## The restricted hull operator of $$M$$-fuzzifying convex structures.(English)Zbl 1364.54011

Summary: 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.

### MSC:

 54A40 Fuzzy topology
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### References:

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