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- Jean-Luc Marichal
- IEEE Trans. Fuzzy Systems
- 2000

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute to the weighted arithmetic mean has to be adopted. We show that, under rather natural conditions, the discrete Choquet integral is an adequate aggregation… (More)

- Jean-Luc Marichal, Marc Roubens
- European Journal of Operational Research
- 2000

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.

There is given a short overview of the monograph ”Aggregation Functions” (M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap), Cambridge University Press (in press) with more details from introductory Chapters 1 and 2.

Let us consider a finite set of alternatives A = {a, b, c, . . .} and a finite set of criteria N = {1, . . . , n} in a multicriteria decision making problem. Each alternative a ∈ A is associated with a profile xa = (x1, . . . , x a n) ∈ IR, where, for any i ∈ N , xi represents the partial score of a related to criterion i. We assume that all the partial… (More)

- Michel Grabisch, Jean-Luc Marichal, Marc Roubens
- Math. Oper. Res.
- 2000

This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius 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.

- Katsushige Fujimoto, Ivan Kojadinovic, Jean-Luc Marichal
- Games and Economic Behavior
- 2006

In the framework of cooperative game theory, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to measure the interaction phenomena among players. Axiomatizations of two classes of interaction indices, namely probabilistic interaction indices and cardinal-probabilistic interaction indices,… (More)

- Jean-Luc Marichal
- European Journal of Operational Research
- 2002

We introduce a measure of entropy for any discrete Choquet capacity and we interpret it in the setting of aggregation by the Choquet integral.

- János C. Fodor, Jean-Luc Marichal, Marc Roubens
- IEEE Trans. Fuzzy Systems
- 1995

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 present the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear… (More)

- Jean-Luc Marichal
- Fuzzy Sets and Systems
- 2000

Aggregation refers to the process of combining numerical values x1, . . . , xm into a single one M (x1, . . . , xm), so that the final result of aggregation takes into account all the individual values. In decision making, values to be aggregated are typically preference or satisfaction degrees and thus belong to the unit interval [0, 1]. This paper aims at… (More)

- Michel Grabisch, Jean-Luc Marichal, Radko Mesiar, Endre Pap
- Inf. Sci.
- 2011

This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic classification on aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary… (More)