Decreasing rearrangement and a fuzzy variational problem Original Research Article

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