Approximation of convex fuzzy sets

摘要

In this paper we introduce the concepts of fuzzy space, the distances between points and sets of this space. In addition, a concept of a polyhedral fuzzy set, a convex hull, and a fuzzy direction are proposed. It is proved that a polyhedral fuzzy set is a convex hull of a finite number of fuzzy points and directions. In accordance with the main result of this paper any convex closed fuzzy set with a continuous membership function can be approximated with any degree of accuracy by a fuzzy polytop.