Fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces

For fuzzy counterparts of hull operators and interval operators, two types of fuzzy hull operators and one type of fuzzy interval operators are proposed. Firstly, the concept of L-hull operators is introduced and the resulting category is shown to be isomorphic to that of L-convex spaces. Secondly, considering the graded inclusions of L-subsets, the notion of L-ordered hull operators is presented, which is shown to be categorically isomorphic to strong L-convex structures. Finally, the concept of L-interval operators is introduced and it is shown that there is a Galois correspondence between the category of L-interval spaces and that of L-convex spaces. In particular, the category of arity 2 L-convex spaces can be reflectively embedded into that of L-interval spaces.