Fuzzy counterparts of partial hull operators in the theory of L-convex systems

Abstract

In this paper, we provide some new characterizations of L-convex systems. For this purpose, we first introduce the concept of partial hull operators and establish the categorical relationship between partial hull operators and convex systems. Then we abstract the relationship between a subset and its partially convex hull in convex system to a binary relation, called enclosed relation. Moreover, we prove that the enclosed relations are equivalent to convex systems. Subsequently, we generalize the concept of partial hull operators and enclosed relations to the fuzzy case, which will be called L-partial hull operators and L-enclosed relations respectively. Finally we explore the categorical isomorphisms between them.