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Using the Sugeno Integral in Optimal Assignment Problems with Qualitative Utilities

This paper is devoted to the assignment problem when the preferences of the agents are defined by qualitative utilities. In this setting, it is not possible to compare assignments by summing up individual utilities because the sum operation becomes meaningless. We study here the optimization of a Sugeno integral of the individual utilities. We show that the problem is NP-hard in the general case, but we also identify special cases that are solvable in polynomial time. Furthermore, we provide a mixed integer programming formulation in the general case, which leads to a compact formulation for k-minitive capacities.