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Paper   IPM / M / 7411
School of Mathematics
  Title:   Decreasing rearrangement and a fuzzy variational problem
  Author(s):  B. Emamizadeh
  Status:   Published
  Journal: Appl. Math. Lett.
  Vol.:  18
  Year:  2005
  Pages:   171-178
  Supported by:  IPM
  Abstract:
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 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.

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