The relationship between L-subuniverses and L-convexities

Article type: Research Article

Authors: Zhong, Yu^{a; b; *} | Yang, Shao-Jun^c | 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 | [c] The Fujian Provincial Key Laboratory of Network Security and Cryptology, College of Mathematics and Informatics, Fujian Normal University, Fuzhou, P.R. China

Correspondence: [*] Corresponding author. Yu Zhong, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China. E-mail: zhongyu199055@126.com.

Abstract: In this paper, the notion of subuniverses in the theory of universal algebras is generalized to L-fuzzy setting, which is called L-subuniverses. Some characterizations and representations of L-subuniverses are given. What is more, the relationship between L-subuniverses and L-convexities is discussed when L is a complete Heyting algebra. It is shown that there exists a one-to-one correspondence between L-subuniverses with the smallest L-subset and induced L-convexities.

Keywords: Convex structure, L-subuniverse, L-convexity, induced L-convexity

DOI: 10.3233/JIFS-162136

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3363-3372, 2017