Marc Roubens

Fuzzy preference modelling and multicriteria decision support

Note: Index. Bibliogr. : p. 239-251 Reference Record created on 2004-09-07, modified on 2016-08-08

Ranking and defuzzification methods based on area compensation

Abstract We present some interesting properties related to the area compensation procedure to compare fuzzy numbers. It has been proved that this method produces more than a fuzzy interval order: it induces a ranking of fuzzy numbers. Some further results are given about the transitivity property and about computational aspects. Extensions to non-normal fuzzy numbers and fuzzy quantities are also proposed.

Fuzzy sets and decision analysis

Abstract This survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill-defined information. Fuzzy MAUT as well as fuzzy outranking methods are reviewed. Aggregation procedures, choice problems and treatment of interactive attributes are covered. Trends in research and open problems are indicated.

Characterization of the ordered weighted averaging operators

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators. The first class corresponds to (MN) aggregators which are stable for the same positive linear transformations and presents the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear transformations with the same unit, independent zeroes and ordered values. These two classes correspond to the weighted ordered averaging operator (OWA) introduced by Yager in 1988. It is also shown that the OWA aggregator can be expressed as a Choquet integral. >

Fuzzy clustering algorithms and their cluster validity

Abstract A non metric clustering algorithm based on a fuzzy objective function which reflects proximity based on some global dissimilarity measure is proposed. The global optimal solution is shown to be difficult to obtain and an alternative iterative procedure is presented. This procedure is easily implemented and converges to a local optimum. Some validity functionals which measure the effectiveness with which cluster structure has been identified are compared in relation with the iterative procedures described in the paper.

Pattern classification problems and fuzzy sets

Abstract A unified presentation of classical clustering algorithms is proposed both for the hard and fuzzy pattern classification problems. Based on two types of objective functions, a new method is presented and compared with the procedures of Dunn and Ruspini. In order to determine the best, or more natural number of fuzzy clusters, two coefficients that measure the “degree of non-fuzziness” of the partition are proposed. Numerous computational results are shown.

Determination of weights of interacting criteria from a reference set

Abstract In this paper, we present a model allowing to determine the weights related to interacting criteria. This is done on the basis of the knowledge of a partial ranking over a reference set of alternatives (prototypes), a partial ranking over the set of criteria, and a partial ranking over the set of interactions between pairs of criteria.

An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games

Abstract. An axiomatization of the interaction between the players of any coalition is given. It is based on three axioms: linearity, dummy and symmetry. These interaction indices extend the Banzhaf and Shapley values when using in addition two equivalent recursive axioms. Lastly, we give an expression of the Banzhaf and Shapley interaction indices in terms of pseudo-Boolean functions.

Preference relations on actions and criteria in multicriteria decision making

Abstract Let A be a finite set of feasible actions which are judged following several criteria. An outranking relation is defined on A by considering preference of the decision maker as a weak order on each criterion and the relation among criteria as a semi-order on the given set of criteria. Several ways of constructing outranking relations have been proposed. One of the most popular, introduced by B. Roy, for instance ELECTRE(s), is based on the use of weights related to criteria. In our approach, the knowledge of weights is replaced by the existence of a semi-order. A case study is developed. It deals with a computer selection problem.

Equivalent Representations of Set Functions

This paper introduces four alternative representations of a set function: the MA¶bius transformation, the co-MA¶bius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation.