IFI-ideals of lattice implication algebras

The notion of IFI —ideal is introduced in lattice implication algebras. Firstly, the equivalent conditions of IF —ideals and IFI —ideals are given in lattice implication algebras. Then the proposition of IFI —ideal is investigated in lattice implication algebras. Next, the relations between IFI —ideal and IF —ideal, between IFI —ideal and IFI —filter, between IFI —ideal and fuzzy impilcative ideals, between IFI —ideal and implicative ideals are discussed in lattice implication algebras. Moreover, the extension theorem of IFI —ideals is obtained, and Ψ( L ) which is composed of all IFI —ideals constitutes a closure system. Finally, we prove that ∀α ∈ [0,1], is an IFI —ideal of lattice implication algebra L if and only if L is a lattice H implication algebra.