The restricted hull operator of M -fuzzifying convex structures

In this paper, the notion of M -fuzzifying restricted hull operators is introduced and several equivalent characterizations are given. It is shown that there is a one-to-one correspondence between M -fuzzifying restricted hull operators and M -fuzzifying convex structures. As applications, some properties of the cut convex structures of an M -fuzzifying convex structure and of M -fuzzifying convexity preserving functions and of M -fuzzifying convex-to-convex functions are derived. In addition, using M -fuzzifying restricted hull operators, some M -fuzzifying convexities are naturally constructed from M -fuzzy quasi-orders.