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In this note we introduce a variational problem with respect to an
integrable fuzzy set $f$. The energy functional is maximized over
a deleted $\sigma$-algebra. Using the decreasing rearrangement of
$f$ we prove the admissible set can be replaced by the more
convenient set of {\it 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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