Evaluation of the quality of the numerical representations compatible with the decision maker’s preferences

In multiple criteria decision problems, the choice of the numerical representation of the value function, among those compatible with the decision maker’s preferences, is often arbitrary. Moreover, for a value function based on a Choquet integral where the number of criteria is very large, it is difficult for the decision maker to provide information obout his preferences which is both in very large quantity and at the same time representative. In this article, in order to avoid an arbitrary choice, we propose indicators which make it possible to evaluate the quality of the numerical representations according to certain expected properties such as coherence, robustness and order preservation. Finally, we propose an application of these indicators for a disaggregation method presented in the literature. This involves establishing a ranking of 100 numerical representations identified by this method related to the proposed indicators.