M -fuzzifying median algebras and its induced convexities

Abstract

In the present paper we introduce the notion of M-fuzzifying median algebras, which is an extended notion of median algebras in van de Vel. It can further induce M-fuzzifying convex spaces and M-fuzzifying interval spaces, respectively. We study some mapping relations of these concepts. Some characterizations and properties of M-fuzzifying median algebras, M-fuzzifying convex spaces and M-fuzzifying interval spaces are given. Specially, an M-fuzzifying median algebra can not only induce an M-fuzzifying geometric interval operator but also obtain a special M-fuzzifying modular space.

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