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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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