A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies

In this paper, by means of the implication operator → on a completely distributive lattice , we define the approximate degrees of -fuzzifying convex structures, -fuzzifying closure systems and -fuzzifying Alexandrov topologies to interpret the approximate degrees to which a mapping is an -fuzzifying convex structure, an -fuzzifying closure system and an -fuzzifying Alexandrov topology from a logical aspect. Moreover, we represent some properties of -fuzzifying convex structures as well as its relations with -fuzzifying closure systems and -fuzzifying Alexandrov topologies by inequalities.