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 n by using the convolution (f g) (x) = sup{f (x − y) Λ g(y) : y ε 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 -convolution, a density result is proved and some applications in Choquet integration of fuzzy numbers are presented.