Neutrosophic subalgebras of several types in $BCK/BCI$-algebras
2
조회
0
다운로드
3
인용
0
참고문헌
키워드
초록
Given $\Phi, \Psi \in \{\in, q, \in\! \vee \, {q}\}$, the notion of $(\Phi,$ $\Psi)$-neutrosophic subalgebras of a $BCK/BCI$-algebra are introduced, and related properties are investigated. Characterizations of an $(\in, \in)$-neutrosophic subalgebra and an $(\in, \in\! \vee \, {q})$-neutrosophic subalgebra are provided. Given special sets, so called neutrosophic $\in$-subsets, neutrosophic $q$-subsets and neutrosophic $\in\! \vee \, {q}$-subsets, conditions for the neutrosophic $\in$-subsets, neutrosophic $q$-subsets and neutrosophic $\in\! \vee \, {q}$-subsets to be subalgebras are discussed. Conditions for a neutrosophic set to be a $(q,$ $\in\! \vee \, {q})$-neutrosophic subalgebra are considered.
Abstract
Given $\Phi, \Psi \in \{\in, q, \in\! \vee \, {q}\}$, the notion of $(\Phi,$ $\Psi)$-neutrosophic subalgebras of a $BCK/BCI$-algebra are introduced, and related properties are investigated. Characterizations of an $(\in, \in)$-neutrosophic subalgebra and an $(\in, \in\! \vee \, {q})$-neutrosophic subalgebra are provided. Given special sets, so called neutrosophic $\in$-subsets, neutrosophic $q$-subsets and neutrosophic $\in\! \vee \, {q}$-subsets, conditions for the neutrosophic $\in$-subsets, neutrosophic $q$-subsets and neutrosophic $\in\! \vee \, {q}$-subsets to be subalgebras are discussed. Conditions for a neutrosophic set to be a $(q,$ $\in\! \vee \, {q})$-neutrosophic subalgebra are considered.
참고문헌 (7)
- A.A.A. Agboola, "On neutrosophic ideals of neutrosophic BCI-algebras", Critical Review, X, pp.93~103 (2015)
- A.A.A. Agboola, "Introduction to neutrosophic BCI=BCK-algebras", Inter. J. Math. Math. Sci (2015)
- Y. S. Huang, "BCI-algebra" (2006), Science Press
- J. Meng, "BCK-algebra" (1994), Kyungmoon Sa Co.
- F. Smarandache, "A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability" (1999), American Reserch Press
- F. Smarandache, "Neutrosophic set-a generalization of the intuitionistic fuzzy set", Int. J. Pure Appl. Math, 24(3), pp.287~297 (2005)