Robust optimization of the Choquet integral

We study the problem of the Choquet integral maximization for the case when preferences of the decision maker do not define a unique capacity but rather some convex set. We introduce a robust version of the problem based on the minimax-regret criterion and construct a global optimization algorithm. It is shown that the decision rule based on regret minimization over a set of capacities is equivalent to maximization of the Choquet integral with respect to a certain capacity belonging to this set. We compare our method to various capacity identification approaches developed in the literature and provide a semantic interpretation in terms of information value.