IFI-ideals of lattice implication algebras

Abstract

The notion of –ideal is introduced in lattice implication algebras. Firstly, the equivalent conditions of –ideals and –ideals are given in lattice implication algebras. Then the proposition of –ideal is investigated in lattice implication algebras. Next, the relations between –ideal and –ideal, between –ideal and –filter, between –ideal and fuzzy impilcative ideals, between –ideal and implicative ideals are discussed in lattice implication algebras. Moreover, the extension theorem of –ideals is obtained, and Ψ() which is composed of all –ideals constitutes a closure system. Finally, we prove that ∀α ∈ [01] = (µ ) is an –ideal of lattice implication algebra if and only if is a lattice implication algebra.

Keywords

• lattice implication algebra
• ideals
• –ideals
• –ideals