Jean-Luc Marichal

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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)
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.
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)
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)
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)