Decreasing rearrangement and a fuzzy variational problem

In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be transformed into a one dimensional setting.