a R&D group on efficient use of energy resources. Since 1999 he isleading the Institute of Systems Engineering and Computersof Coimbra. Hiscurrent research interests are energy planning, load modelling, energy markettransformation.
Benedetto Matarazzois Full Professor at the Faculty of Economics of CataniaUniversity. He has been committee member of scientific societies of operationalresearch. He has been organiser, member of the programme committee, andinvited speaker in many scientific conferences. He is memberof the editorialboards of the European Journal of Operational Research, Journal of Multi-Criteria Decision Analysis, Foundations of Computing and Decision Sciences.He has been chairman of the programme committee of EURO XVI (Brussels,1998). His research is in the fields of MCDA and rough sets. He has been invitedprofessor at and co-operates with several European universities. He receivedthe Best Theoretical Paper Award by the Decision Sciences Institute (Athens,1999). He is member of the Organising Committee of the International SummerSchool on MCDA, of which he organized the first (Catania, 1983) and the VIIth(Catania, 2000) editions.
Nikolaos F. Matsatsinis is Associate Professor of Information and DecisionSupport Systems at the Department of Production Engineering and Manage-ment, Technical University of Crete (Greece). He received his B.A. in Physicsfrom Aristotle University of Thessaloniki (Greece) and hisPh.D. in IntelligenceDecision Support Systems from Technical University of Crete (Greece) in 1980and 1995, respectively. He is the author or co-author of five books and over 35articles in international scientific journals and books. Heteaches the followingcourses: Decision Support Systems, Knowledge Engineering, Electronic Com-merce, Advanced Issues in Information and Decision Systems(postgraduate)and Distributed Artificial Intelligence and Multi-Agent Systems (postgraduate).His research interests fall into the areas of decision support systems, artificialintelligent and multi-agent systems, e-business, e-marketing, multicriteria de-cision analysis, and group decision support systems.
Alexander Mechitov received his Ph.D. degree in Management InformationSystems from the Institute of Systems Analysis of the Russian Academy ofSciences (Moscow) in 1988. He is presently a Professor of MISin the MichaelE. Stephens College of Business, University of Montevallo.He has co-authoredtwo books and has published over 40 refereed journal articles on multicriteriadecision theory and applications. His research interests include multicriteriadecision making, behavioral decision making, risk analysis, and expert systems.
Patrick Meyer is currently working as a Researcher at the University of Lux-embourg. He received a Master in Mathematics in 2003 at the Faculte Polytech-nique of Mons in Belgium. At present, he is working on his Ph.D. thesis. Hismain research interests are multiple criteria decision aiding and data mining. Hehas worked on projects involving financial portfolio management (CELOFA)and analysis of large amounts of financial data from stocks (MIKADO). He hascontributed to the development of the TOMASO method for ordinal multiplecriteria sorting and has implemented the tool in a software package.
Helen Moshkovich received her Ph.D. degree in Management InformationSystems/Management Science from the Institute of Systems Analysis of theRussian Academy of Sciences (Moscow) in 1984. She is presently a Professorof MIS/Quantitative Methods in the Michael E. Stephens College of Business,University of Montevallo. Before that, she was with the Russian Academy ofSciences for 22 years. She has co-authored four books and haspublished over 50refereed journal articles on multicriteria decision theory and applications. Herresearch interests include multicriteria decision making, behavioral decisionmaking, decision support systems, and data mining.
Vincent Mousseauis Assistant Professor at the University of Paris Dauphineand member of the LAMSADE research laboratory. He received his Ph.D. inComputer Science/Operations Research in 1993. His reseachinterest lies inthe field of multiple criteria decision Aid and more specifically on preferencemodeling and elicitation, experimental analysis of decision behavior, and imple-mentation of multiple criteria methodologies in real worlddecision problems.His work has been published in international journals such as EJOR, Journal ofGlobal Optimization, and JMCDA.
Giuseppe Mundagot a “Laurea” degree in Economics from the University ofCatania, Italy (1988). He made his Ph.D. studies with the Free University of Am-sterdam, where he got a Ph.D. in Economics and Econometrics (1993). At themoment he is tenured Professor of Economics of Natural Resources and Multi-Criteria Decision Analysis at Universitat Autonoma de Barcelona. Previouslyhe has worked at the Joint Research Centre of the European Commission (Isprasite). He has been visiting lecturer at Universite Pantheon-Sorbonne, Universityof Naples Federico II, Centre d’Economie et d’Ethique pour l’ Environnementet le Developpement (C3ED), University of Pisa and various universities andresearch centres in South-America. He has also been consultant for the Inter-American Development Bank, the European Commission, DG XII, and forthe European Environment Agency. He has published one book and about 40articles and book chapters.
Subhash C. Narula is a Professor of Management Science and Statistics inthe Department of Management, School of Business, VirginiaCommonwealthUniversity, Richmond, Virginia, USA. He received his Ph.D.in Industrial and
Management Engineering from the University of Iowa. Prior to his current po-sition, he held faculty positions at the State University ofNew York at Buffalo,Buffalo, New York, Rensselaer Polytechnic Institute, Troy, New York. During1992-93, he was Chair of Optimization at the Linkoping Institute of Technol-ogy, Linkoping, Sweden. He is an elected Fellow of the American StatisticalAssociation and the American Society for Quality. He is a recipient of the Con-stantine Porphyrogenetus International Association Award and was awardedthe Distinguished Scholar Award of VCU in 2000. He has published papers inthe leading journals of statistics, operations research and management science,contributed papers in national and international proceedings, and chapters tobooks.
Stefan Nickel is Full Professor (Chair) of Operations Research and Logisticsat the Saarland University. He is also head of the optimization department ofthe Fraunhofer Institute for Industrial Mathematics. Stefan Nickel received hisDiploma, his Ph.D. and his Habilitation in Mathematics at the University ofKaiserslautern, in 1992, 1995, and 1999. From 1992 he workedwith the De-partment of Mathematics, University of Kaiserslautern as aResearch Associate.From 1995 to 1999, he was an Assistant Professor at the Department of Math-ematics at the University of Kaiserslautern. He is interested in location theory,combinatorial optimization, real world problems and computational geometry.Stefan Nickel is associate editor of Operations Research Letters and memberof the editorial board of Computers & Operations Research.
David L. Olson is the James and H.K. Stuart Professor of MIS at the Univer-sity of Nebraska. He has published research in over 60 refereed journal articles,primarily on the topic of multiple objective decision-making. He has authoredthree books, including Decision Aids for Selection Problems, and coauthoredsix others. He is a member of the Association for InformationSystems, theDecision Sciences Institute, the Institute for OperationsResearch and Manage-ment Sciences, and the Multiple Criteria Decision Making Society. He was withTexas A&M University from 1981 through 2001 where he held a Lowry Maysendowed professorship.
Meltem Ozturk received her B.E. degree in Industrial Engineering at the Uni-versity of Galatasaray (Turkey) in 2000 and her DEA at the Universite ParisDauphine in 2001. Since 2001 she is a Research Assistant and aPh.D. Can-didate in Computer Sciences at LAMSADE, Universite Paris Dauphine. Herresearch interest lies in the field of multiple criteria decision aid, non classicallogics (fuzzy set theory, Belnap logics etc.), and more specifically their use inpreference modeling and aggregation methods.
Marc Pirlot is Professor of Mathematics and Operations Research at the In-stitute of Engineering, Mons, Belgium. He obtained his Ph.D. in Mathematics
from the University of Mons in 1981. His main research interests are multicri-teria decision analysis and metaheuristics for combinatorial optimizaztion. Heis the co-author or editor of four books and of more than 50 refereed papers ininternational journals or conference proceedings. He has been president of theOperations Research Society of Belgium and is currently associate editor of theJournal of Multi-Criteria Decision Analysis and of Mathematiques et SciencesHumaines.
Justo Puertois Full Professor (Chair) of Statistics and Operations Research atthe University of Seville, where he has taught different subjects in the under-graduate and graduate programs of Mathematics, Statistics, Biology, ComputerScience, and Chemistry among others. Besides, he has been visiting profes-sor at several universities: NorthWestern University (USA), Kaiserslautern andChemnitz (Germany), Bologna (Italy), Hirosaki (Japan), etc. Justo Puerto re-ceived his Ph.D. in Mathematics at the University of Sevillein 1990. He is inter-ested in location theory, game theory, combinatorial and classical optimization,computational geometry and mathematical education. He haspublished over 60papers in professional journals. Justo Puerto has a large experience in the coor-dination of R&D projects and currently is associate editor of TOP, the Spanishjournal of Operations Research.
Antonio Rodríguez-Chıa received his Ph.D. degree in Mathematics (Statisticsand Operations Research) from the Faculty of Mathematics atSevilla Universityin 1998. From 1994 to 1998, he worked in Department of Mathematics at CadizUniversity as a Research Associate. Since 1998 he is Full Professor of theDepartment of Statistics and Operations Research in the Sciences Faculty atCadiz University. He is interested in location theory and game theory.
Marc Roubenshas been Professor of Statistics and Operations Research attheFaculte Polytechnique de Mons from 1971 to 1989 and is currently ScientificAdvisor of that institution. He has been with the Departmentof Mathematics,University of Liege, where he was Professor from 1986 to 2002. His primaryinterests have been in several areas of fuzzy sets theory (preference modelling,clustering and control), operations research (multiple criteria decision aid) andstatistics (time series analysis , data mining) He is co-author of a book withPhilippe Vincke on preference modeling and another book with Janos Fodoron fuzzy preference modelling and multiple criteria decision support. ProfessorRoubens has been on the editorial boards of two international journals (FuzzySets and Systems, European Journal of Operations Research)and is AssociateEditor of the International Journal of Approximate Reasoning. He has beenpresident of the Belgian Operations Research Society and president of the Eu-ropean Chapter of the International Fuzzy Systems Association.
Bernard Roy is Emeritus Professor at Universite Paris-Dauphine. He is thefounder and, since 1999, honorary director of LAMSADE, a research group
centered on the theme of decision aiding. Since 1980, he his scientific adviserof the Paris city transport authority. He is Graduate of the Institute of Statisticsof Paris University (1957) and Doctor des Sciences Mathematiques of Facultyof Paris (1961). After an extensive consulting experience at SEMA-METRA,he joined the Universite Paris-Dauphine in 1972 and created LAMSADE. In1975 he founded the EURO Working Group “Multiple Criteria Decision Aid-ing” which invariably held two annual meetings since then. He is Doctor Hon-oris Causa from several universities. He received the EURO Gold Medal (thehighest distinction granted by EURO, the Association of European OperationalResearch Societies) in 1992 and the MCDM Gold Medal granted by the In-ternational MCDM Society in 1995. He his the author of several books andhundreds of research papers.
Thomas Saatyholds the Chair of University Professor, Katz Graduate Schoolof Business, University of Pittsburgh. He has a Ph.D. in Mathematics fromYale University. Previously he was Professor at the WhartonSchool, Univer-sity of Pennsylvania, prior to which he was involved in research at the ArmsControl and Disarmament Agency, the State Department, in Washington, onnuclear arms reduction negotiations with the Soviets in Geneva. His current re-search is in decision-making, planning, conflict resolution and neural synthesis.He developed the Analytic Hierarchy Process (AHP) and its generalization tofeedback, the Analytic Network Process (ANP) (co-developed Expert Choicefor AHP and SuperDecisions for ANP) to deal with decision-making, weaponstradeoffs, and resource allocation. He has written more than 300 articles and33 books on mathematics, operations research and decision-making. His latestbooks are The Brain: Unraveling the Mystery of How It Works and CreativeThinking, Problem Solving & Decision Making. He has consulted for manycorporations and governments.
Yannis Siskosreceived his Doctorat d’Etat (1984) in Management Sciencefrom the University of Paris-Dauphine (France) and his DEA (1977) and Doc-torat 3e Cycle (1979) in Computer Science and Operational Research from theUniversity Pierre et Marie Curie (France). He is presently Professor of Deci-sion Science at the Department of Informatics, University of Piraeus. During1984-2001 he was Professor at the Technical University of Crete and found-ing director of the Decision Support Systems Laboratory. Hehas been visitingprofessor at the University of Paris-Dauphine (France), the University of Aix-Marseille II (France), the University of Laval (Canada), and the University ofCyprus. He is presently President of the Hellenic Operational Research Societyand his research interests fall into the areas of multicriteria decision supportsystems, service quality, and mathematical programming. He is the author ofseveral books and over sixty articles in international scientific journals.
Roman Slowinski is Professor and Head of the Laboratory of Intelligent De-cision Support Systems within the Institute of Computing Science, PoznanUniversity of Technology, Poland. He received a M.Sc. in Computer Science,Ph.D. in Operations Research, and Habilitation in Computing Science from thePoznan University of Technology in 1974, 1977, and 1981, respectively. Hehas been Professor on European Chair at the University of Paris Dauphine andinvited professor at the Swiss Federal Institute of Technology in Lausanne andat the University of Catania. His research concerns operational research andartificial intelligence, including multiple-criteria decision analysis, preferencemodelling, knowledge-based decision support in medicine,technology and eco-nomics, project scheduling, and rough set theory approach to knowledge anddata engineering. He is laureate of the EURO Gold Medal (1991) and DoctorHonoris Causa of Polytechnic Faculty of Mons (2000) and University of ParisDauphine (2001). Since 1999 he is co-editor-in-chief of theEuropean Journalof Operational Research.
Charles H. Smith received an M.B.A. from the College of William and Mary(Williamsburg, VA) in 1981. Previously he received his Ph.D. in Mathematicsfrom the University of Maryland in 1975. Since 1982 he has taught in the Schoolof Business at Virginia Commonwealth University, where he is currently As-sociate Professor in the Department of Management. His research publicationshave been in the areas of applied decision analysis and operations managementin addition to multiple criteria decision making.
Jaap Spronk is Full Professor of Finance & Investment (since 1982, tenure),Vice-Dean and Director of Bachelor & Master Programs in Economics, Eras-mus University, Rotterdam. He obtained a Ph.D. in Economics(InteractiveMultiple Goal Programming for Financial Planning, 1980) atErasmus Univer-sity. His main current research interests include: financial risk management,performance evaluation, financial modelling, financial management and strat-egy. The main areas of application are the following: professional investment,banking, transportation, aviation in particular, government and state agencies.Scientific board functions include: founder (1986) and chairman of the EUROWorking Group on Financial Modelling, member of the executive committeeof the Special Interest Group on MCDM (1980-1992), president (1991-1992)of EURO (Association of European Operational Research Societies). He hasbeen initiator (1983) of the First International Summer School on Multiple Cri-teria Decision Methods, Applications and Software. His honours include theGold Medal of the International Society of Multiple Criteria Decision Making(2002).
Ralph E. Steuer is the Charles S. Sanford, Sr. Chair of Business in the TerryCollege of Business, University of Georgia, USA. His degrees are an Sc.B.from Brown University, an M.B.A. from Cornell University, and a Ph.D. from
the University of North Carolina. Dr. Steuer is the author of“Multiple CriteriaOptimization: Theory, Computation and Application,” the ADBASE multipleobjective linear programming package, and over 85 scientific publications. He isa co-founder of the International Society on Multiple Criteria Decision Makingand was editor of the Society’s newsletter, MCDM WorldScan,for seventeenyears. Dr. Steuer’s interests are in efficient sets and surfaces, models with mul-tiple criteria, portfolio theory in finance, and interactive procedures in multiplecriteria optimization.
Theodor J Stewarthas been Professor of Statistical Sciences at the Universityof Cape Town since 1984, with main responsibility for operational researchand decision analysis. He has published widely in these areas, including a re-cent book co-authored with Valerie Belton of the Universityof Strathclyde,on Multiple Criteria Decision Analysis. Professor Stewarthas been involvedin many applications of these topics in private and public sectors, linked pri-marily to strategic planning and natural resources management. Recent workhas included water resources management, project prioritization problems, andstrategic bundling of assets for the electricity industry.He is on the editorialboards of four international journals, including a period as guest editor of anumber of issues of International Transactions in Operational Research. He isvice president (at large) of the International Federation of Operational ResearchSocieties, and is president elect of the International Society of Multiple CriteriaDecision Making.
Alexis Tsoukiasis a Senior Researcher of CNRS within the LAMSADE, Uni-versite Paris Dauphine. He holds a Ph.D. in Systems and Computer ScienceEngineering from Politecnico di Torino, Italy. He is authoror editor of threebooks and has published more than 50 papers in journals and contributed vol-umes on several fields including multiple criteria decisionaiding, preferencemodelling, formal logic, artificial intelligence etc.. He has served on differenteditorial boards and at different positions to several European working groupsand OR societies. Presently he is president elect of EURO, the European asso-ciation of OR societies within IFORS.
Jean-Claude Vansnickis Professor at the Warocque Faculty of Managementof the University of Mons-Hainaut, Belgium and member of theWarocque Re-search Center. He received, in 1973, his Ph.D. in Mathematics from the FreeUniversity of Brussels and, in 1974, the Royal Academy of Belgium award (Sec-tion Mathematical Sciences). Since then, he has extended his areas of interest tomeasurement theory and decision aid. His paper “Strength ofPreference. Theo-retical and Practical Aspects” was selected as National Contribution of Belgiumfor the Tenth Triennial Conference of the International Federation of Opera-tional Research Societies (IFORS 84). He is member of groupson multicriteria
analysis and was guest professor at several International Summer Schools onMulticriteria Decision Aid. He is co-author of the MACBETH approach.
Philippe Vincke is Full Professor and the director of the Service de Mathemati-ques de la Gestion, and vice-rector of the Universite Libre de Bruxelles. His re-search interests are preference modelling, aggregation, axiomatics of decision-aid methods and applications of Operations Research and Decision Aid (throughindustrial collaborations). He was president of EURO (European Associationof Operational Research) in 2001 and 2002 and is currently vice-president ofIFORS (International Federation of Operational Research Societies). He is au-thor or co-author of five books and about 100 papers in international journals.
H. Roland Weistroffer received his M.A. degree in Mathematics from DukeUniversity in 1973, and his Doctor of Science degree in applied mathematicsfrom the Free University Berlin in 1976. He taught computer science at theUniversity of Natal in Durban, South Africa, from 1978 to 1979, and was aChief Research Officer in operations research at the Centre for Scientific andIndustrial Research in Pretoria, South Africa, from 1980 to1983. Since thenhe has been at Virginia Commonwealth University in Richmond, Virginia. Heis currently an Associate Professor in the Information Systems Department inthe School of Business. His research interests are in decision support systems,multiple criteria decision making, and object oriented modeling.
Margaret M. Wiecek is Professor in the Department of Mathematical Sciencesat Clemson University. She obtained a M.S. degree in Electrical Engineeringand a Ph.D. degree in Systems Engineering from the University of Mining andMetallurgy in Krakow. Her research area includes theory, methodology, andapplications of mathematical programmingwithspecial interest in multi-criteriaoptimizationanddecision-making. She has been the Sofia Kovalevskaia VisitingProfessor and Mercator Visiting Professor at the University of Kaiserslauternand a visiting professor at the University of Copenhagen. She has published oversixty research articles. In the United States, her researchhas been funded bythe National Automotive Research Center, the National Institute of Science andTechnology, the National Science Foundation, and the Officeof Naval Research.She is a member of the Institute for Operations Research and ManagementSciences, the Mathematical Programming Society, and the Multiple CriteriaDecision Making Society.
Constantin Zopounidis is Professor of Financial Management and OperationsResearch and Chairman of the Department of Production Engineering and Man-agement, Technical University of Crete, Greece. He holds a Doctorat D’Etatin Management Science and a D.E.A. in Financial Management,both from theUniversity of Paris-IX Dauphine, France. Prof. Zopounidis’ research interestsinclude multiple criteria decision making, financial engineering and financialrisk management. His work has been published in such journals as Decision
Sciences, European Journal of Operational Research, Decision Support Sys-tems, The Journal of the Operational Research Society, Expert Systems withApplications, Global Finance Journal, International Journal of Intelligent Sys-tems in Accounting, Finance and Management and Computational Economics.He edited or co-edited more than 20 books on financial management and mul-ticriteria decision aid.