Characterizations of M-fuzzifying convex spaces via Galois connections

Article type: Research Article

Authors: Zhang, Shao-Yu^{; *}

Affiliations: Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China

Correspondence: [*] Corresponding author. Shao-Yu Zhang, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, P.R. China. E-mail: shaoyugc163.com.

Abstract: This paper introduces a special Galois connection combined with the wedge-below relation. Furthermore, by using this tool, it is shown that the category of M-fuzzifying betweenness spaces and the category of M-fuzzifying convex spaces are isomorphic and the category of arity-2 M-fuzzifying convex spaces can be embedded in the category of M-fuzzifying interval spaces as a reflective subcategory.

Keywords: Fuzzy convex structure, fuzzy betweenness space, fuzzy interval space, arity-2 fuzzy convexity

DOI: 10.3233/JIFS-210060

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 11915-11925, 2021