Philippe Vincke

Multicriteria analysis: survey and new directions

Abstract Before the advent of multicriteria analysis, decision problems often took the form of the optimization of an objective function or a utility function. This approach has the advantage of resulting in well-defined mathematical problems but is not always representative of reality: in fact the comparison of several possible decisions is rarely made according to a single point of view and the preferences on a point of view are in many cases only modelled with difficulty by a function. The aim of this paper is to survey the different directions in which multicriteria analysis has developed: multiattribute utility theory, outranking relations, interactive methods. The methodology recently proposed by B. Roy is also presented.

Evaluation and Decision Models

1. Introduction. 2. Choosing on the basis of several opinions. 3. Building and aggregating evaluations. 4. Constructing measures. 5. Assessing competing projects. 6. Comparing on several attributes. 7. Deciding automatically. 8. Dealing with uncertainty. 9. Supporting decisions. Appendix A. Appendix B. 10. Conclusion. Bibliography. Index.

Biorder families, valued relations and preference modelling

Abstract Several compatibility conditions are studied for families of interval orders or semiorders, involving for instance step-type matrices and functional representations. Our approach uses the basic notion of biorder or Guttman scale. The results answer a question raised by Roberts, who in fact treated the particular case of nested families. They provide in a very general setting various formalizations for the notion of probabilistic consistency of a subject in a binary choice process. Other possible applications are also mentioned.

Robust solutions and methods in decision-aid

It often happens in decision-aid that the values of data used in models and of parameters used in methods are ill-determined: several scenarios are possible for the data and several values are plausible for the parameters of the methods. The role of the scientist in such situations is to provide information about the validity of the proposed solutions for different sets of acceptable values for the model and the method. This paper introduces a theoretical framework allowing to deal with such questions. Copyright

Description and analysis of some representative interactive multicriteria procedures

Interactive multicriteria procedures have met with a very great success forabout 15 years. We present here some of them which seem to be representative of the literature. Each description is followed by a detailed analysis of the method. This analysis consists of comments about the underlying approach, technical aspects and practical considerations. A final section provides general comments.

About the applicability of MCDA to some robustness problems

Coping with uncertainties or ignorance in decision problems may lead to the idea that several scenarios can occur or that several sets of data can constitute a good representation of the reality. In consequence, numerous authors have focused on the robust aspect of these problems. In such a context, one can consider that a scenario (or a particular instance of the data) permits to partially qualify the solutions, just as a criterion does. In other words, the evaluation of a specific solution for a given scenario could be perceived as the evaluation of this solution according to one particular criterion. With this in mind, the applicability of classic multicriteria concepts to the robustness framework, in the context of optimization problems, is explored. We achieve this by studying their similarities and differences. The distinguishing characteristics bring us to introduce a new problematic: the multicriteria evaluation of robustness.

A new axiomatic foundation of partial comparability

The paper presents some results obtained in searching for a new axiomatic foundation for partial comparability (PC) in the frame of non-conventional preference modeling. The basic idea is to define an extended preference structure able to represent lack of information, uncertainty, ambiguity, multidimensional and conflicting preferences, using formal logic as the basic formalism.A four-valued paraconsistent logic is therefore described in the paper as a more suitable language for the purposes of the research. The concepts of partition, general binary relations properties, fundamental relational system of preferences (f.r.s.p.), maximal f.r.s.p. and well founded f.r.s.p. are then introduced and some theorems are demonstrated in order to provide the axiomatic foundation of PC. The main result obtained is a preference structure that is a maximal well founded f.r.s.p. This preference structure facilitates a more flexible, reliable and robust preference modeling. Moreover it can be viewed as a generalization of the conventional approach, so that all the results obtained until now can be used under it.Two examples are provided at the end of the paper in order to give an account of the operational potentialities of the new theory, mainly in the area of multicriteria decision aid and social choice theory. Further research directions conclude the paper.

Analysis of multicriteria decision aid in Europe

Abstract As asked by the editors of this special issue, the purpose of this paper is to analyze the existing literature on multicriteria decision-aid, to bring out the successes and the difficulties of this field and to propose some ways of research. Furthermore, as mentioned in the title, this analysis is essentially devoted to the research in Europe, even if some comments are concerned with the American literature. This paper is not a survey of all what has been done in multicriteria decision-aid, but we have tried to approach its main aspects.

Pseudo-orders: definition, properties and numerical representation

The purpose of this paper is to present a structure, called pseudo-order, which could be taken as a model of preference for a decision-maker who hesitates, for cairs of actions, between indefference and preference. We will study its properties, particularly concerning its functional representation: the results obtained generalize the properties of such well-known structures as complete preorders and semi-orders.

An outranking method under uncertainty

Abstract The uncertainty of consequences and the imprecision of data often imply, in multicriteria decision problems, the use of probability distributions to characterize the evaluation of each action with respect to eacg criterion. To keep as much information as possible, the analysis should treat directly these probability distributions instead of reducing them to single values such as mean or median. In this context, the paper proposes a multicriteria procedure which transforms these distributive evaluations of actions, according to decisionmakers preferences, in order to progress to a ranking of these actions. The procedure consists, for each couple of actions, to construct a distributive preference degree with respect to each criterion and a distributive outranking degree over all criteria. These distributive outranking degrees are then explored in order to rank the actions, totally or partially.