Further results on (∈, ∈)-neutrosophic subalgebras and ideals in BCK/BCI-algebras

• Main Authors: G. Muhiuddin, Hashem Bordbar, Florentin Smarandache, Young Bae Jun
• Format: Article
• Language: English
• Published: University of New Mexico 2018-05-01
• Series: Neutrosophic Sets and Systems
• Subjects: ∈)-neutrosophic subalgebra; (∈; neutrosophic subalgebra
• Online Access: http://fs.gallup.unm.edu/NSS/FurtherResultsOnNeutrosophic.pdf

Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈, ∈)-neutrosophic ideal. The relation between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (∈,∈)-neutrosophic subalgebra to be a (∈, ∈)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (∈, ∈)-neutrosophic ideal is established. Equivalence relations on the family of all (∈, ∈)-neutrosophic ideals are introduced, and related properties are investigated.