M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces

Article type: Research Article

Authors: Xiu, Zhen-Yu^a | Pang, Bin^{b; *}

Affiliations: [a] College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, P.R. China | [b] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China

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

Abstract: In this paper, the relations between M-fuzzifying cotopologies and M-fuzzifying closure systems, and the relations between M-fuzzifying convex structures and M-fuzzifying closure systems are studied, respectively. A categorical approach is provided to present these relations. It is shown that the category of M-fuzzifying cotopological spaces and the category of M-fuzzifying convex spaces are both bicoreflective subcategories of the category of M-fuzzifying closure spaces.

Keywords: M-fuzzifying cotopology, M-fuzzifying convex structure, M-fuzzifying closure system, Bicoreflective subcategory

DOI: 10.3233/JIFS-16661

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 613-620, 2017