BCI-implicative ideals of BCI-algebras using neutrosophic quadruple structure

Abstract

Neutrosophic quadruple structure is used to study BCI-implicative ideal in BCI-algebra. The conceot of neutrosophic quadruple BCI-implicative ideal based on nonempty subsets in BCI-algebra is introduced, and their related properties are investigated. Relationship between neutrosophic quadruple ideal, neutrosophic quadruple BCI-implicative ideal, neutrosophic quadruple BCI-positive implicative ideal and neutrosophic quadruple BCIcommutative ideal are consulted. Conditions for the neutrosophic quadruple set to be neutrosophic quadruple BCI-implicative ideal are provided. A characterization of a neutrosophic quadruple BCI-implicative ideal is displayed, and the extension property of neutrosophic quadruple BCI-implicative ideal is established.