Abstract (EN)

This work deals with the problem of the existence of a Multicriteria Decision Aiding model, based on the Choquet integral, that represents the preferences of a decision maker. Given some preferences on a set of actions, our aim is to determine if those preferences are compatible with a Choquet integral model, where the utility function associated to each criterion and the capacity on the subsets of criteria are to be defined. Computing simultaneously the utility functions and the capacity leads to solving a mixed integer program with some quadratic constraints, which can not be performed efficiently. We propose here to solve this problem by using a linear approximation of the quadratic terms given by the Taylor’s formula, and then apply a standard mixed integer programming solver. We illustrate and analyze our approach with some numerical experiments.