Many-valued convex structures induced by fuzzy inclusion orders

Article type: Research Article

Authors: Wang, Kai^{a; b; *} | Shi, Fu-Gui^{a; b}

Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | [b] Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China

Correspondence: [*] Corresponding author. Kai Wang. E-mail: wangkai5111@126.com.

Abstract: In this paper we introduce the concept of strong L-convexity by making use of the fuzzy inclusion order on the fuzzy power set. And the category of strong L-convex spaces is topological and is a co-reflective subcategory of the category of bi-stratified L-convex spaces. It is apparently different from the strong L-topology in the sense of Zhang that is exactly bi-stratified L-topology. Finally, we present that strong L-convexities can be characterized by algebraic L-ordered closure operators.

Keywords: Fuzzy inclusion order, fuzzy convexity, strong L-convexity, algebraic L-ordered closure operator

DOI: 10.3233/JIFS-181103

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 4, pp. 3373-3383, 2019