Decomposition of Fuzzy Sets and Multilinearization for the Extension Principle

In this article we present a proposal for the descomposition of large uncertainties associated with a fuzzy set $u$ and the multilinearization of a function $f$ to be used in the approximation of the fuzzy set $\hat{f}(u) obtained by extension principle. Also, we present conditions on $f$ assuring that $\hat{f}$ preserves differentiability.