Free join- and meet-completions of L-ordered sets

Article type: Research Article

Authors: Wang, Hai-Wei | Zhao, Bin^{; *}

Affiliations: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P.R. China

Correspondence: [*] Corresponding author. Bin Zhao, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P.R. China. E-mail: zhaobinmath@mail.xjtu.edu.cn.

Abstract: In this paper, the free join- and meet-completions of an L-ordered set are built and characterized. Then we give the definitions of Δ1-directed objects and intermediate structures, and show that the Δ1-directed object precisely is the Dedekind-MacNeille completion of the intermediate structure in the bounded L-lattice case.

Keywords: Fuzzy order, Free join-completion, Δ₁-directed object, Intermediate structure

DOI: 10.3233/JIFS-182583

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 6283-6293, 2019