L-fuzzifying convex structures as L-convex structures

In this paper, the concepts of fuzzifying L-hull spaces and fuzzifying L-convex spaces are introduced and the resulting categories are shown to be isomorphic to that of L-fuzzifying convex spaces. As applications of these concepts, it is shown that the category of L-fuzzifying convex spaces can be embedded in the category of L-convex spaces as a simultaneously bireflective and bicoreflective subcategory.