Approximation of fuzzy numbers using the convolution method

Abstract

In this study, we consider the use of the convolution method for constructing approximations comprising fuzzy number sequences with useful properties for a general fuzzy number. We show that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers with finite non-differentiable points. In previous studies, this convolution method was only used for constructing differentiable approximations of continuous fuzzy numbers, the possible non-differentiable points of which were the two endpoints of the 1-cut. The construction of smoothers is a key step in the process for producing approximations. We also show that if appropriate smoothers are selected, then we can use the convolution method to provide approximations that are differentiable, Lipschitz, and that also preserve the core.