Minimax Regret Approaches for Preference Elicitation with Rank-Dependent Aggregators

Recently there has been a growing interest in non-linear aggregation models to represent the preferences of a decision maker in a multicriteria decision problem. Such models are expressive as they are able to represent synergies (positive and negative) between attributes or criteria, thus modeling different decision behaviors. They also make it possible to generate Pareto-optimal solutions that cannot be obtained by optimizing a linear combination of criteria. This is the case of rank-dependent aggregation functions such as Ordered Weighted Averages and their weighted extensions, but more generally of Choquet integrals. A key question is how to assess the parameters of such models to best fit decision maker’s behaviors or preferences. In this work, adopting a principled decision-theoretic approach, we consider the optimization problem induced by adaptive elicitation using the minimax regret criterion.