Some Fuzzy LI - Ideals in Lattice Implication Algebras

Abstract

The purpose of this paper is to introduce the notions of fuzzy prime LI - ideals and fuzzy maximal LI - ideals in lattice implication algebras. Some properties of fuzzy ILI - ideals are investigated. Nine characterizations of fuzzy prime LI - ideals in lattice implication algebras and eight characterizations of fuzzy prime LI - ideals in lattice H implication algebras are obtained. The extension properties of fuzzy prime LI - ideals is given. The relations among various fuzzy LI - ideals and LI - ideals are established, respectively. We introduce the notion of fuzzy zero LI - ideals of lattice implication algebras. Finally we describe some classes of lattice implication algebras via fuzzy ILI - ideals (resp. fuzzy prime LI - ideals, fuzzy maximal LI - ideals).