MULTIPLE CRITERIA
DECISION ANALYSIS:
STATE OF THE ART SURVEYS
Edited by
JOSÉ FIGUEIRA
University of Coimbra
SALVATORE GRECO
University of Catania
MATTHIAS EHRGOTT
University of Auckland
Kluwer Academic Publishers
Boston/Dordrecht/London
Contents
List of Figures
ix
List of Tables
xvi
Introduction
xvii
José Figueira, Salvatore Greco, Matthias Ehrgott
1.
2.
Human Reflection about Decision
Technical Reflection about Decision: MCDA Researchers
before MCDA
3.
The Reasons for this Collection of State-of-the-Art Surveys
4.
A Guided Tour of the Book
5.
Acknowledgment to the Referees
References
Part I
xvii
xviii
xx
xxi
xxx
xxx
An Overview of MCDA Techniques Today
1
Paradigms and Challenges
Bernard Roy
What Are the Expectations that Multicriteria Decision Aiding
(MCDA) Responds to?
2.
Three Basic Concepts
3.
How to Take Into Account Imperfect Knowledge?
4.
An Operational Point of View
5.
Conclusion
References
3
1.
4
7
12
14
17
18
Part II
Foundations of MCDA
2
Preference Modelling
Meltem Öztürk, Alexis Tsoukiàs, Philippe Vincke
1.
Introduction
2.
Purpose
3.
Nature of Information
4.
Notation and Basic Definitions
5.
Languages
6.
Preference Structures
7.
Domains and Numerical Representations
8.
Logic of Preferences
9.
Conclusion
References
27
28
28
30
32
33
39
48
56
59
60
3
Conjoint measurement tools for MCDM
Denis Bouyssou, Marc Pirlot
1.
Introduction and Motivation
2.
Definitions and Notation
3.
The Additive Value Model in the “Rich” Case
4.
The Additive Value Model in the “Finite” Case
5.
Extensions
References
73
74
89
92
102
112
119
Part III Outranking Methods
4
ELECTRE Methods
José Figueira, Vincent Mousseau, Bernard Roy
1.
Introduction: A Brief History
2.
Main Features of ELECTRE Methods
3.
A Short Description of ELECTRE Methods
4.
Recent Developments and Future Issues
5.
Software and Applications
6.
Conclusion
References
133
134
136
139
149
151
153
153
5
PROMETHEE Methods
Jean-Pierre Brans, Bertrand Mareschal
1.
History
2.
Multicriteria Problems
3.
The PROMETHEE Preference Modelling Information
4.
The PROMETHEE I and II Rankings
5.
The GAIA Visual Interactive Module
6.
The PROMETHEE VI Sensitivity Tool (The “Human Brain”)
7.
PROMETHEE V: MCDA under Constraints
8.
The PROMETHEE GDSS Procedure
9.
The DECISION LAB Software
References
163
164
164
168
171
175
181
182
183
186
189
6
Other Outranking Approaches
Jean-Marc Martel, Benedetto Matarazzo
1.
Introduction
2.
Other Outranking Methods
3.
Pairwise Criterion Comparison Approach
4.
One Outranking Method for Stochastic Data
5.
Conclusions
References
Part IV
197
198
198
221
254
259
260
Multiattribute Utility and Value Theories
7
MAUT – Multiattribute Utility Theory
James S. Dyer
1.
2.
3.
4.
5.
Introduction
Preference Representations Under Certainty and Under Risk
Ordinal Multiattribute Preference Functions for the Case of
Certainty
Cardinal Multiattribute Preference Functions for the Case of
Risk
Measurable Multiattribute Preference Functions for the Case
of
Certainty
265
266
267
273
278
281
6.
The Relationships Among the Multiattribute Preference Functions
7.
Concluding Remarks
References
290
292
294
8
UTA Methods
Yannis Siskos, Evangelos Grigoroudis, Nikolaos F. Matsatsinis
297
1.
Introduction
2.
The UTA Method
3.
Variants of the UTA Method
4.
Applications and UTA-based DSS
5.
Concluding Remarks and Future Research
References
298
302
313
328
334
335
9
The Analytic Hierarchy and Analytic Network Processes for the
Measurement of Intangible Criteria and for Decision-Making
Thomas L. Saaty
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Introduction
Pairwise Comparisons; Inconsistency and the Principal Eigenvector
Stimulus Response and the Fundamental Scale
Hospice Decision
Rating Alternatives One at a Time in the AHP – Absolute
Measurement
Paired Comparisons Imply Dependence
When is a Positive Reciprocal Matrix Consistent?
In the Analytic Hierarchy Process Additive Composition is
Necessary
Benefits, Opportunities, Costs and Risks
On the Admission of China to the World Trade Organization
(WTO)
The Analytic Network Process (ANP)
Two Examples of Estimating Market Share – The ANP with
a Single Benefits Control Criterion
Outline of the Steps of the ANP
Complex Decisions with Dependence and Feedback
Conclusions
345
346
348
354
359
369
372
373
375
377
378
382
389
400
403
405
References
406
10
On the Mathematical Foundation of MACBETH
Carlos A. Bana e Costa, Jean-Marie De Corte, Jean-Claude Vansnick
1.
Introduction
2.
Previous Research and Software Evolution
3.
Types of Preferential Information
4.
Numerical Representation of the Preferential Information
5.
Consistency – Inconsistency
6.
Consistency Test for Preferential Information
7.
Dealing with Inconsistency
8.
The MACBETH Scale
9.
Discussion About a Scale
10.
MACBETH and MCDA
References
Part V
409
410
412
414
415
416
417
420
432
435
437
438
Non-Classical MCDA Approaches
11
Dealing with Uncertainties in MCDA
Theodor J Stewart
1.
What is Uncertainty?
2.
Probabilistic Models and Expected Utility
3.
Pairwise Comparisons
4.
Risk Measures as Surrogate Criteria
5.
Scenario Planning and MCDA
6.
Implications for Practice
References
445
446
450
454
457
460
466
467
12
Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid
Patrick Meyer, Marc Roubens
1.
2.
3.
4.
5.
Introduction
The Data Set
Valued Preference Relation and Outranking Relation
Aggregation Procedures
The Sorting Problem
471
472
474
475
478
482
6.
The Tomaso Method
7.
The Choice Problem
8.
Conclusion
References
483
502
503
504
13
Decision Rule Approach
Salvatore Greco, Benedetto Matarazzo, Roman Słowińxski
1.
2.
Introduction
Dominance-based Rough Set Approach (DRSA) to Multiplecriteria Classification
3.
Variable-Consistency Dominance-Based Rough Set Approach
(VC-DRSA)
4.
Induction of Decision Rules from Rough Approximations of
Upward and Downward Unions of Decision Classes
5.
Extensions of DRSA
6.
DRSA for Multiple-criteria Choice and Ranking
7.
Conclusions
References
507
508
511
525
527
536
544
555
557
14
Fuzzy Measures and Integrals in MCDA
Michel Grabisch, Christophe Labreuche
1.
Introduction
2.
Measurement Theoretic Foundations
3.
Unipolar Scales
4.
Bipolar Scales
5.
Ordinal Scales
6.
Concluding Remarks
References
563
564
566
570
583
595
604
604
15
Verbal Decision Analysis
Helen Moshkovich, Alexander Mechitov, David Olson
1.
2.
3.
4.
Features of Unstructured Decision Problems
Main Principles of Verbal Decision Analysis
Decision Methods for Multicriteria Alternatives Ranking
Decision Methods for Multicriteria Alternatives’ Classification
609
610
610
615
625
5.
Place of Verbal Decision Analysis in MCDA
6.
Conclusion
References
Part VI
628
633
634
Multiobjective Mathematical Programming
16
Interactive Methods
Pekka Korhonen
1.
Introduction
2.
Basic Definitions and Some Theory
3.
Principles for Implementing Interactive Methods
4.
Generating Nondominated Solutions
5.
Solving Multiple Objective Problems
6.
Final Solution
7.
Examples of Software Systems: VIG and VIMDA
8.
Concluding Remarks
References
641
642
643
645
649
652
656
657
661
662
17
Multiobjective Programming
Matthias Ehrgott, Margaret M. Wiecek
667
1.
Introduction
2.
Problem Formulation and Solution Concepts
3.
Properties of the Solution Sets
4.
Conditions for Efficiency
5.
Generation of the Solution Sets
6.
Approximation of the Pareto Set
7.
Specially Structured Problems
8.
Current and Future Research Directions
9.
Conclusions
References
668
Multiple Objective Linear Programming with Fuzzy Coefficients
Masahiro Inuiguchi
723
669
673
675
676
692
696
707
708
708
18
1.
2.
Introduction
Problem Statement and Approaches
724
725
3.
Modality Constrained Programming Approach
4.
Modality Goal Programming
5.
Modal Efficiency Approach
6.
Concluding Remarks
References
731
749
754
757
757
19
MCDM Location Problems
Stefan Nickel, Justo Puerto, Antonio M. Rodrı́guez-Chı́a
1.
Introduction
2.
Location Problems
3.
Continuous Multicriteria Location Problems
4.
Multicriteria Network Location Problems
5.
Multicriteria Discrete Location Problems
6.
Conclusions
References
761
762
764
767
776
783
787
787
Part VII Applications
20
Multicriteria Decision Aid/Analysis in Finance
Jaap Spronk, Ralph E. Steuer, Constantin Zopounidis
1.
Introduction
2.
Financial Decision Making
3.
MCDA in Portfolio Decision-Making Theory
4.
MCDA in Discrete Financial Decision-Making Problems
5.
Conclusions and Future Perspectives
References
799
800
801
819
835
848
849
21
MCDA and Energy Planning
Danae Diakoulaki, Carlos Henggeler Antunes, António Gomes Martins
1.
Introduction
2.
Multiobjective Programming Models for Energy Planning
3.
Energy Planning Decisions with Discrete Alternatives
4.
Conclusions
References
859
860
863
874
890
891
22
Multicriteria Analysis in Telecommunication Network Planning and
Design – Problems and Issues
João Clı́maco, José Craveirinha
1.
2.
Motivation
Overview of Current Evolutions in Telecommunication Networks and Services
3.
Multicriteria Analysis in Telecommunication Network Planning and Design
4.
Review and Discussion of Applications of MA to Telecommunication Network Planning
5.
Future Trends
References
899
900
900
908
912
941
944
23
Multiple Criteria Decision Analysis and Sustainable Development
Giuseppe Munda
1.
2.
The Concept of Sustainable Development
Measuring Sustainability: The Issue of Sustainability Assessment Indexes
3.
A Defensible Axiomatic Setting for Sustainability Composite
Indicators
4.
Warning! Not Always Rankings Have to Be Trusted ...
5.
The Issue of the “Quality of the Social Decision Processes”
6.
The Issue of Consistency in Multi-Criteria Evaluation of
Sustainability Policies
7.
Conclusion
References
953
954
958
963
966
971
976
980
981
Part VIII MCDM Software
24
Multiple Criteria Decision Support Software
H. Roland Weistroffer, Charles H. Smith, Subhash C. Narula
1.
Introduction
2.
Software Overview
3.
Concluding Remarks
References
989
990
990
1009
1011
Contributing Authors
1019
Index
1035
Introduction
José Figueira, Salvatore Greco, Matthias Ehrgott
1.
Human Reflection about Decision
Decision has inspired reflection of many thinkers since the ancient times. The
great philosophers Aristotle, Plato, and Thomas Aquinas, to mention only a
few names, discussed the capacity of humans to decide and in some manners
claimed that this possibility is what distinguishes humans from animals. To
illustrate some important aspects of decision, let us briefly quote two important
thinkers: Ignatius of Loyola (1491-1556) and Benjamin Franklin (1706-1790).
To consider, reckoning up, how many advantages and utilities follow for me from
holding the proposed office or benefice [...] , and, to consider likewise, on the
contrary, the disadvantages and dangers which there are in having it. Doing the
same in the second part, that is, looking at the advantages and utilities there are
in not having it, and likewise, on the contrary, the disadvantages and dangers in
not having the same. [...] After I have thus discussed and reckoned up on all sides
about the thing proposed, to look where reason more inclines: and so, according
to the greater inclination of reason, [...], deliberation should be made on the thing
proposed.
This fragment from the “Spiritual Exercises” of St. Ignatius of Loyola [14]
has been taken from a paper by Fortemps and Słowiński [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 I
will tell you how. [...], my way is to divide half a sheet of paper by a line into two
columns; writing over the one Pro, and over the other Con. [...] When I have thus
got them all together in one view, I endeavor to estimate their respective weights;
and where I find two, one on each side, that seem equal, I strike them both out. If
I find a reason pro equal to some two reasons con, I strike out the three. If I judge
some two reasons con, equal to three reasons pro, I strike out the five; and thus
proceeding 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, I
come to a determination accordingly. [...] I have found great advantage from this
kind of equation, and what might be called moral or prudential algebra. Wishing
sincerely that you may determine for the best, I am ever, my dear friend, yours
most affectionately.
B. Franklin
This letter from Benjamin Franklin to Joseph Prestly has been taken from a
paper by MacCrimmon [17].
What is interesting in the above two quotations is the fact that decision is
strongly related to the comparison of different points of view, some in favour
and some against a certain decision. This means that decision is intrinsically
related to a plurality of points of view, which can roughly be defined as criteria.
Contrary to this very natural observation, for many years the only way to state a
decision problem was considered to be the definition of a single criterion, which
amalgamates the multidimensional aspects of the decision situation into a single
scale of measure. For example, even today the textbooks of Operations Research
suggest to deal with a decision problem as follows: to first define an objective
function, i.e., a single point of view like a comprehensive profit index (or a
comprehensive cost index) representing the preferability (or dis-preferability)
of the considered actions and then to maximize (minimize) this objective. This
is a very reductive, and in some sense also unnatural, way to look at a decision
problem. Thus, for at least thirty years, a new way to look at decision problems
has more and more gained the attention of researchers and practitioners. This is
the approach considered by Loyola and Franklin, i.e., the approach of explicitly
taking into account the pros and the cons of a plurality of points of view, in other
words the domain of Multiple Criteria Decision Analysis (MCDA). Therefore,
MCDA intuition is closely related to the way humans have always been making
decisions. Consequently, despite the diversity of MCDA approaches, methods
and techniques, the basic ingredients of MCDA are very simple: a finite or
infinite set of actions (alternatives, solutions, courses of action, ...), at least two
criteria, and, obviously, at least one decision-maker (DM). Given these basic
elements, MCDA is an activity which helps making decisions mainly in terms
of choosing, ranking or sorting the actions.
2.
Technical Reflection about Decision: MCDA
Researchers before MCDA
Of course, not only philosophers reasoned about decision-making. Many important technical aspects of MCDA are linked to classic works in economics, in
particular, welfare economics, utility theory and voting oriented social choice
theory (see [28]). Aggregating the opinion or the preferences of voters or individuals of a community into collective or social preferences is quite similar a
problem to devising comprehensive preferences of a decision-maker from a set
of conflicting criteria in MCDA [7].
Despite the importance of Ramon Llull’s (1232-1316) and Nicolaus Cusanus’s (1401-1464) concerns about and interests in this very topic, the origins
of voting systems are often attributed to Le Chevalier Jean-Charles de Borda
(1733-1799) and Marie Jean Antoine Nicolas de Caritat (1743-1794), Le Marquis de Condorcet. However, Ramon Llull introduced the pairwise comparison
concept before Condorcet [13], while Nicolaus Cusanus introduced the scoring method about three and a half centuries before Borda [27]. Furthermore, it
should be noted that a letter from Pliny the Younger (≈ AD 105) to Titus Aristo
shows that he introduced the ternary approval voting strategy and was interested
in voting systems a long time before Ramon Llull and Nicolaus Cusanus [18,
Chapter 2]. Anyway, Borda’s scoring method [4] has some similarities with
current utility and value theories as has Condorcet’s method [10] with the outranking approach of MCDA. In the same line of concerns, i.e., the aggregation
of individual preferences into collective ones, Jeremy Bentham (1748-1832)
introduced the utilitarian calculus to derive the total utility for the society from
the aggregation of the personal interests of the individuals of a community
[3]. Inspired by Bentham’s works, Francis Ysidro Edgeworth (1845-1926), a
utilitarian economist, was mainly concerned with the maximization of the utility of the different competing agents in economy. Edgeworth tried to find the
competitive equilibrium points for the different agents. He proposed to draw
indifference curves (lines of equal utility) for each agent and then derive the
contract curve, a curve that corresponds to the notion of the Pareto or efficient
set [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 a
certain position when it is impossible to find a way of moving from that position very slightly in such a manner that the ophelimity enjoyed by each of the
individuals of that collectivity increases or decreases. That is to say, any small
displacement in departing from that position necessarily has the effect of increasing 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, which
today is one of the fundamental concepts in MCDA.
MCDA also benefits from the birth and development of game theory. Félix
Edouard Justin Emile Borel (1871-1956) and John von Neumann (1903-1957)
are considered the founders of game theory [5, 6, 20, 19]. Many concepts from
this discipline had a strong impact on the development of MCDA.
The concept of efficient point was first introduced in 1951 by Tjalling Koopmans (1910-1985) in his paper “Analysis of production as an efficient combination of activities” [15]:
A possible point in the commodity space is called efficient whenever an increase
in one of its coordinates (the net output of one good) can be achieved only at the
cost of a decrease in some other coordinate (the net output of a good).
In the same year (1951) Harold William Kuhn (born 1925) and Albert William
Tucker (1905-1995) introduced the concept of vector maximum problem [16].
In the sixties, basic MCDA concepts were explicitly considered for the first
time. As two examples we mention Charnes’ and Cooper’s works on goal programming [8] and the proposition of ELECTRE methods by Roy [23]. The
seventies saw what is conventionally considered the “official” starting point of
MCDA, the conference on “Multiple Criteria Decision Making” organised in
1972 by Cochrane and Zeleny at Columbia University in South Carolina [9].
Since then MCDA has seen a tremendous growth which continues today.
3.
The Reasons for this Collection of State-of-the-Art
Surveys
The idea of MCDA is so natural and attractive that thousands of articles and
dozens of books have been devoted to the subject, with many scientific journals
regularly publishing articles about MCDA. To propose a new collection of stateof-the-art surveys of MCDA in so rich a context may seem a rash enterprise.
Indeed, some objections come to mind. There are many and good handbooks
and reviews on the subject (to give an idea consider [1, 11, 25, 26, 29]). The main
ideas are well established for some years and one may question the contributions
this volume can provide. Moreover, the field is so large and comprises developments so heterogeneous that it is almost hopeless to think that an exhaustive
vision 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 agree
with the above remarks. However, we believe that a new and comprehensive
collection of state-of-the-art surveys on MCDA can be very useful. The main
reasons which, despite our original resistance, brought us to propose this book
are the following:
1 Many of the existing handbooks and reviews are not too recent. Since
MCDA is a field which is developing very quickly this is an important
reason.
2 Even though the field of research and application of MCDA is so large,
there are some main central themes around which MCDA research and
applications have been developed. Therefore our approach was to try to
present the – at least in our opinion – most important of these ideas.
With reference to the first point, we can say that we observed many theoretical
developments which changed MCDA over the last ten years. We tried to consider
these changes as much as possible and in this perspective strong points of the
book are the following:
1 It presents the most up-to-date discussions on well established methodologies and theories such as outranking based methods and MAUT.
2 The book also contains surveys of new, recently emerged fields such as
conjoint measurement, fuzzy preferences, fuzzy integrals, rough sets and
others.
Following these points we drafted a list of topics and asked well known
researchers to present them. We encouraged the authors to cooperate with the
aim to present different perspectives if topics had some overlap. We asked the
authors to present a comprehensive presentation of the most important aspects
of the field covered by their chapters, a simple yet concise style of exposition,
and considerable space devoted to bibliography and survey of relevant literature.
We also requested a sufficiently didactic presentation and a text that is useful for
researchers in MCDA as well as for people interested in real life applications.
The importance of these requirements is related also to the specific way
the MCDA community looks at its research field. It can be summarized in the
observation that there is a very strong and vital link between theoretical and
methodological developments on the one hand and real applications on the
other hand. Thus, the validity of theoretical and methodological developments
can only be measured in terms of the progress given to real world practice.
Moreover, interest of MCDA to deal with concrete problems is related to the
consideration of a sound theoretical basis which ensures the correct application
of the methodologies taken into account.
In fact, not only the chapters of our book but rather all MCDA contributions
should satisfy the requirements stated out above, because they should be not too
“esoteric” and therefore understandable for students, theoretically well founded,
and applicable to some advantage in reality.
4.
A Guided Tour of the Book
Of course, this book can be read from the first to the last page. However, we think
that this is not the only possibility and it may not even be the most interesting
possibility. In the following we propose a guided tour of the book suggesting
some 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, methodologies, and techniques, but a specific perspective to deal with decision problems. Losing this perspective, even the most rigorous theoretical developments
and 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 of
MCDA. We share this conviction with most MCDA researchers. Bernard Roy
discusses these “pre-theoretical” assumptions of MCDA and gives an overview
of the field. Bernard Roy, besides giving many important theoretical contributions, engaged himself in thorough reflections on the meaning and the value of
MCDA, proposing some basic key concepts that are accepted throughout the
MCDA community.
4.2
Part II: Foundations of MCDA
This part of the book is related to a fundamental problem of MCDA, the representation of preferences. Classically, for example in economics, it is supposed
that preference can be represented by a utility function assigning a numerical value to each action such that the more preferable an action, the larger its
numerical value. Moreover, it is very often assumed that the comprehensive
evaluation of an action can be seen as the sum of its numerical values for the
considered criteria. Let us call this the classical model. It is very simple but not
too realistic. Indeed, there is a lot of research studying under which conditions
the classical model holds. These conditions are very often quite strict and it is
not reasonable to assume that they are satisfied in all real world situations. Thus,
other models relaxing the conditions underlying the classical model have been
proposed. This is a very rich field of research, which is first of all important
for those interested in the theoretical aspects of MCDA. However, it is also of
interest to readers engaged in applications of MCDA. In fact, when we adopt a
formal model it is necessary to know what conditions are supposed to be satisfied by the preferences of the DM. In the two chapters of this part problems
related to the representations of preferences are discussed.
Meltem Öztürk, Alexis Tsoukiàs, and Philippe Vincke present a very exhaustive review of preference modelling, starting from classical results but arriving
at the frontier of some challenging issues of scientific activity related to fuzzy
logic and non-classical logic.
Denis Bouyssou and Marc Pirlot discuss the axiomatic basis of the different
models to aggregate multiple criteria preferences. We believe that this chapter
is very important for the future of MCDA. Initially, the emphasis of MCDA
research was on proposal of new methods. But gradually the necessity to understand the basic conditions underlying each method and its specific axiomatization became more and more apparent. This is the first book on MCDA with
so 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 decision
methods 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 nature
of the problem, an outranking relation is a binary relation S defined on the set
of potential actions A such that aSb if there are enough arguments to decide
that a is at least as good as b, whereas there is no essential argument to refute
that statement [24]. Methods which strictly apply this definition of outranking
relation are the ELECTRE methods. They are very important in many respects,
not least historically, since ELECTRE I was the first outranking method [2].
However, within the class of outranking methods we generally consider all
methods which are based on pairwise comparison of actions. Thus, another
class of very well known multiple criteria methods, PROMETHEE methods,
are considered in this part of the book. Besides ELECTRE and PROMETHEE
methods, many other interesting MCDA methods are based on the pairwise comparison of actions. José Figueira, Vincent Mousseau and Bernard Roy present
the ELECTRE methods; Jean-Pierre Brans and Bertrand Mareschal present
the PROMETHEE methods and Jean-Marc Martel and Benedetto Matarazzo
review 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 is
a real number representing the preferability of the considered action. Very often
the utility is the sum of the marginal utilities that each criterion assigns to the
considered action. Thus, this approach very often coincides with what we called
the classical approach before. As we noted in commenting Part I, this approach
is very simple at first glance. It is often applied in real life, e.g., every time
we aggregate some indices by means of a weighted sum we are applying this
approach. Despite its simplicity the approach presents some technical problems.
The first are related to the axiomatic basis and to the construction of marginal
utility functions (i.e., the utility functions relative to each single criterion),
both in case of decision under certainty and uncertainty. These problems are
considered by James Dyer in a comprehensive chapter about the fundamentals
of this approach.
Yannis Siskos, Vangelis Grigoroudis and Nikolaos Matsatsinis present the
very well known UTA methods, which on the basis of the philosophy of the
aggregation-disaggregation approach and using linear programming, build a
MAUT model that is as consistent as possible with the DM’s preferences expressed in actual previous decisions or on a “training sample”. The philosophy
of aggregation-disaggregation can be summarized as follows: How is it possible to assess the decision-maker’s preference model leading to exactly the same
decision as the actual one or at least the most “similar” decision?
Thomas Saaty presents a very well known methodology to build utility functions, the AHP (Analytic Hierarchy Process) and its more recent extension,
the ANP (Analytic Network Process). AHP is a theory of measurement that
uses pairwise comparisons along with expert judgments to deal with the measurement of qualitative or intangible criteria. The ANP is a general theory of
relative measurement used to derive composite priority ratio scales from individual ratio scales that represent relative measurements of the influence of
elements that interact with respect to control criteria. The ANP captures the
outcome of dependence and feedback within and between clusters of elements.
Therefore AHP with its dependence assumptions on clusters and elements is a
special case of the ANP.
Carlos Bana e Costa, Jean-Claude Vansnick, and Jean-Marie De Corte present
another MCDA methodology based on the additive utility model. This methodology is MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). It is an MCDA approach that requires only qualitative judgements about differences of values of attractiveness of one action over another
action to help an individual or a group to quantify the relative preferability of
different actions. In simple words, the MACBETH approach tries to answer the
following questions: How can we build an interval scale of preferences on a set
of actions without forcing evaluators to produce direct numerical representations of their preferences? How can we coherently aggregate these qualitative
evaluations using an additive utility model?
4.5
Part V: Non-Classical MCDA Approaches
Many approaches have been proposed in MCDA besides outranking methods
and multiattribute utility theory. In this part of the book we try to collect information about some of the most interesting proposals. First, the question of
uncertainty in MCDA is considered. Theo Stewart discusses risk and uncertainty
in MCDA. It is necessary to distinguish between internal uncertainties (related
to decision-maker values and judgements) and external uncertainties (related
to imperfect knowledge concerning consequences of actions). The latter, corresponding to the most accepted interpretation of uncertainty in the specialized
literature, has been considered in the chapter. Four broad approaches for dealing with external uncertainties are discussed. These are multiattribute utility
theory and some extensions; stochastic dominance concepts, primarily in the
context of pairwise comparisons of alternatives; the use of surrogate risk measures such as additional decision criteria; and the integration of MCDA and
scenario planning.
The second consideration is the fuzzy set approach to MCDA. Most real
world decision problems take place in a complex environment where conflicting systems of logic, uncertain and imprecise knowledge, and possibly vague
preferences have to be considered. To face such complexity, preference modeling requires the use of specific tools, techniques, and concepts which allow the
available information to be represented with the appropriate granularity. In this
perspective, fuzzy set theory has received a lot of attention in MCDA for a long
time. Patrick Meyer and Marc Roubens present the fuzzy set approach to MCDA
for choice, ranking, and sorting problems. In this chapter, several MCDA approaches based on fuzzy evaluations are reviewed. The authors give details on
a sorting procedure for the assignment of alternatives to graded classes when
the available information is given by interacting points of view and a subset
of prototypic alternatives whose assignment is given beforehand. A software
dedicated to that approach (TOMASO) is briefly presented. Finally they recall
the concepts of good and bad choices based on dominant and absorbent kernels
in the valued digraph that corresponds to an ordinal valued outranking relation.
Salvatore Greco, Benedetto Matarazzo and Roman Słowiński present the
decision rule approach to MCDA. This approach represents the preferences in
terms of “if ..., then ...” decision rules such as, for example, “if the maximum
speed of car x is at least 175 km/h and its price is at most $12000, then car
x is comprehensively at least medium”. This approach is related to rough set
theory and to artificial intelligence. Its main advantages are the following. The
DM gives information in the form of examples of decisions, which requires
relatively low cognitive effort and which is quite natural. The decision model is
also expressed in a very natural way by decision rules. This permits an absolute
transparency of the methodology for the DM. Another interesting feature of
the decision rule approach is its flexibility, since any decision model can be
expressed in terms of decision rules and, even better, the decision rule model
can be much more general than all other existing decision models used in
MCDA.
Michel Grabisch and Christophe Labreuche present the fuzzy integral approach that is known in MCDA for the last two decades. In very simple words
this methodology permits a flexible modeling of the importance of criteria. Indeed, fuzzy integrals are based on a capacity which assigns an importance to
each subset of criteria and not only to each single criterion. Thus, the importance
of a given set of criteria is not necessarily equal to the sum of the importance
of the criteria from the considered subset. Consequently, if the importance of
the whole subset of criteria is smaller than the sum of the importances of its
individual criteria, then we observe a redundancy between criteria, which in
some way represents overlapping points of view. On the other hand, if the importance of the whole subset of criteria is larger than the sum of the importances
of its members, then we observe a synergy between criteria, the evaluations of
which reinforce one another. On the basis of the importance of criteria measured
by means of a capacity, the criteria are aggregated by means of specific fuzzy
integrals, the most important of which are the Choquet integral (for cardinal
evaluations) and the Sugeno integral (for ordinal evaluations).
Finally, Helen Moshkovich, Alexander Mechitov and David Olson present
the verbal decision methods MCDA. This is a class of methods originated from
the work of one of the MCDA pioneers, the late Oleg Larichev. The idea of
verbal decision analysis is to build a decision model using mostly qualitative
information expressed in terms of a language that is natural for the DM. Moreover, measurement of criteria and preference elicitation should be psychologically valid. The methods, besides being mathematically sound, should check
the 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 maximization or minimization of an objective function subject to some constraints.
A very rich and powerful arsenal of methodologies and techniques has been
developed and continues to be developed within Operations Research. However, it is very difficult to summarize all the points of view related to the desired
results of the decision at hand in only one objective function. Thus, it seems
natural to consider a very general formulation of decision problems where a set
of objective functions representing different criteria have to be “optimized”. To
deal with these types of problems requires not only to generalize the methodologies developed for classical single objective optimization problems, but also
to introduce new methodologies and techniques permitting to compare different
objectives according to the preferences of the DM. In this part of the book we
tried to give adequate space to these two sides of multiobjective programming
problems.
Emphasis on the side of gathering information from the decision-maker and
consequent preference representation is given in the first chapter of this part, in
which Pekka Korhonen introduces the main concepts and basic ideas of interactive methods dealing with multiobjective programming problems. The basic
observation is that, since the DM tries to “maximize” a set of criteria in conflict with each other and an increment of one criterion can only be reached by
accepting a decrement of at one or more other criteria, we need to compare the
advantages coming from increments with respect to some criteria with the disadvantages coming from corresponding decrements of other criteria. A utility
or value function representing DM preferences would seem the most appropriate for this aim, but the key assumption in multiple objective programming
is that this utility function is unknown. Therefore many methodologies have
been proposed with the aim of developing a fruitful dialogue with the DM permitting, on the one hand, to provide the DM with relevant information about
non-dominated solutions and, on the other hand, to obtain useful information
about the preferences of the DM. This dialogue is generally assisted by specific software, very often employing graphical representations of the results. It
permits to define a solution which the DM can accept as a good compromise.
In the next chapter, Matthias Ehrgott and Margaret Wiecek introduce mathematical methods to solve multiobjective programming (MOP) problems. In
their survey, they present solution concepts of MOP, properties of efficient and
nondominated sets, optimality conditions, solution techniques, approximation
of efficient and nondominated sets, and specially-structured problems including
linear and discrete MOPs as well as selected nonlinear MOPs. The contents of
the chapter have been selected on the idea that the primary (although not necessarily the ultimate) goal of multiobjective programming is to seek solutions
of MOPs and therefore a special attention was paid to methods suitable for
finding these solutions. Since the ultimate goal of MOP problem is selection of
a preferred solution, for which an adequate representation of DM preferences
is necessary, this chapter is well complemented by the previous one.
Masahiro Inuiguchi deals with multiple objective programming problems
with fuzzy coefficients. The introduction of fuzziness in multiple objective
programming is due to the observation that in real world problems imprecise
specifications of parameters fluctuating in certain ranges are very usual. For
example, let us consider an activity for which the acceptable expense is 100
million dollars. However, the DM may accept the expense of 100.1 million dollars if the objective functions take much better values by this small violation of
the constraint. Due to their specific nature, fuzzy multiobjective programming
problems need an interpretation which leads to specific approaches to the problem. Since fuzzy programming has a relatively long history, many approaches
related to different interpretations of the fuzzy MOP have been proposed. In this
chapter the approach based on necessity and possibility is considered, as many
of the approaches proposed in the specialized literature are of this type. The
difference to other approaches often lies solely in the measures employed for
the evaluation of a fuzzy event. Thus, describing the approaches based on possibility and necessity measures would be sufficient to acknowledge the essence
of multiple objective programming problems with fuzzy coefficients.
Finally, this part is concluded by a chapter that deals with an area of Operations Research in which multiobjective programming has been used quite
frequently. Stefan Nickel, Justo Puerto and Antonio Rodrı́guez-Chı́a present
the multiple criteria approach to locational analysis. An important characteristic of location models is their intrinsic multiple criteria nature. In this context
different criteria are related to one or several new facilities and depend on the
distances of these facilities to the set of fixed or demand facilities. There are at
least two natural ways of deriving the different criteria. First, a decision about a
new facility to be located is typically a group decision and each decision maker
will have his own preferences, which may be expressed by a corresponding
criterion. Secondly, the functions may represent different evaluation criteria
for the new facility to be located, like cost, reachability, risk, etc. The chapter
provides a broad overview of the most representative multiple criteria location
problems 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 MCDA
research are measured by the number and quality of the decisions supported by
MCDA methodologies. Applications in this case discriminate between results
that are really interesting for MCDA and results that, even though beautiful
and interesting for economics, mathematics, psychology, or other scientific
fields, are not interesting for MCDA. The applications of MCDA in real world
problems are very numerous and in very different fields. Therefore, it was clear
from the outset that it would be impossible to cover all the fields of application
of MCDA. We decided to select some of the most significant areas.
Jaap Spronk, Ralph Steuer and Constantin Zopounidis discuss the contributions of MCDA in finance. A very valuable feature of their chapter is the focus
on justification of the multidimensional character of financial decisions and the
use of different MCDA methodologies to support them. The presentation of
the contributions of MCDA in finance permits to structure complex evaluation
problems in a scientific context and in a transparent and flexible way, with the
introduction of both quantitative (i.e., financial ratios) and qualitative criteria
in the evaluation process.
Danae Diakoulaki, Carlos Henggeler Antunes and António Gomes Martins
present applications of MCDA in energy planning problems. In modern technologically developed societies, decisions concerning energy planning must be
made in complex and sometimes ill-structured contexts, characterized by technological evolution, changes in market structures, and new societal concerns.
Decisions to be made by different agents (at utility companies, regulatory bodies, and governments) must take into account several aspects of evaluation such
as technical, socio-economic, and environmental ones, at various levels of decision making (ranging from the operational to the strategic level) and with
different time frames. Thus, energy planning problems inherently involve multiple, conflicting and incommensurate axes of evaluation. The chapter aims at
examining to which extent the use of MCDA in energy planning applications
has been influenced by those changes currently underway in the energy sector,
in the overall socio-economic context, and in particular to which extent it is
adapted to the new needs and structuring and modelling requirements.
João Clı́maco and José Craveirinha present multiple criteria decision analysis
in telecommunication network planning and design. Decision making processes
in this field take place in an increasingly complex and turbulent environment
involving multiple and potentially conflicting options. Telecommunication networks is an area where different socio-economic decisions involving communication issues have to be made, but it is also an area where technological
issues are of paramount importance. This interaction between a complex socioeconomic environment and the extremely fast development of new telecommunication technologies and services justifies the interest in using multiple criteria
evaluation in decision making processes. The chapter presents a review of contributions in these areas, with particular emphasis on network modernisation
planning and routing problems and outlines an agenda of current and future
research trends and issues for MCDA in this area.
Finally, Giuseppe Munda addresses applications of MCDA in problems concerning sustainable development. Sustainable development is strongly related
to environmental questions, i.e., sustainable development generalizes environmental management taking into account not only an ecological but also socioeconomic, technical and ethical perspectives. Ecological problems were among
the first to be dealt with by MCDA. Therefore, there is a strong tradition in this
field and many interesting stimuli for MCDA research came from there. The
extensive perspective of sustainable development is very significant because it
improves the quality of decisions concerning the environment taking into account other criteria, which are not strictly environmental but which strongly
interact with it. In making sustainability policies operational, basic questions
to be answered are sustainability of what and whom? As a consequence, sustainability issues are characterised by a high degree of conflict. Therefore, in
this context MCDA appears as an adequate approach.
4.8
Part VIII: MCDM Software
Application of an MCDA method requires such a considerable amount of computation that even the development of many MCDA methodologies without
the use of a specialized software is hardly imaginable. While software is an
even more important element in the application of MCDA methodologies, this
does not mean that to have a good software is sufficient to apply an MCDA
methodology correctly. Clearly, software is a tool and it should be used as a
tool. Before using a software, it is necessary to have a sound knowledge of the
adopted methodology and of the decision problem at hand.
After these remarks about cautious use of software, the problem is: What
software is available for MCDA? Heinz Roland Weistroffer, Subhash Narula
and Charles H. Smith present well known MCDA software packages. While
there is certainly some MCDA software available that is not present in the
chapter, 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 a
software for adoption in an application.
5.
Acknowledgment to the Referees
The editors are very grateful to Euro Beinat, Nabil Belacel, Denis Bouyssou, John Buchanan, João Clı́maco, Danae Diakoulaki, Luı́s Dias, Michael
Doumpos, Ernest Forman, Philippe Fortemps, Lorraine Gardiner, Christophe
Gonzales, Michel Grabisch, Winfried Hallerbach, Raimo P. Hämäläinen, Carlos 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 Słowiński, Jerzy Stefanowsky, Ralph Steuer, Theo Stewart, Christianne Tammer,
Jean-Claude Vansnick, Luis Vargas, Philippe Vincke, Peter Wakker, Margaret
Wiecek, Szymon Wilk who served as referees for this volume.
The editors would also like to express their gratitude to people who supported
them with very valuable advice along all the preparation of the book: Bernard
Roy, Denis Bouyssou, Benedetto Matarazzo, Roman Słowiński, Gary Folven
and Frederick S. Hillier.
Acknowledgments
José Figueira was supported by the grant SFRH/BDP/6800/2001 (Fundação
para a Ciência e Tecnologia, Portugal) and gratefully acknowledges DIMACS
Research Center at Rutgers University and LAMSADE at University ParisDauphine for the welcome during his sabbatical leave and the short visits to
the 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/Embassy
of France in Lisbon (500B4) and Program Pessoa 2004. Matthias Ehrgott was
partially supported by University of Auckland grant 3602178/9275 and by the
Deutsche Forschungsgemeinschaft grant Ka 477/27-1.
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I
AN OVERVIEW OF MCDA
TECHNIQUES TODAY
Chapter 1
PARADIGMS AND CHALLENGES
Bernard Roy
LAMSADE
Université Paris-Dauphine
Place du Maréchal De Lattre de Tassigny, 75775 Paris Cedex 16
France
roy@lamsade.dauphine.fr
Abstract
The purpose of this introductory part is to present an overall view of what MCDA
is today. In Section 1, I will attempt to bring answers to questions such as: what
is it reasonable to expect from MCDA? Why decision aiding is more often multicriteria than monocriterion? What are the main limitations to objectivity? Section
2 will be devoted to a presentation of the conceptual architecture that constitutes
the main keys for analyzing and structuring problem situations. Decision aiding
cannot and must not be envisaged jointly with a hypothesis of perfect knowledge.
Different ways for apprehending the various sources of imperfect knowledge will
be introduced in Section 3. A robustness analysis is necessary in most cases. The
crucial question of how can we take into account all criteria comprehensively in
order to compare potential actions to one another will be tackled in Section 4. In
this introductory part, I will only present a general framework for positioning the
main operational approaches that exist today. In Section 5, I will discuss some
more philosophical aspects of MCDA. For providing some aid in a decision context, we have to choose among different paths which one seems to be the most
appropriate, or how to combine some of them: the path of realism which leads
to the quest for a discussion for discovering, the axiomatic path which is often
associated with the quest of norms for prescribing, or the path of constructivism
which 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
Meltem Öztürk, Alexis Tsoukiàs
LAMSADE-CNRS, Université Paris Dauphine,
75775 Paris Cedex 16,
France
{ozturk,tsoukias}@lamsade.dauphine.fr
Philippe Vincke
Université Libre de Bruxelles
CP 210/1, Bld. du Triomphe, 1050 Bruxelles,
Belgium
pvincke@smg.ulb.ac.be
Abstract
This chapter provides the reader with a presentation of preference modelling
fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology,
mathematical programming, even medicine, archaeology, and obviously decision
analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the chapter. We
start by discussing different reasons for constructing a model or preference. We
then go through a number of issues that influence the construction of preference
models. Different formalisations besides classical logic such as fuzzy sets and
non-classical logics become necessary. We then present different types of preference structures reflecting the behavior of a decision-maker: classical, extended
and valued ones. It is relevant to have a numerical representation of preferences:
functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In Section 8, we briefly
explore the concept of deontic logic (logic of preference) and other formalisms
associated with “compact representation of preferences” introduced for special
purposes. 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 Bouyssou
CNRS
LAMSADE, Université Paris Dauphine
F-75775 Paris Cedex 16
France
bouyssou@lamsade.dauphine.fr
Marc Pirlot
Faculté Polytechnique de Mons
9, rue de Houdain
B-7000 Mons
Belgium
marc.pirlot@fpms.ac.be
Abstract
This paper offers a brief and nontechnical introduction to the use of conjoint
measurement in multiple criteria decision making. The emphasis is on the, central,
additive value function model. We outline its axiomatic foundations and present
various possible assessment techniques to implement it. Some extensions of this
model, e.g. nonadditive models or models tolerating intransitive preferences are
then briefly reviewed.
Keywords:
Conjoint Measurement, additive value function, preference modelling.
III
OUTRANKING METHODS
Chapter 4
ELECTRE METHODS
José Figueira
Faculdade de Economia and INESC-Coimbra
Universidade de Coimbra
Av. Dias da Silva, 165, 3004-512 Coimbra
Portugal
figueira@fe.uc.pt
Vincent Mousseau, Bernard Roy
LAMSADE
Université Paris-Dauphine
Place du Maréchal De Lattre de Tassigny, 75775 Paris Cedex 16
France
{mousseau,roy}@lamsade.dauphine.fr
Abstract
Over the last three decades a large body of research in the field of ELECTRE family methods appeared. This research has been conducted by several researchers
mainly in Europe. The purpose of this chapter is to present a survey of the ELECTRE methods since their first appearance in mid-sixties, when ELECTRE I was
proposed by Bernard Roy and his colleagues at SEMA consultancy company.
The chapter is organized in five sections. The first section presents a brief history
of ELECTRE methods. The second section is devoted to the main features of
ELECTRE methods. The third section describes the different ELECTRE methods existing in the literature according to the three main problematics: choosing,
ranking and sorting. The fourth section presents the recent developments and
future issues on ELECTRE methods. Finally, the fifth section is devoted to the
software and applications. An extensive and up-to-date bibliography is also provided in the end of this chapter.
Keywords:
Multiple criteria decision aiding, Outranking approaches, ELECTRE methods.
Chapter 5
PROMETHEE METHODS
Jean-Pierre Brans
Centrum voor Statistiek en Operationeel Onderzoek
Vrije Universiteit Brussel
Pleinlaan 2, B-1050 Brussels
Belgium
jpbrans@vub.ac.be
Bertrand Mareschal
Service de Mathématiques de la Gestion
Université Libre de Bruxelles
Boulevard du Triomphe CP 210-01, B-1050 Brussels
Belgium
bmaresc@ulb.ac.be
Abstract
This paper gives an overview of the PROMETHEE-GAIA methodology for
MCDA. It starts with general comments on multicriteria problems, stressing that
a multicriteria problem cannot be treated without additional information related
to the preferences and the priorities of the decision-makers. The information requested by PROMETHEE and GAIA is particularly clear and easy to define for
both decision-makers and analysts. It consists in a preference function associated to each criterion as well as weights describing their relative importance. The
PROMETHEE I, the PROMETHEE II complete ranking, as well as the GAIA
visual interactive module are then described and commented. The two next sections are devoted to the PROMETHEE VI sensitivity analysis procedure (human
brain) and to the PROMETHEE V procedure for multiple selection of alternatives
under constraints. An overview of the PROMETHEE GDSS procedure for group
decision making is then given. Finally the DECISION LAB software implementation of the PROMETHEE-GAIA methodology is described using a numerical
example.
Keywords:
MCDA, outranking methods, PROMETHEE-GAIA, DECISION LAB.
Chapter 6
OTHER OUTRANKING APPROACHES
Jean-Marc Martel
Facultés des Sciences de l’Administration
University of Laval
Canada
jean-marc.martel@fsa.ulaval.ca
Benedetto Matarazzo
Department of Economics and Quantitative Methods
University of Catania
Corso Italia, 55, Catania
Italy
matarazz@unict.it
Abstract
In this chapter, we shortly describe some outranking methods other than ELECTRE and PROMETHEE. All these methods (QUALIFLEX, REGIME, ORESTE,
ARGUS, EVAMIX, TACTIC and MELCHIOR) propose definitions and computations of particular binary relations, more or less linked to the basic idea of the
original ELECTRE methods. Beside them, we will also describe other outranking methods (MAPPAC, PRAGMA, IDRA and PACMAN) that have been developed in the framework of the Pairwise Criterion Comparison Approach (PCCA)
methodology, whose peculiar feature is to split the binary relations construction
phase in two steps: in the first one, each pair of actions is compared with respect
to two criteria a time; in the second step, all these partial preference indices are
aggregated in order to obtain the final binary relations. Finally, one outranking
method for stochastic data (the Martel and Zaras’ method) is presented, based on
the use of stochastic dominance relations between each pair of alternatives.
Keywords:
Multiple criteria decision analysis, outranking methods, pairwise criteria comparison approach.
IV
MULTIATTRIBUTE UTILITY AND
VALUE THEORIES
Chapter 7
MAUT – MULTIATTRIBUTE UTILITY
THEORY
James S. Dyer
Department of Management Science and Information Systems
The Graduate School of Business
University of Texas at Austin
Austin, TX 78712
USA
Jim.Dyer@bus.utexas.edu
Abstract
In this chapter, we provide a review of multiattribute utility theory. We begin with
a brief review of single-attribute preference theory, and we explore preference
representations that measure a decision maker’s strength of preference and her
preferences for risky alternatives. We emphasize the distinction between these
two cases, and then explore the implications for multiattribute preference models. We describe the multiattribute decision problem, and discuss the conditions
that allow a multiattribute preference function to be decomposed into additive
and multiplicative forms under conditions of certainty and risk. The relationships among these distinct types of multiattribute preference functions are then
explored, and issues related to their assessment and applications are surveyed.
Keywords:
Multiattribute utility theory, additive value functions, preference modeling.
Chapter 8
UTA METHODS
Yannis Siskos
University of Piraeus
Department of Informatics
80 Karaoli & Dimitriou Str.
18534 Piraeus, Greece
ysiskos@unipi.gr
Evangelos Grigoroudis, Nikolaos F. Matsatsinis
Technical University of Crete
Decision Support Systems Laboratory
University Campus, Kounoupidiana
73100 Chania,– Greece
{vangelis,nikos}@ergasya.tuc.gr
Abstract
UTA methods refer to the philosophy of assessing a set of value or utility functions, assuming the axiomatic basis of MAUT and adopting the preference disaggregation principle. UTA methodology uses linear programming techniques in
order to optimally infer additive value/utility functions, so that these functions are
as consistent as possible with the global decision-maker’s preferences (inference
principle). The main objective of this chapter is to analytically present the UTA
method and its variants and to summarize the progress made in this field. The
historical background and the philosophy of the aggregation-disaggregation approach are firstly given. The detailed presentation of the basic UTA algorithm is
presented, including discussion on the stability and sensitivity analyses. Several
variants of the UTA method, which incorporate different forms of optimality criteria, are also discussed. The implementation of the UTA methods is illustrated by a
general overview of UTA-based DSSs, as well as real-world decision-making applications. Finally, several potential future research developments are discussed.
Keywords:
UTA methods, preference disaggregation, ordinal regression, additive utility, multicriteria analysis.
Chapter 9
THE ANALYTIC HIERARCHY AND
ANALYTIC NETWORK PROCESSES
FOR THE MEASUREMENT OF
INTANGIBLE CRITERIA AND
FOR DECISION-MAKING
Thomas L. Saaty
Katz Graduate School of Business
University of Pittsburgh
USA
saaty@katz.pitt.edu
Abstract
The Analytic Hierarchy Process (AHP) and its generalization to dependence and
feedback, the Analytic Network Process (ANP), are theories of relative measurement of intangible criteria. With this approach to relative measurement, a scale
of priorities is derived from pairwise comparison measurements only after the
elements to be measured are known. The ability to do pairwise comparisons is
our biological heritage and we need it to cope with a world where everything
is relative and constantly changing. In traditional measurement one has a scale
that one applies to measure any element that comes along that has the property
the scale is for, and elements are measured one by one, not by comparing them
with each other. In the AHP paired comparisons are made with judgments using
numerical values taken from the AHP absolute fundamental scale of 1-9. A scale
of relative values is derived from all these paired comparisons and it also belongs
to an absolute scale that is invariant under the identity transformation like the
system of real numbers. The AHP/ANP is useful for making multicriteria decisions involving benefits, opportunities, costs and risks. The ideas are developed
in stages and illustrated with examples of real life decisions. The subject is transparent and despite some mathematics, it is easy to understand why it is done the
way 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 MATHEMATICAL
FOUNDATIONS OF MACBETH
Carlos A. Bana e Costa
Centre for Management Studies of Instituto Superior Técnico
Technical University of Lisbon
Av. Rovisco Pais, 1049-001 Lisbon, Portugal
and
Department of Operational Research, London School of Economics
Houghton Street, London WC2A 2AE, U.K.
carlosbana@netcabo.pt,c.bana@lse.ac.uk
Jean-Marie De Corte, Jean-Claude Vansnick
Centre de Recherche Warocqué, Université de Mons-Hainaut
Place du Parc, 20, 7000 Mons
Belgium
{Jean-Marie.DeCorte,Jean-Claude.Vansnick}@umh.ac.be
Abstract
MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) is a multicriteria decision analysis approach that requires only qualitative
judgements about differences of value to help an individual or a group quantify
the relative attractiveness of options. This chapter presents an up-to-date survey of the mathematical foundations of MACBETH. Reference is also made to
real-world applications and an extensive bibliography, spanning back to the early
1990’s, is provided.
Keywords:
MACBETH, questioning procedure, qualitative judgements, judgmental inconsistency, cardinal value measurement, interaction.
V
NON-CLASSICAL MCDA
APPROACHES
Chapter 11
DEALING WITH UNCERTAINTIES
IN MCDA
Theodor J Stewart
Department of Statistical Sciences
University of Cape Town
Rondebosch 7701
South Africa
tjstew@stats.uct.ac.za
Abstract
Many MCDA models are based on essentially deterministic evaluations of the
consequences of each action in terms of each criterion, possibly subjecting final
results and recommendations to a degree of sensitivity analysis. In many situations, such an approach may be justified when the primary source of complexity
in decision making relates to the multicriteria nature of the problem rather than
to the stochastic nature of individual consequences. Nevertheless, situations do
arise, especially in strategic planning problems, when risks and uncertainties are
as critical as the issue of conflicting management goals. In such situations, more
formal modelling of these uncertainties become necessary.
In this paper, we start by reviewing the meaning and origin of risk and uncertainty. We recognize both internal uncertainties (related to decision maker values
and judgements) and external uncertainties (related to imperfect knowledge concerning consequences of action), but for this paper focus on the latter. Four broad
approaches to dealing with external uncertainties are discussed. These are multiattribute utility theory and some extensions; stochastic dominance concepts,
primarily in the context of pairwise comparisons of alternatives; the use of surrogate risk measures as additional decision criteria; and the integration of MCDA
and scenario planning. To a large extent, the concepts carry through to all schools
of MCDA. A number of potential areas for research are identified, while some
suggestions for practice are included in the final section.
Keywords:
Multicriteria analysis, multiobjective programming, uncertainty, risk, utility theory.
Chapter 12
CHOICE, RANKING AND SORTING
IN FUZZY MULTIPLE CRITERIA
DECISION AID
Patrick Meyer, Marc Roubens
Department of Mathematics
University of Liège
Grande Traverse, 12
4000 Liège
Belgium
patrick.meyer@internet.lu, m.roubens@ulg.ac.be
Abstract
In this chapter we survey several approaches to derive a recommendation from
some preference models for multiple criteria decision aid. Depending on the
specificities of the decision problem, the recommendation can be a selection of
the best alternatives, a ranking of these alternatives or a sorting. We detail a sorting
procedure for the assignment of alternatives to graded classes when the available
information is given by interacting points of view and a subset of prototypic
alternatives whose assignment is given beforehand. A software dedicated to that
approach (Tomaso) is briefly presented. Finally we define the concepts of good
and bad choices based on dominant and absorbant kernels in the valued digraph
that corresponds to an ordinal valued outranking relation.
Keywords:
Aggregation with fuzzy environment, fuzzy choice, ordinal ordered sorting, choquet integral, Tomaso.
Chapter 13
DECISION RULE APPROACH
Salvatore Greco, Benedetto Matarazzo
Faculty of Economics, University of Catania
Corso Italia 55, 95129 Catania
Italy
{salgreco,matarazzo}@unict.it
Roman Słowiński
Institute of Computing Science, Poznań University of Technology, 60-965 Poznań and
Systems Research Institute, Polish Academy of Sciences, 01-447 Warsaw
Poland
Roman.Slowinski@cs.put.poznan.pl
Abstract
We present the methodology of Multiple-Criteria Decision Aiding (MCDA) based
on preference modelling in terms of “if. . . , then . . . ” decision rules. The basic
assumption of the decision rule approach is that the decision maker (DM) accepts
to give preferential information in terms of examples of decisions and looks for
simple rules justifying her decisions. An important advantage of this approach
is the possibility of handling inconsistencies in the preferential information, resulting from hesitations of the DM. The proposed methodology is based on the
elementary, natural and rational principle of dominance. It says that if action x
is at least as good as action y on each criterion from a considered family, then
x is also comprehensively at least as good as y. The set of decision rules constituting the preference model is induced from the preferential information using a
knowledge discovery technique properly modified, so as to handle the dominance
principle. The mathematical basis of the decision rule approach to MCDA is the
Dominance-based Rough Set Approach (DRSA) developed by the authors. We
present some basic applications of this approach, along with didactic examples
whose aim is to show in an easy way how DRSA can be used in various contexts
of MCDA.
Keywords:
Dominance, rough sets, decision rules, multiple criteria classification, choice and
ranking.
Chapter 14
FUZZY MEASURES AND INTEGRALS IN MCDA
Michel Grabisch
Université Paris I – Panthéon-Sorbonne
LIP6, 8 rue du Capitaine Scott
75015 Paris, France
michel.grabisch@lip6.fr
Christophe Labreuche
Thales Research & Technology
Domaine de Corbeville
91404 Orsay Cedex, France
christophe.labreuche@thalesgroup.com
Abstract
This chapter aims at a unified presentation of various methods of MCDA based
on fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet and
Sugeno integral. A first section sets the position of the problem of multicriteria
decision making, and describes the various possible scales of measurement (cardinal unipolar and bipolar, and ordinal). Then a whole section is devoted to each
case in detail: after introducing necessary concepts, the methodology is described,
and the problem of the practical identification of fuzzy measures is given. The
important concept of interaction between criteria, central in this chapter, is explained in detail. It is shown how it leads to k-additive fuzzy measures. The case
of bipolar scales leads to the general model based on bi-capacities, encompassing
usual models based on capacities. A general definition of interaction for bipolar
scales is introduced. The case of ordinal scales leads to the use of Sugeno integral, and its symmetrized version when one considers symmetric ordinal scales.
A practical methodology for the identification of fuzzy measures in this context
is given.
Keywords:
Choquet integral, fuzzy measure, interaction, bi-capacities.
Chapter 15
VERBAL DECISION ANALYSIS
Helen Moshkovich, Alexander Mechitov
College of Business
The University of Montevallo
Montevallo, AL 35115
USA
MoshHM,Mechitov@montevallo.edu
David Olson
Department of Management
University of Nebraska, Lincoln
Lincoln, NE 68588-0491
USA
dolson3@unl.edu
Abstract
Verbal Decision Analysis is a new methodological approach for the construction
of decisions methods with multiple criteria. The approach is based on cognitive
psychology, applied mathematics, and computer science. Problems of eliciting
exact quantitative estimations from the decision makers may be overcome by
using preferential information from the decision makers in the ordinal form (e.g.,
“more preferable”, “less preferable”,...). This type of judgments is known to be
much more stable and consistent. Ways of how to obtain and use ordinal judgments for multicriteria alternatives’ evaluation are discussed. Decision methods
ZAPROS, and ORCLASS based on the approach are briefly described.
Keywords:
Decision analysis, multiple criteria, ordinal judgments, preference elicitation,
ZAPROS, ORCLASS.
VI
MULTIOBJECTIVE MATHEMATICAL
PROGRAMMING
Chapter 16
INTERACTIVE METHODS
Pekka Korhonen
Helsinki School of Economics
Department of Economics and Management Science
Runeberginkatu 14–16, 00100 Helsinki
Finland
Pekka.Korhonen@hkkk.fi
Abstract
We provide an introduction to the use of interactive methods in multiple objective
programming. We focus on discussing the principles to implement those methods.
Our purpose is not to review existing procedures, but some examples are picked
to illustrate the main ideas behind those procedures. Furthermore, we discuss two
available software systems developed to implement interactive methods.
Keywords:
Decision making, multiple objective, multiple criteria, interactive, behavioral.
Chapter 17
MULTIOBJECTIVE PROGRAMMING
Matthias Ehrgott
Department of Engineering Science
The University of Auckland
Private Bag 92019, Auckland
New Zealand
m.ehrgott@auckland.ac.nz, wmalgor@clemson.edu
Margaret M. Wiecek
Department of Mathematical Sciences
Clemson University
Clemson, SC 29634-0975
USA
wmalgor@clemson.edu
Abstract
We present our view of the state of the art in multiobjective programming. After
an introduction we formulate the multiobjective program (MOP) and define the
most important solution concepts. We then summarize the properties of efficient
and nondominated sets. In Section 4 optimality conditions are reviewed. The main
part of the chapter consists of Sections 5 and 6 that deal with solution techniques
for MOPs and approximation of efficient and nondominated sets. In Section 7 we
discuss specially-structured problems including linear and discrete MOPs as well
as selected nonlinear MOPs. In Section 8 we present our perspective on future
research directions.
Keywords:
Multiobjective programming, efficient solution, nondominated solution, scalarization, approximation.
Chapter 18
MULTIPLE OBJECTIVE LINEAR
PROGRAMMING WITH FUZZY
COEFFICIENTS
Masahiro Inuiguchi
Department of Systems Innovation
Graduate School of Engineering Science, Osaka University
1-3, Machikaneyama, Toyonaka, Osaka 560-8531
Japan
inuiguti@sys.es.osaka-u.ac.jp
Abstract
In this paper, we treat multiple objective programming problems with fuzzy coefficients. We introduce the approaches based on possibility and necessity measures. Our aim in this paper is to describe the treatments of the problem rather
than the solution method for the problem. We describe the modality constrained
programming approach, the modality goal programming approach and modal
efficiency approach. In the first approach, we discuss treatments of fuzziness in
the programming problems. The extensions of a fuzzy relation to the relation
between fuzzy numbers are developed in order to treat generalized constraints.
In the second approach, we show that two kinds of differences between a fuzzy
objective function value and a fuzzy target are conceivable under the fuzziness.
We describe the distinction of their applications in programming problems. In the
third approach, we describe how the efficiency can be extended to multiple objective programming problems with fuzzy coefficients. Necessary and sufficient
conditions 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, possibility
measure, necessity measure.
Chapter 19
MCDM LOCATION PROBLEMS
Stefan Nickel
Fakultät für Rechts- und Wirtschaftswissenschaften, Universität des Saarlands
66041 Saarbrücken, Germany
and
Fraunhofer Insitute for Industrial Mathematics (ITWM)
67663 Kaiserslautern, Germany
s.nickel@wiwi.uni-sb.de
Justo Puerto
Facultad de Matemáticas
Universidad de Sevilla
41012 Seville, Spain
puerto@us.es
Antonio M. Rodrı́guez-Chı́a
Facultad de Ciencias
Universidad de Cádiz
11510 Puerto Real (Cádiz), Spain
antonio.rodriguezchia@uca.es
Abstract
In this chapter, we provide a broad overview of the most representative multicriteria location problems as well as of the most relevant achievements in this
field, indicating the relationship between them whenever possible. We consider a
large number of references which have been classified in three sections depending
on the type of decision space where the analyzed models are stated. Therefore,
we distinguish between continuous, network, and discrete multicriteria location
problems.
Keywords:
Locational Analysis, multicriteria location problems, point-objective location
problems, multiobjective location problems.
VII
APPLICATIONS
Chapter 20
MULTICRITERIA DECISION AID/
ANALYSIS IN FINANCE
Jaap Spronk
Erasmus University Rotterdam, Department of Finance and Investment
P.O.Box 1738, 3000 DR Rotterdam, The Netherlands
spronk@few.eur.nl
Ralph E. Steuer
University of Georgia, Department of Banking and Finance, Terry College of Business, Athens,
Georgia 30602-6253
USA
rsteuer@uga.edu
Constantin Zopounidis
Technical University of Crete, Department of Production Engineering and Management,
Financial Engineering Laboratory, University Campus, 73100 Chania, Greece
kostas@dpem.tuc.gr
Abstract
Over the past decades the complexity of financial decisions has increased rapidly,
thus highlighting the importance of developing and implementing sophisticated
and efficient quantitative analysis techniques for supporting and aiding financial
decision making. Multicriteria decision aid (MCDA), an advanced branch of operations research, provides financial decision makers and analysts with a wide
range of methodologies well-suited for the complexity of modern financial decision making. The aim of this chapter is to provide an in-depth presentation of the
contributions 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 Diakoulaki
National Technical University of Athens
Department of Chemical Engineering
Labortaory of Industrial and Energy Economics
Zografou Campus, 15780 Athens
Greece
diak@chemeng.ntua.gr
Carlos Henggeler Antunes, António Gomes Martins
University of Coimbra and INESC Coimbra
Department of Electrical Engineering and Computers
Polo II, Pinhal de Marrocos, 3030 Coimbra
Portugal
cantunes,amartins@inescc.pt
Abstract
The growing environmental awareness and the apparent conflict between economic and environmental objectives was the main impetus that pushed energy
planners during the early eighties towards the use of MCDA methods. Thereafter,
the rapid changes and the increasing complexity of the energy market gave rise to
further methodological developments. Although the energy market restructuring
and ongoing liberalization seemed to restrict the purpose for centralized energy
decisions, they added new dimensions in energy planning. Increasing competition
along with the prerequisite for sustainability have broadened the energy application field by bringing out new challenges for the development of integrated
multicriteria and multi-stakeholders approaches also taking uncertainty into consideration. This paper aims at illustrating the evolution of MCDA approaches, in
the context of the emerging problems faced by energy planners and other stakeholders involved in energy-related decision situations, one of the most active and
exciting areas of application of MCDA models and methods.
Keywords:
Multicriteria, multiobjective, energy planning, electricity.
Chapter 22
MULTICRITERIA ANALYSIS IN
TELECOMMUNICATION NETWORK
PLANNING AND DESIGN –
PROBLEMS AND ISSUES
João Clı́maco
Faculty of Economics
The University of Coimbra and INESC – Coimbra
Portugal
jclimaco@inescc.pt
José Craveirinha
Department of Electrical Engineering Sience and Computers
Faculty of Science and Technology
The University of Coimbra and INESC – Coimbra
Portugal
jcrav@deec.uc.pt
Abstract
The interaction between a complex socio-economic environment and the extremely fast pace of development of new telecommunication technologies and
services justifies the interest in using multicriteria evaluation in decision making
processes associated with several phases of network planning and design. Based
on an overview of current and foreseen evolutions in telecommunication network
technologies and services we begin by identifying and discussing challenges and
issues concerning the use of multicriteria analysis (M.A.) in telecommunication
network planning and design problems. Next we present a review of contributions
in these areas, with particular emphasis on network modernisation planning and
routing problems. We will also outline an agenda of current and future research
trends and issues in this application area of multicriteria modelling.
Keywords:
Telecommunication planning and design, multicriteria analysis.
Chapter 23
MULTIPLE CRITERIA DECISION
ANALYSIS AND SUSTAINABLE
DEVELOPMENT
Giuseppe Munda
Universitat Autonoma de Barcelona
Department of Economics and Economic History, Edifici B
and
Institute for Environmental Sciences and Technologies
08193, Bellaterra, Barcelona, Spain
giuseppe.munda@uab.es
Abstract
Sustainable development is a multidimensional concept, including socio-economic, ecological, technical and ethical perspectives. In making sustainability
policies operational, basic questions to be answered are sustainability of what
and whom? As a consequence, sustainability issues are characterised by a high
degree of conflict. The main objective of this Chapter is to show that multiplecriteria decision analysis is an adequate approach for dealing with sustainability
conflicts at both micro and macro levels of analysis. To achieve this objective,
lessons, learned from both theoretical arguments and empirical experience, are
reviewed. Guidelines of “good practice” are suggested too.
Keywords:
Sustainable development, economics, complex systems, incommensurability, social choice, social multi-criteria evaluation.
VIII
MCDM SOFTWARE
Chapter 24
MULTIPLE CRITERIA DECISION
SUPPORT SOFTWARE
H. Roland Weistroffer, Charles H. Smith, Subhash C. Narula
School of Business
Virginia Commonwealth University
Box 844000, Richmond, Virginia 23284-4000
USA
{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 in
the literature to solve multiple criteria decision-making problems, and there is an
abundance of software that implements these approaches. Much of the software
is still quasi-experimental, developed by academic researchers to test specific
algorithms or to solve a specific problem on an ad hoc basis.
Keywords:
DSS, MCDSS, software packages.
Contributing Authors
Carlos A. Bana e Costa is Full Professor of Decision and Information at the
Technical University of Lisbon “Instituto Superior Técnico” (IST), Department
of Engineering and Management, Centennial Professor of Operational Research
at the London School of Economics and Political Science, and president of the
Center of Management Studies of IST. His primary interests are in the fields
of management and decision sciences, namely multicriteria decision analysis
and decision conferencing, and he has published widely in these areas. He is
co-author of the MACBETH approach. He is also a decision-aid consultant of
many private and public organizations in Portugal, Brazil and other countries,
following the socio-technical facilitation perspective shared by the members of
the International Decision Conferencing Forum.
Denis Bouyssou holds a doctorate in Operations Research. He is presently
senior researcher at the Centre National de Recherche Scientifique (CNRS).
His research interests include decision theory, social choice theory, and multiple
criteria decision making.
Jean-Pierre Brans received his Ph.D. in Mathematics at the ULB/VUB University of Brussels (1966). He has been Professor in these Universities since 1964
and dean of the VUB-Solvay Business school (1975-78). He has held visiting
professorships at the universities of Kinshasa, Constantine, Aix-en-Provence,
ENSTA (Paris), AIT (Bangkok), KUL (Leuven), and Lulea (Sweden). He has
taught courses taught on statistical analysis, OR, MCDA, mathematical programming, and system dynamics. Dr. Brans has been president of the Belgian
OR 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 of
the first one in Brussels (1975), initiator of the EURO Summer Institutes and
organisor of the two first ones, initiator of the MINI EURO Conferences and
organisor of the 1st, the 7th and the 12th ones. He has presented over 100 invited lectures all over the world and published over 100 papers in international
scientific journals. He is the initiator of the PROMETHEE-GAIA Methodology
and has written one book on this subject with B. Mareschal. He received the
EURO Gold Medal 1994 and Doctor Honoris Causa from Copenhagen (2000)
and Fribourg (2002). He has been elected Professor of the Year by the students
of the VUB Brussels (2002).
João C. N. Clı́maco is Full Professor at the School of Economics, University of
Coimbra, and researcher at the Systems Engineering and Computers Institute
INESC Coimbra. Currently he is president of the Scientific Committee of INESC Coimbra. He obtained an M.Sc. in Control Systems from Imperial College,
University of London, and the Diploma of Membership of the Imperial College
of Science and Technology (1978), a Ph.D. (1982) in Electrical Engineering
from the University of Coimbra, and the Aggregation (1989) from the University of Coimbra. His current interests of research are in multicriteria decision
making, group decision and negotiation, decision support systems, and telecommunication planning, design, and management. He is author (or co-author) of
more than seventy papers published in refereed international scientific journals
and about thirty papers (or chapters) published in thematic scientific books. He
belongs to the editorial board of the “Group Decision and Negotiation Journal”
and of “Investigação Operacional”. He was vice-president of APDIO and of
ALIO. Currently he belongs to the international executive committee of the
International Society on MCDM.
José Manuel F. Craveirinha is Full Professor in Telecommunications at the
Department of Electrical Engineering Science of the Faculty of Sciences and
Technology of the University of Coimbra, Portugal, since 1997. He obtained
the following degrees: Undergraduate Diploma in Electrical Engineering Science (E.E.S.) – Telecommunications & Electronics at IST, Lisbon Technical
University (1975); M.Sc. (1981) and Ph.D. (1984) in E.E.S. at the University
of Essex (UK) and Doctor of Science in E.E.S – Telecommunications at the
University of Coimbra (1996). Previous positions were: Associate Professor,
Assistant Professor, and Assistant Lecturer at FCUT, Coimbra University, and
telecommunications R&D engineer at CET-Portugal Telecom. He has coordinated a research group in teletraffic theory & network planning at INESCCoimbra 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 publications
in modelling of teletraffic, reliability analysis and planning of telecommunication networks. His main present interests are in traffic modelling and routing in
Internet and multiple objective routing in multiservice networks.
Jean-Marie De Corte is Assistant Professor at the University of Mons-Hainaut
and member of the Warocqué Research Center. He received his Ph.D. in Mathematics in 2002. His current research interest is in the field of multiple criteria
decision aid, more specifically on development of algorithms for “minimal solving” of inconsistencies and for several robustness analyses in the framework of
the MACBETH approach. He is also the designer of the MACBETH software.
His work has been published in international journals such as Omega.
Danae Diakoulaki received her Ph.D. degree in Engineering (Operations Management) at the National Technical University of Athens (NTUA) in 1988. She
is currently an Associate Professor at the Chemical Engineering Department
of NTUA and heads the area of energy and environmental management at the
Laboratory of Industrial and Energy Economics. Her research activities concern mainly the use of MCDA methods in energy and environmental planning
as well as the exploitation of energy externalities in energy policy making. She
has participated in several national and European Commission research projects
and published numerous articles in refereed international journals.
James S. Dyer occupies the Fondren Centennial Chair in Business in the College of Business Administration, University of Texas at Austin. Dr. Dyer’s
research and teaching interests include risk management and capital budgeting,
and he has published extensively on these subjects in various journals, including Management Science and Operations Research. He is the former Chair of
the Decision Analysis Society of the Operations Research Society of America
(now INFORMS). He is the Area Editor for the field of decision analysis for
the journal Operations Research. In 2002 he received the Ramsey Award for
outstanding career achievements from the Decision Analysis Society. Dr. Dyer
has consulted with a number of companies regarding the application of decision 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 Department of Engineering Science, The University of Auckland, New Zealand.
He obtained his Diploma, Ph.D. and Dr. habil. degrees in Mathematics from the
University of Kaiserslautern, Germany, in 1992, 1997, and 2001, respectively.
From 1997 to 2000 he was Assistant Professor at the University of Kaiserslautern. He has been invited professor at Université de Valenciennes, Copenhagen University and Mercator Visiting Profesor at the University of Kaiserslautern. Dr. Ehrgott is the author or editor of six books, and has written more
than 30 refereed articles on multiobjective and combinatorial optimization that
have been published in international journals or proceedings volumes. He is a
member of the international executive committee of the MCDM Society, member of the council of the Operations Research Society of New Zealand, editor
of OR Spectrum and associate editor of Asia Pacific Journal of Operational
Research. He received the Wiley Prize for best applied paper in MCDA at the
International Conference on MCDM in 2002.
José Figueira is an Associate Professor at the School of Economics of the
University of Coimbra, Portugal, and researcher at INESC-Coimbra and LAMSADE, Paris-Dauphine University, France. He obtained his Ph.D. (1996) in
Operations Research from the University of Paris-Dauphine. He has been invited researcher London School of Economics, Rutgers University, Auckland
University, University of Catania, University of Talca, Free University of Brussels, Clemson University, University of Georgia, University of Valenciennes
and Carnegie Mellon University. His current research interests are in decision
analysis, integer programming, network flows and multiple criteria decision
aiding. His works have been published in international journals such as European Journal of Operational Research, Computers & Operations Research,
Journal of the Operational Research Society, Journal of Mathematical Modelling and Algorithms, European Business Review. He is the current editor of
the newsletter of the European Working Group on MCDA.
Michel Grabisch received his Graduate Engineer Diploma in 1979 and his
Ph.D. degree in signal processing in 1982, both from Ecole Nationale des
Ingénieurs Electriciens de Grenoble (ENSIEG). From 1984 to 1993 he worked
at Thomson-Sintra Activités Sous-Marines and from 1993 to 2000 at Central
Research Laboratory of Thomson-CSF. He spent two years from 1989 to 1991 at
Tokyo Institute of Technology, Japan, and participated in the LIFE (Laboratory
for International Fuzzy Engineering Research) project. From 2000 to 2002 he
was Associate Professor at Université Pierre et Marie Curie, Paris. Since 2002,
he is Professor of Computer Science at Université Panthéon-Sorbonne, Paris.
He is area editor of IEEE Transactions on Fuzzy Systems, Fuzzy Optimization
and Decision, and belongs to the editorial board of Fuzzy Sets and Systems.
His interests are fuzzy measure and capacity theory, decision making, fuzzy
sets and possibility theory as well as discrete mathematics.
Salvatore Greco is Full Professor at the Faculty of Economics of Catania University since 2001. His main research interests are in the field of multicriteria
decision aid, in the application of the rough set approach to decision analysis, in
the axiomatic foundation of multicriteria methodology and in the fuzzy integral
approach to MCDA. In these fields he cooperates with many researchers of different countries. He received the Best Theoretical Paper Award by the Decision
Sciences Institute (Athens, 1999). Together with Benedetto Matarazzo, he organized the VIIth International Summer School on MCDA (Catania, 2000). He
is author of many articles published in international journals and specialized
books. He has been invited professor at Poznan Technical University and at
the University of Paris Dauphine. He has been invited speaker in international
conferences. He is referee of the most relevant journals in the field of decision
analysis.
Evangelos Grigoroudis received his M.Sc. and Ph.D. degrees in Decision Sciences and Operations Research from the Technical University of Crete (Greece)
in 1996 and 1999, respectively. He is Lecturer on Management of Quality Processes at the Department of Production Engineering and Management, Technical University of Crete. During 1999-2002 he was Adjunct Professor at the
Department of Political Sciences, University of Crete. He is member of the In-
ternational Society on Multiple Criteria Decision Making, the EURO Working
Groups on Multicriteria Aid for Decisions and Financial Modelling, the American Society for Quality, the Hellenic Operational Research Society, and the
Hellenic Institute of Production and Operations Management. He is the author
of a book on the measurement of service quality and a large number of research
reports and papers in scientific journals and conference proceedings. His research interests include operational research, multicriteria decision analysis,
and management and control of quality.
Carlos Henggeler-Antunes received his Ph.D. degree in Electrical Engineering (Optimization and Systems Theory) from the University of Coimbra in
1992. Presently, he is an Associate Professor at the Department of Electrical Engineering and Computers, University of Coimbra, and director of the
R&D Institute INESC Coimbra. His research interests include multiple objective 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 Decision Support Models” (2004). His most recent works have been published
in 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 Osaka
Prefecture University in 1991. He worked as a Research Associate at Osaka
Prefecture University and an Associate Professor at Hiroshima University and
later at Osaka University. Presently, he is a Full Professor at the Department
of Systems Innovation, Graduate School of Engineering Science, Osaka University. He is an editor of two books and has written more than 100 refereed
journal and proceedings articles. He is an area editor of Fuzzy Optimization and
Decision Making and a member of editorial committee of Fuzzy Sets and Systems. He received the Best Paper Award by Japan Society for Fuzzy Theory and
Systems in 1997. He is interested in possibility theory, fuzzy mathematical programming, rough sets, Dempster-Shafer’s theory of evidence, and approximate
reasoning.
Pekka J. Korhonen has been Professor of Statistics at the Helsinki School of
Economics, Finland since 1988. He received a Ph.D. in Applied Mathematics
from the University of Helsinki. His research interests are MCDM, productivity/efficiency analysis, and computational statistics. Over 60 refereed journal
articles have appeared in journals like Journal of the Operational Research Society, Management Science, European Journal of Operational Research, Naval
Research Logistics, Operations Research, etc. He is member of the editorial
boards of the journals Theory and Decision, Group Decision and Negotiation,
and Journal of Productivity Analysis. He was the President of International
Society on MCDM during 1996-2000, and is currently the member of the international executive committee. In the ISI Web of Science, there are about 750
citations to his scientific work. The George Cantor-Prize was awarded to him
by the International Society on MCDM in 1994. He is an honorary chairman
of the Finnish Operations Research Society.
Christophe Labreuche received a Graduate Engineer Diploma from Ecole
Centrale de Lyon and a Master in Numerical Analysis, both in 1993. He received a Ph.D. degree in Applied Mathematics in 1997 from Université de Paris
IX Dauphine. His first publications were in the areas of partial differential equations and more specifically scattering and inverse scattering. He was working
at University of Delaware (USA) during the 1995/1996 academic year. From
1997 to 1998 he was working at the research lab of Thales in numerical analysis. Then he joined the advanced software department to work on multicriteria
decision aid. On top of conducting industrial applications on MCDA and developing a software on MCDA, he works in the areas of fuzzy logic as well
as fuzzy measure theory, fuzzy integrals and their application in MCDA. His
field 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 Free
University of Brussels (1989). He has been Professor at the ULB since 1993.
He has been part-time professor at the UMH (Université de Mons-Hainaut, Belgium), HEC-Liège (Belgium), EDHEC (Lille, France) and Université de Lille-3
(France) as well as visiting professor at Ecole des Mines de Nancy (France). He
taught courses in statistics, operations research, decision aid, computer science
and mathematics. He is chairman of IDM (Innovative Decision for Management – www.idm-belgium.com) and iitiator of the QED multicriteria decision
aid web project (www.qed-solutions.com).
Jean-Marc Martel received B.Sc. and M.Sc. degrees in Mathematics at Laval
University in 1963 and 1965 and a Ph.D. degree in Applied Economics (Quantitative Methods) at Leuven University in 1975. Since 1965 he has been working
at the Faculty of Business Adminstration of Laval University, from 1965 to 1976
as Associate Professor and from 1976 to 2000 as Full Professor in the Department of Operations and Decision Systems. Since 2001 he is Emeritus Professor
at Laval University and since 2002 member of Royal Society of Canada He has
been invited professor at several universities and research centers. He has been
organiser of FRANCORO III (Québec, 2001), MOPGP’98, the 48th meeting of
the European Working Group on MCDA and the Fourth International Summer
School on MCDA (Québec, 1991). His main research interests are multi-criteria
decision aid under uncertainty, Bayesian analysis, information value, group decision and participative processes.
António Gomes Martins received his Ph.D. degree in Electrical Engineering
from the University of Coimbra in 1985. He is presently Full Professor at the
Department of Electrical Engineering at this University, where he is responsible for a R&D group on efficient use of energy resources. Since 1999 he is
leading the Institute of Systems Engineering and Computers of Coimbra. His
current research interests are energy planning, load modelling, energy market
transformation.
Benedetto Matarazzo is Full Professor at the Faculty of Economics of Catania
University. He has been committee member of scientific societies of operational
research. He has been organiser, member of the programme committee, and
invited speaker in many scientific conferences. He is member of the editorial
boards of the European Journal of Operational Research, Journal of MultiCriteria 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 invited
professor at and co-operates with several European universities. He received
the Best Theoretical Paper Award by the Decision Sciences Institute (Athens,
1999). He is member of the Organising Committee of the International Summer
School 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 Decision
Support Systems at the Department of Production Engineering and Management, Technical University of Crete (Greece). He received his B.A. in Physics
from Aristotle University of Thessaloniki (Greece) and his Ph.D. in Intelligence
Decision Support Systems from Technical University of Crete (Greece) in 1980
and 1995, respectively. He is the author or co-author of five books and over 35
articles in international scientific journals and books. He teaches the following
courses: Decision Support Systems, Knowledge Engineering, Electronic Commerce, 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, artificial
intelligent and multi-agent systems, e-business, e-marketing, multicriteria decision analysis, and group decision support systems.
Alexander Mechitov received his Ph.D. degree in Management Information
Systems from the Institute of Systems Analysis of the Russian Academy of
Sciences (Moscow) in 1988. He is presently a Professor of MIS in the Michael
E. Stephens College of Business, University of Montevallo. He has co-authored
two books and has published over 40 refereed journal articles on multicriteria
decision theory and applications. His research interests include multicriteria
decision making, behavioral decision making, risk analysis, and expert systems.
Patrick Meyer is currently working as a Researcher at the University of Luxembourg. He received a Master in Mathematics in 2003 at the Faculté Polytechnique of Mons in Belgium. At present, he is working on his Ph.D. thesis. His
main research interests are multiple criteria decision aiding and data mining. He
has worked on projects involving financial portfolio management (CELOFA)
and analysis of large amounts of financial data from stocks (MIKADO). He has
contributed to the development of the TOMASO method for ordinal multiple
criteria sorting and has implemented the tool in a software package.
Helen Moshkovich received her Ph.D. degree in Management Information
Systems/Management Science from the Institute of Systems Analysis of the
Russian Academy of Sciences (Moscow) in 1984. She is presently a Professor
of MIS/Quantitative Methods in the Michael E. Stephens College of Business,
University of Montevallo. Before that, she was with the Russian Academy of
Sciences for 22 years. She has co-authored four books and has published over 50
refereed journal articles on multicriteria decision theory and applications. Her
research interests include multicriteria decision making, behavioral decision
making, decision support systems, and data mining.
Vincent Mousseau is Assistant Professor at the University of Paris Dauphine
and member of the LAMSADE research laboratory. He received his Ph.D. in
Computer Science/Operations Research in 1993. His reseach interest lies in
the field of multiple criteria decision Aid and more specifically on preference
modeling and elicitation, experimental analysis of decision behavior, and implementation of multiple criteria methodologies in real world decision problems.
His work has been published in international journals such as EJOR, Journal of
Global Optimization, and JMCDA.
Giuseppe Munda got a “Laurea” degree in Economics from the University of
Catania, Italy (1988). He made his Ph.D. studies with the Free University of Amsterdam, where he got a Ph.D. in Economics and Econometrics (1993). At the
moment he is tenured Professor of Economics of Natural Resources and MultiCriteria Decision Analysis at Universitat Autonoma de Barcelona. Previously
he has worked at the Joint Research Centre of the European Commission (Ispra
site). He has been visiting lecturer at Université Panthéon-Sorbonne, University
of Naples Federico II, Centre d’Economie et d’Ethique pour l’ Environnement
et le Développement (C3ED), University of Pisa and various universities and
research centres in South-America. He has also been consultant for the InterAmerican Development Bank, the European Commission, DG XII, and for
the European Environment Agency. He has published one book and about 40
articles and book chapters.
Subhash C. Narula is a Professor of Management Science and Statistics in
the Department of Management, School of Business, Virginia Commonwealth
University, Richmond, Virginia, USA. He received his Ph.D. in Industrial and
Management Engineering from the University of Iowa. Prior to his current position, he held faculty positions at the State University of New York at Buffalo,
Buffalo, New York, Rensselaer Polytechnic Institute, Troy, New York. During
1992-93, he was Chair of Optimization at the Linkoping Institute of Technology, Linkoping, Sweden. He is an elected Fellow of the American Statistical
Association and the American Society for Quality. He is a recipient of the Constantine Porphyrogenetus International Association Award and was awarded
the Distinguished Scholar Award of VCU in 2000. He has published papers in
the leading journals of statistics, operations research and management science,
contributed papers in national and international proceedings, and chapters to
books.
Stefan Nickel is Full Professor (Chair) of Operations Research and Logistics
at the Saarland University. He is also head of the optimization department of
the Fraunhofer Institute for Industrial Mathematics. Stefan Nickel received his
Diploma, his Ph.D. and his Habilitation in Mathematics at the University of
Kaiserslautern, in 1992, 1995, and 1999. From 1992 he worked with the Department of Mathematics, University of Kaiserslautern as a Research Associate.
From 1995 to 1999, he was an Assistant Professor at the Department of Mathematics 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 member
of the editorial board of Computers & Operations Research.
David L. Olson is the James and H.K. Stuart Professor of MIS at the University of Nebraska. He has published research in over 60 refereed journal articles,
primarily on the topic of multiple objective decision-making. He has authored
three books, including Decision Aids for Selection Problems, and coauthored
six others. He is a member of the Association for Information Systems, the
Decision Sciences Institute, the Institute for Operations Research and Management Sciences, and the Multiple Criteria Decision Making Society. He was with
Texas A&M University from 1981 through 2001 where he held a Lowry Mays
endowed professorship.
Meltem Öztürk received her B.E. degree in Industrial Engineering at the University of Galatasaray (Turkey) in 2000 and her DEA at the Université Paris
Dauphine in 2001. Since 2001 she is a Research Assistant and a Ph.D. Candidate in Computer Sciences at LAMSADE, Université Paris Dauphine. Her
research interest lies in the field of multiple criteria decision aid, non classical
logics (fuzzy set theory, Belnap logics etc.), and more specifically their use in
preference modeling and aggregation methods.
Marc Pirlot is Professor of Mathematics and Operations Research at the Institute of Engineering, Mons, Belgium. He obtained his Ph.D. in Mathematics
from the University of Mons in 1981. His main research interests are multicriteria decision analysis and metaheuristics for combinatorial optimizaztion. He
is the co-author or editor of four books and of more than 50 refereed papers in
international journals or conference proceedings. He has been president of the
Operations Research Society of Belgium and is currently associate editor of the
Journal of Multi-Criteria Decision Analysis and of Mathématiques et Sciences
Humaines.
Justo Puerto is Full Professor (Chair) of Statistics and Operations Research at
the University of Seville, where he has taught different subjects in the undergraduate and graduate programs of Mathematics, Statistics, Biology, Computer
Science, and Chemistry among others. Besides, he has been visiting professor at several universities: NorthWestern University (USA), Kaiserslautern and
Chemnitz (Germany), Bologna (Italy), Hirosaki (Japan), etc. Justo Puerto received his Ph.D. in Mathematics at the University of Seville in 1990. He is interested in location theory, game theory, combinatorial and classical optimization,
computational geometry and mathematical education. He has published over 60
papers in professional journals. Justo Puerto has a large experience in the coordination of R&D projects and currently is associate editor of TOP, the Spanish
journal of Operations Research.
Antonio Rodríguez-Chı́a received his Ph.D. degree in Mathematics (Statistics
and Operations Research) from the Faculty of Mathematics at Sevilla University
in 1998. From 1994 to 1998, he worked in Department of Mathematics at Cadiz
University as a Research Associate. Since 1998 he is Full Professor of the
Department of Statistics and Operations Research in the Sciences Faculty at
Cadiz University. He is interested in location theory and game theory.
Marc Roubens has been Professor of Statistics and Operations Research at the
Faculté Polytechnique de Mons from 1971 to 1989 and is currently Scientific
Advisor of that institution. He has been with the Department of Mathematics,
University of Liège, where he was Professor from 1986 to 2002. His primary
interests have been in several areas of fuzzy sets theory (preference modelling,
clustering and control), operations research (multiple criteria decision aid) and
statistics (time series analysis , data mining) He is co-author of a book with
Philippe Vincke on preference modeling and another book with Janos Fodor
on fuzzy preference modelling and multiple criteria decision support. Professor
Roubens has been on the editorial boards of two international journals (Fuzzy
Sets and Systems, European Journal of Operations Research) and is Associate
Editor of the International Journal of Approximate Reasoning. He has been
president of the Belgian Operations Research Society and president of the European Chapter of the International Fuzzy Systems Association.
Bernard Roy is Emeritus Professor at Université Paris-Dauphine. He is the
founder and, since 1999, honorary director of LAMSADE, a research group
centered on the theme of decision aiding. Since 1980, he his scientific adviser
of the Paris city transport authority. He is Graduate of the Institute of Statistics
of Paris University (1957) and Doctor dés Sciences Mathématiques of Faculty
of Paris (1961). After an extensive consulting experience at SEMA-METRA,
he joined the Université Paris-Dauphine in 1972 and created LAMSADE. In
1975 he founded the EURO Working Group “Multiple Criteria Decision Aiding” which invariably held two annual meetings since then. He is Doctor Honoris Causa from several universities. He received the EURO Gold Medal (the
highest distinction granted by EURO, the Association of European Operational
Research Societies) in 1992 and the MCDM Gold Medal granted by the International MCDM Society in 1995. He his the author of several books and
hundreds of research papers.
Thomas Saaty holds the Chair of University Professor, Katz Graduate School
of Business, University of Pittsburgh. He has a Ph.D. in Mathematics from
Yale University. Previously he was Professor at the Wharton School, University of Pennsylvania, prior to which he was involved in research at the Arms
Control and Disarmament Agency, the State Department, in Washington, on
nuclear arms reduction negotiations with the Soviets in Geneva. His current research is in decision-making, planning, conflict resolution and neural synthesis.
He developed the Analytic Hierarchy Process (AHP) and its generalization to
feedback, the Analytic Network Process (ANP) (co-developed Expert Choice
for AHP and SuperDecisions for ANP) to deal with decision-making, weapons
tradeoffs, and resource allocation. He has written more than 300 articles and
33 books on mathematics, operations research and decision-making. His latest
books are The Brain: Unraveling the Mystery of How It Works and Creative
Thinking, Problem Solving & Decision Making. He has consulted for many
corporations and governments.
Yannis Siskos received his Doctorat d’Etat (1984) in Management Science
from the University of Paris-Dauphine (France) and his DEA (1977) and Doctorat 3e Cycle (1979) in Computer Science and Operational Research from the
University Pierre et Marie Curie (France). He is presently Professor of Decision Science at the Department of Informatics, University of Piraeus. During
1984-2001 he was Professor at the Technical University of Crete and founding director of the Decision Support Systems Laboratory. He has been visiting
professor at the University of Paris-Dauphine (France), the University of AixMarseille II (France), the University of Laval (Canada), and the University of
Cyprus. He is presently President of the Hellenic Operational Research Society
and his research interests fall into the areas of multicriteria decision support
systems, service quality, and mathematical programming. He is the author of
several books and over sixty articles in international scientific journals.
Roman Slowinski is Professor and Head of the Laboratory of Intelligent Decision Support Systems within the Institute of Computing Science, Poznan
University of Technology, Poland. He received a M.Sc. in Computer Science,
Ph.D. in Operations Research, and Habilitation in Computing Science from the
Poznan University of Technology in 1974, 1977, and 1981, respectively. He
has been Professor on European Chair at the University of Paris Dauphine and
invited professor at the Swiss Federal Institute of Technology in Lausanne and
at the University of Catania. His research concerns operational research and
artificial intelligence, including multiple-criteria decision analysis, preference
modelling, knowledge-based decision support in medicine, technology and economics, project scheduling, and rough set theory approach to knowledge and
data engineering. He is laureate of the EURO Gold Medal (1991) and Doctor
Honoris Causa of Polytechnic Faculty of Mons (2000) and University of Paris
Dauphine (2001). Since 1999 he is co-editor-in-chief of the European Journal
of 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 Mathematics
from the University of Maryland in 1975. Since 1982 he has taught in the School
of Business at Virginia Commonwealth University, where he is currently Associate Professor in the Department of Management. His research publications
have been in the areas of applied decision analysis and operations management
in 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, Erasmus University, Rotterdam. He obtained a Ph.D. in Economics (Interactive
Multiple Goal Programming for Financial Planning, 1980) at Erasmus University. His main current research interests include: financial risk management,
performance evaluation, financial modelling, financial management and strategy. 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 EURO
Working Group on Financial Modelling, member of the executive committee
of the Special Interest Group on MCDM (1980-1992), president (1991-1992)
of EURO (Association of European Operational Research Societies). He has
been initiator (1983) of the First International Summer School on Multiple Criteria Decision Methods, Applications and Software. His honours include the
Gold 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 Terry
College 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 Criteria
Optimization: Theory, Computation and Application,” the ADBASE multiple
objective linear programming package, and over 85 scientific publications. He is
a co-founder of the International Society on Multiple Criteria Decision Making
and was editor of the Society’s newsletter, MCDM WorldScan, for seventeen
years. Dr. Steuer’s interests are in efficient sets and surfaces, models with multiple criteria, portfolio theory in finance, and interactive procedures in multiple
criteria optimization.
Theodor J Stewart has been Professor of Statistical Sciences at the University
of Cape Town since 1984, with main responsibility for operational research
and decision analysis. He has published widely in these areas, including a recent book co-authored with Valerie Belton of the University of Strathclyde,
on Multiple Criteria Decision Analysis. Professor Stewart has been involved
in many applications of these topics in private and public sectors, linked primarily to strategic planning and natural resources management. Recent work
has included water resources management, project prioritization problems, and
strategic bundling of assets for the electricity industry. He is on the editorial
boards of four international journals, including a period as guest editor of a
number of issues of International Transactions in Operational Research. He is
vice president (at large) of the International Federation of Operational Research
Societies, and is president elect of the International Society of Multiple Criteria
Decision Making.
Alexis Tsoukiàs is a Senior Researcher of CNRS within the LAMSADE, Université Paris Dauphine. He holds a Ph.D. in Systems and Computer Science
Engineering from Politecnico di Torino, Italy. He is author or editor of three
books and has published more than 50 papers in journals and contributed volumes on several fields including multiple criteria decision aiding, preference
modelling, formal logic, artificial intelligence etc.. He has served on different
editorial boards and at different positions to several European working groups
and OR societies. Presently he is president elect of EURO, the European association of OR societies within IFORS.
Jean-Claude Vansnick is Professor at the Warocqué Faculty of Management
of the University of Mons-Hainaut, Belgium and member of the Warocqué Research Center. He received, in 1973, his Ph.D. in Mathematics from the Free
University of Brussels and, in 1974, the Royal Academy of Belgium award (Section Mathematical Sciences). Since then, he has extended his areas of interest to
measurement theory and decision aid. His paper “Strength of Preference. Theoretical and Practical Aspects” was selected as National Contribution of Belgium
for the Tenth Triennial Conference of the International Federation of Operational Research Societies (IFORS 84). He is member of groups on multicriteria
analysis and was guest professor at several International Summer Schools on
Multicriteria Decision Aid. He is co-author of the MACBETH approach.
Philippe Vincke is Full Professor and the director of the Service de Mathématiques de la Gestion, and vice-rector of the Université Libre de Bruxelles. His research interests are preference modelling, aggregation, axiomatics of decisionaid methods and applications of Operations Research and Decision Aid (through
industrial collaborations). He was president of EURO (European Association
of Operational Research) in 2001 and 2002 and is currently vice-president of
IFORS (International Federation of Operational Research Societies). He is author or co-author of five books and about 100 papers in international journals.
H. Roland Weistroffer received his M.A. degree in Mathematics from Duke
University in 1973, and his Doctor of Science degree in applied mathematics
from the Free University Berlin in 1976. He taught computer science at the
University of Natal in Durban, South Africa, from 1978 to 1979, and was a
Chief Research Officer in operations research at the Centre for Scientific and
Industrial Research in Pretoria, South Africa, from 1980 to 1983. Since then
he has been at Virginia Commonwealth University in Richmond, Virginia. He
is currently an Associate Professor in the Information Systems Department in
the 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 Sciences
at Clemson University. She obtained a M.S. degree in Electrical Engineering
and a Ph.D. degree in Systems Engineering from the University of Mining and
Metallurgy in Krakow. Her research area includes theory, methodology, and
applications of mathematical programming with special interest in multi-criteria
optimization and decision-making. She has been the Sofia Kovalevskaia Visiting
Professor and Mercator Visiting Professor at the University of Kaiserslautern
and a visiting professor at the University of Copenhagen. She has published over
sixty research articles. In the United States, her research has been funded by
the National Automotive Research Center, the National Institute of Science and
Technology, the National Science Foundation, and the Office of Naval Research.
She is a member of the Institute for Operations Research and Management
Sciences, the Mathematical Programming Society, and the Multiple Criteria
Decision Making Society.
Constantin Zopounidis is Professor of Financial Management and Operations
Research and Chairman of the Department of Production Engineering and Management, Technical University of Crete, Greece. He holds a Doctorat D’Etat
in Management Science and a D.E.A. in Financial Management, both from the
University of Paris-IX Dauphine, France. Prof. Zopounidis’ research interests
include multiple criteria decision making, financial engineering and financial
risk management. His work has been published in such journals as Decision
Sciences, European Journal of Operational Research, Decision Support Systems, The Journal of the Operational Research Society, Expert Systems with
Applications, Global Finance Journal, International Journal of Intelligent Systems in Accounting, Finance and Management and Computational Economics.
He edited or co-edited more than 20 books on financial management and multicriteria decision aid.