Neutrosophic quadruple ideals in neutrosophic quadruple BCI-algebras

Abstract

In the present paper, we discuss the Neutrosophic quadruple q-ideals and (regular) neutrosophic quadruple ideals and investigate their related properties. Also, for any two nonempty subsets U and V of a BCI-algebra S, conditions for the set NQ(U, V) to be a (regular) neutrosophic quadruple ideal and a neutrosophic quadruple q-ideal of a neutrosophic quadruple BCI-algebra NQ(S) are discussed. Furthermore, we prove that let U, V, I and J be ideals of a BCI-algebra S such that I subset of U and J subset of V. If I and J are q-ideals of S, then the neutrosophic quadruple (U, V)-set NQ(U, V) is a neutrosophic quadruple q-ideal of NQ(S).