Study on the properties of A-subset

Article type: Research Article

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

Affiliations: [a] School of Math, YiBin University, YiBin, P.R. China | [b] Department of Mathematics, Zhenzhou University, Zhenzhou, P.R. China | [c] Department of Mathematics, Southwest Jiaotong University, Chengdu, P.R. China

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

Abstract: The concept of A-subset is introduced in lattice implication algebras. Firstly, the properties of the A-subset are discussed when A is a general set of lattice implication algebras. Next, the properties of A-subset are investigated when the A is an LI-ideal of lattice implication algebras. We obtain some properties of A-subset and prove that B(A)(the A-subset of B) is an LI-ideal in lattice implication algebras. Finally, the properties of A-subset are investigated in lattice implication product algebras. We prove that the A-subset of ∏i=1nBi is the product of A-subset of Bi (i = 1,  2, ⋯ ,  n) respectively ((∏i=1nBi)(∏i=1nAi)=(∏i=1nBi(Ai))) .

Keywords: Lattice implication algebras, LI-ideal, A-subset, lattice implication product algebras

DOI: 10.3233/JIFS-17779

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3939-3947, 2017