Commutative neutrosophic quadruple ideals of neutrosophic quadruple BCK-algebras

Commutative neutrosophic quadruple ideals and BCK-algebras are discussed, and related properties are investigated. Conditions for the neutrosophic quadruple BCK-algebra to be commutative are considered. Given subsets A and B of a neutrosophic quadruple BCK-algebra, conditions for the set NQ(A;B) to be a commutative ideal of a neutrosophic quadruple BCK-algebra are provided.