(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.