IFI-ideals of lattice implication algebras

摘要

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 (A)α∈ [0,1],A = (μ_(0,α),μ_(0,α)) is an IFI-ideal of lattice implication algebra L if and only if L is a lattice H implication algebra.