M-fuzzifying median algebras and its induced convexities

Article type: Research Article

Authors: Liu, Qi | Shi, Fu-Gui^{; *}

Affiliations: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China

Correspondence: [*] Corresponding author. Fu-Gui Shi, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China. E-mail: [email protected].

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.

Keywords: M-fuzzifying median algebra, M-fuzzifying convex structure, M-fuzzifying interval operator, M-fuzzifying modula operator

DOI: 10.3233/JIFS-172271

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 2, pp. 1927-1935, 2019