On A-subsets in lattice implication algebras

Article type: Research Article

Authors: Long, Xiqing^{a; *} | Liu, Yi^b | Xu, Yang^c

Affiliations: [a] School of Mathematics, YiBin University, YiBin, P.R. China | [b] Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang, P.R. China | [c] Department of Mathematics, Southwest Jiaotong University, Chengdu, P.R. China

Correspondence: [*] Corresponding author. Xiqing Long, School of Mathematics, YiBin University, YiBin. P.R. China. Tel.: +86 158 83156579; E-mail: [email protected].

Abstract: In this paper, we further study the theory of A-subsets in lattice implication algebras. To begin with, we introduce the propositions of homomorphism image and original image of A-subsets in lattice implication algebras. In addition, the notion of A*-subsets is introduced and some properties of A*-subsets are also investigated in lattice implication algebras. Finally, we introduce the notion of involutory LI-ideals with respect to an LI-ideal A and denote the set of all of them by SA (L). Then SA (L) can be made into a complete Boolean lattice and a lattice implication algebra with respect to the suit operations, respectively.

Keywords: Lattice implication algebras, LI-ideal, A-subset, homomorphism

DOI: 10.3233/JIFS-172169

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 2189-2198, 2018