Implicative falling neutrosophic ideals of BCK-algebras

Abstract

The notions of an implicative (∈, ∈)-neutrosophic ideal and an implicative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of an implicative (∈, ∈)-neutrosophic ideal are considered, and relations between an implicative (∈, ∈)-neutrosophic ideal and an (∈, ∈)-neutrosophic ideal are discussed. Conditions for an (∈, ∈)-neutrosophic ideal to be an implicative (∈, ∈)-neutrosophic ideal are provided, and relations between an implicative (∈, ∈)-neutrosophic ideal, a falling neutrosophic ideal, and an implicative falling neutrosophic ideal are studied. Conditions for a falling neutrosophic ideal to be implicative are provided. Relations between the implicative falling neutrosophic ideal, commutative falling neutrosophic ideal and positive implicative falling neutrosophic ideal are discussed.