Some properties of \(M\)-fuzzifying convexities induced by \(M\)-orders. (English) Zbl 1397.52001
Summary: In this paper, the notions of geometric interval spaces, convex geometries, and base-point orders in the theory of convexity spaces are generalized to \(M\)-fuzzifying convexity spaces. Using \(M\)-fuzzifying restricted hull operators, the \(M\)-fuzzifying convexity spaces induced by \(M\)-orders are defined conveniently. Then it is shown that \(M\)-fuzzifying convexity spaces induced by \(M\)-orders are \(M\)-fuzzifying JHC and arity \(\leqslant 2\), and if the \(M\)-order is strongly anti-symmetric, then the \(M\)-fuzzifying convexity space is an \(M\)-fuzzifying convex geometry and its segment operator is an \(M\)-fuzzifying geometric interval operator.
Keywords:
\(M\)-fuzzifying convexity space; \(M\)-fuzzifying geometric interval space; \(M\)-fuzzifying convex geometry; base-point \(M\)-orderReferences:
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