Fuzzification of the category of (L, M)-fuzzy convex spaces

In this paper, a fuzzy approach to the category of (L, M) -fuzzy convex spaces (denoted by LM-FCon) is introduced. To be specific, the objects and morphisms of LM-FCon are given some degree value, denoted by ω(X, C) and μ(f) respectively, which extends the LM-FCon to the fuzzy case. What is more, we show that the set C_α(L, M, X) = \{C : L^X → M ω(X, C) ≥ α\} is a bounded complete lattice and discuss the relationships among C_α(L, M, X) , L -convex structures and (L, M) -fuzzy convex structures. Finally, subspace, product space, join space and quotient space of C_α(L, M, X) are studied and related properties are obtained.