A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies. (English) Zbl 1430.54016
Summary: In this paper, by means of the implication operator \(\rightarrow\) on a completely distributive lattice \(M\), we define the approximate degrees of \(M\)-fuzzifying convex structures, \(M\)-fuzzifying closure systems and \(M\)-fuzzifying Alexandrov topologies to interpret the approximate degrees to which a mapping is an \(M\)-fuzzifying convex structure, an \(M\)-fuzzifying closure system and an \(M\)-fuzzifying Alexandrov topology from a logical aspect. Moreover, we represent some properties of \(M\)-fuzzifying convex structures as well as its relations with \(M\)-fuzzifying closure systems and \(M\)-fuzzifying Alexandrov topologies by inequalities.
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