Convex invariants of M-fuzzifying convex spaces

Article type: Research Article

Authors: Yang, Shaojun^{a; c; e} | Huang, Xinyi^{b; d; *}

Affiliations: [a] School of Mathematics and Statistics, Fujian Normal University, Fuzhou, China | [b] College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China | [c] Center for Applied Mathematics of Fujian Province, Fujian Normal University, Fuzhou, China | [d] Fujian Provincial Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou, China | [e] State Key Laboratory of Cryptology, Beijing, China

Correspondence: [*] Corresponding author. Xinyi Huang, E-mail: xyhuang81@yahoo.com.

Abstract: The numbers of Helly, Carathéodory and Radon are a central theme in classic convex spaces and each of them is invariant under isomorphism. The theory of M-fuzzifying convex spaces is an active research field since it is presented. This paper focus on convex invariants of M-fuzzifying convex spaces. The degrees of Helly independent, Carathéodory independent and Radon independent of non-empty set are defined in the framework of M-fuzzifying convex spaces. By those definitions, we introduce the Helly number, Carathéodory number and Radon number of M-fuzzifying convex spaces. Finally, we inspect M-fuzzifying topology and M-fuzzifying JHC which are characterized by convex invariants of M-fuzzifying convex spaces.

Keywords: Helly number, Carathéodory number, Radon number

DOI: 10.3233/JIFS-213081

Journal: Journal of Intelligent & Fuzzy Systems, vol. 43, no. 1, pp. 1077-1090, 2022