On the extension of pseudo-Boolean functions for the aggregation of interacting criteria

The paper presents an analysis on the use of integrals defined for non-additive measures (or capacities) as the Choquet and the Sipos integral, and the multilinear model, all seen as extensions of pseudo-Boolean functions, and used as a means to model interaction between criteria in a multicriteria decision making problem. The emphasis is put on the use, besides classical comparative information about difference of attractiveness between acts, and on the existence, for each point of view, of a “neutral level”, allowing to introduce the absolute notion of attractive or repulsive act. It is shown that in this case, the Sipos integral is a suitable notion, although not unique. Properties of the Sipos integral as a new way of aggregating criteria are shown, with emphasis on the interaction among criteria.