Polarity of generalized neutrosophic subalgebras in BCK/BCI-algebras

Abstract

k-polar generalized neutrosophic set is introduced, and it is applied to BCK/BCI-algebras. The notions of 1-polar generalized subalgebra, 1-polar generalized (is an element of, is an element of boolean OR q)-neutrosophic subalgebra and 1-polar generalized (q, is an element of boolean OR q)-neutrosophic subalgebra are defined, and several properties are investigated. Characterizations of 1-polar generalized neutrosophic subalgebra and 1-polar generalized (is an element of, is an element of boolean OR q)-neutrosophic subalgebra are discussed, and the necessity and possibility operator of k-polar generalized neutrosophic subalgebra are are considered. We show that the generaliged neutrosophic q-sets and the generaliged neutrosophic is an element of boolean OR q-sets subalgebras by using the k-polar generalized (is an element of, is an element of boolean OR q)-neutrosophic subalgebra and the 1-polar generalized (q, is an element of boolean OR q)-neutrosophic subalgebra. A 1-polar generalized (is an element of, is an element of boolean OR q)-neutrosophic subalgebra is established by using the generaliged neutrosophic is an element of boolean OR q-sets, conditions for a k-polar generalized neutrosophic set to be a k-polar generalized neutrosophic subalgebra and a 1-polar generalized (q, is an element of boolean OR q)-neutrosophic subalgebra are provided.