Optimization issues for fuzzy measures

Abstract

In this paper, we address the problem of identification of fuzzy measures through different representations, namely the Mobius, the Shapley and the Banzhaf interaction rep resentations. In the first part of the paper, we recall the main results concerning these representations, and give a simple algorithm to compute them. Then we determine the bounds of the Mobius and the interaction representations for fuzzy measures. Lastly, the identification of fuzzy measures by minimizing a quadratic error criterion is addressed. We give expressions of the quadratic program for all the considered representations, and study the uniqueness of the solution.