Positive Implicative Ideals of BCK-Algebras Based on Intuitionistic Falling Shadows

Abstract

The concepts of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are introduced, and several properties are investigated. Characterizations of a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are obtained, and relations between a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal and an intuitionistic fuzzy ideal are discussed. Conditions for an intuitionistic fuzzy ideal to be a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal are provided, and relations between a positive implicative ( ∈ , ∈)-intuitionistic fuzzy ideal, a falling intuitionistic fuzzy ideal and a positive implicative falling intuitionistic fuzzy ideal are considered. Conditions for a falling intuitionistic fuzzy ideal to be positive implicative are given.