Polarity of generalized neutrosophic subalgebras in BCK/BCI-algebras

• Main Authors: Rajab Ali Borzooei, Florentin Smarandache, Young Bae Jun
• Format: Article
• Language: English
• Published: University of New Mexico 2020-03-01
• Series: Neutrosophic Sets and Systems
• Subjects: k-polar generalized neutrosophic subalgebra; k-polar generalized (∈; ∈ ∨q)-neutrosophic subalgebra; k-polar generalized (q; ∈∨q)-neutrosophic subalgebra.
• Online Access: http://fs.unm.edu/NSS/Polarityofgeneralizedneutrosophic9.pdf

: 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 (∈, ∈ ∨q)-neutrosophic subalgebra and k-polar generalized (q, ∈ ∨q)-neutrosophic subalgebra are defined, and several properties are investigated. Characterizations of k-polar generalized neutrosophic subalgebra and k-polar generalized (∈, ∈ ∨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 ∈∨q-sets subalgebras by using the k-polar generalized (∈, ∈ ∨q)-neutrosophic subalgebra and the k-polar generalized (q, ∈ ∨q)-neutrosophic subalgebra. A k-polar generalized (∈, ∈ ∨q)-neutrosophic subalgebra is established by using the generaliged neutrosophic ∈ ∨qsets, conditions for a k-polar generalized neutrosophic set to be a k-polar generalized neutrosophic subalgebra and a k-polar generalized (q, ∈∨q)-neutrosophic subalgebra are provided.