L-fuzzy convexity induced by L-convex degree on vector spaces

Article type: Research Article

Authors: Wen, Yu-Fei^{a; b} | Zhong, Yu^{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, the degree to which an L-subset of a vector space is an L-convex set is introduced and their characterizations are given. Besides, we obtain an L-fuzzy convexity induced by L-convex degrees, and analyze their L-fuzzy convexity preserving mappings and L-fuzzy convex-to-convex mappings.

Keywords: L-fuzzy convexity, L-convex degree, L-fuzzy convexity preserving mapping, L-fuzzy convex-to-convex mapping

DOI: 10.3233/JIFS-17912

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 4031-4041, 2017