Assessing non-additive utility for Multicriteria decision aid

In the framework of Multi-Attribute Utility Theory (MAUT) several methods have been proposed to build a Decision-Maker's (DM) utility function representing his/her preferences. Among such methods, the UTA method infers an additive utility function from a set of exemplary decisions using linear programming. However, the UTA method does not guarantee to find a utility function which is coherent with the available information. This drawback is due to the underlying utility model of UTA, viz. the additive one, which does not allow to include additional information such as an interaction among criteria. In this paper we present a methodology for building a non-additive utility function, in the framework of the so called fuzzy integrals, which permits to model preference structures with interaction between criteria. Like in the UTA method, we aim at searching a utility function representing the DM's preferences, but unlike UTA, the functional form is a specific fuzzy integral (Choquet integral). As a result, we obtain weights which can be interpreted as the "importance" of coalitions of criteria, exploiting the potential interaction between criteria, as already proposed by other authors. However, within the same framework, we obtain also the marginal utility functions relative to each one of the considered criteria, that are evaluated on a common scale, as a consequence of the implemented methodology. Finally, we illustrate our approach with an example.