(L,M)-fuzzy convex structures

In this paper, the notion of (L, M)-fuzzy convex structures is introduced. It is a generalization of L-convex structures and M-fuzzifying convex structures. In our definition of (L, M)-fuzzy convex structures, each L-fuzzy subset can be regarded as an L-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of (L, M)-fuzzy convex structures, the concepts of quotient structures, substructures and products are presented and their fundamental properties are discussed. Finally, we create a functor ω from MYCS to LMCS and show that MYCS can be embedded in LMCS as a coreflective subcategory, where MYCS and LMCS denote the category of M-fuzzifying convex structures and the category of (L, M)-fuzzy convex structures, respectively. 0c 2017 All rights reserved.