Convolution of fuzzy sets and applications
The purpose of this work is studying the approximation in D-metric of upper semi-continuous and normal fuzzy sets with compact support on R-n by using the convolution (fdelg)(x) = sup{f(x - y) boolean AND g(y) : y is an element of X} between two fuzzy sets, where the distance D(f, g) is the supremum of the Hausdorff distances of their corresponding level sets. In particular, by using del-convolution, a density result is proved and some applications in Choquet integration of fuzzy numbers are presented. (C) 2003 Elsevier Ltd. All rights reserved.
convolution fuzzy sets hausdorff metric choquet's integrals