A natural method of constructing many-valued convex structures

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. Fu-Gui Shi. E-mail: fuguishi@bit.edu.cn.

Abstract: In this paper we give a natural method of constructing a bi-stratified [0, 1]-convexity by a [0, 1]-valued interval operator, where the concept of bi-stratified [0, 1]-convexities is firstly introduced. And its convex hull operators can be characterized by [0, 1]-valued interval operators. Finally, we discuss the relationship between bi-stratified [0, 1]-convexities and [0, 1]-valued interval operators from a categorical aspect.

Keywords: [0, 1]-valued interval operator, fuzzy convexity, bi-stratified fuzzy convexity, convex hull operator

DOI: 10.3233/JIFS-18891

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 3, pp. 2705-2713, 2019