On the characterizations of complete distributive lattices by up-sets¹

Article type: Research Article

Authors: He, Peng^{a; *} | Wang, Xue-ping^{b; 2}

Affiliations: [a] College of Applied Mathematics, Chengdu University of Information Technology Chengdu, People’s Republic of China | [b] School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, People’s Republic of China

Correspondence: [*] Corresponding author. Peng He, College of Applied Mathematics, Chengdu University of Information Technology Chengdu 610225, People’s Republic of China. E-mail: hepeng@cuit.edu.cn.

Note: [1] Supported by National Natural Science Foundation of China (Nos. 11901064 and 12071325).

Note: [2] xpwang1@hotmail.com.

Abstract: This paper first describes a characterization of a lattice L which can be represented as the collection of all up-sets of a poset. It then obtains a representation of a complete distributive lattice L0 which can be embedded into the lattice L such that all infima, suprema, the top and bottom elements are preserved under the embedding by defining a monotonic operator on a poset. This paper finally studies the algebraic characterization of a finite distributive.

Keywords: 03E72, 06D05

Keywords: L-fuzzy set, cut set, complete distributive lattice, embedding, monotonic operator

DOI: 10.3233/JIFS-201430

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 5, pp. 9021-9030, 2021