Formulations of L-convex hulls on some algebraic structures

Article type: Research Article

Authors: 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. Tel.: +86 134 8881 1735; E-mail: fuguishi@bit.edu.cn.

Abstract: With a complete Heyting algebra L as the truth value table, we introduce L-ordered convex spaces, L-semilattice convex spaces, L-lattice convex spaces and L-standard convex spaces. These kinds of structures can be extracted from posets, semilattices, lattices and vector spaces. Above all, we obtain their corresponding L-convex hull formulae and analyze their corresponding L-convexity-preserving (resp., L-convex-to-convex) mappings.

Keywords: Convexity, L-convex space, L-convex hull, L-convexity-preserving mapping, L-convex-to-convex mapping

DOI: 10.3233/JIFS-161927

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1385-1395, 2017