k-polar generalized neutrosophic set is introduced, and it is applied to BCK/BCI-algebras. The notions of k-polar generalized subalgebra, k-polar generalized (2; 2 _q)-neutrosophic subalgebra and k-polar generalized (q; 2 _q)-neutrosophic subalgebra are defined, and several properties are investigated. Characterizations of k-polar generalized neutrosophic subalgebra and k-polar generalized (2; 2 _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 neutrosophic2_q-sets subalgebras by using the k-polar generalized (2; 2 _q)-neutrosophic subalgebra and the k-polar generalized (q; 2 _q)-neutrosophic subalgebra. A k-polar generalized (2; 2 _q)-neutrosophic subalgebra is established by using the generaliged neutrosophic 2 _q- sets, conditions for a k-polar generalized neutrosophic set to be a k-polar generalized neutrosophic subalgebra and a k-polar generalized (q;2_q)-neutrosophic subalgebra are provided.