1 Affiliation : Department of Mathematics, University of Payame Noor, Tehran, Iran
Email : m.hamidi@pnu.ac.ir
2 Affiliation : Mathematics & Science, University of New Mexico, Gallup Campus, USA
Email : smarand@unm.ed
Abstract :
This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK algebra and shows that Neutro-BCK-algebra are different from BCKalgebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hassdiagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.
Keywords :
Neutro-BCK-algebra , NeutroPoset , Neutro-Hass diagram.
References :
[1] M. Al-Tahan, Neutrosophic N -Ideals (N -Subalgebras) of Subtraction Algebra. International Journal ofNeutrosophic Science, 3, no.1, pp.44-53,2020.
[2] Y. Imai and K. Iseki, On axioms systems of propositional calculi , XIV, Proc. Japan Academy, 42, pp.19-22,1966.
[3] T. Jech, Set Theory , The 3rd Millennium Edition, Springer Monographs in Mathematics, 2002.
[4] A. Rezaei, F. Smarandache, The Neutrosophic Triplet of BI-algebras, Neutrosophic Sets and Systems, 33, pp. 313-321, 2020.
[5] A. Rezaei, F. Smarandache, On Neutro-BE-algebras and Anti-BE-algebras,International Journal of Neutrosophic Science, 4, no. 1, pp. 08–15,2020
[6] F. Smarandache, A. Rezaei, H.S. Kim, A new trend to extensions of CI-algebras,International Journal ofNeutrosophic Science, 5 , no.1, pp. 8–15,2020.
[7] F. Smarandache, Neutro algebra is a generalization of partial algebra,International Journal of Neutrosophic Science, 2 , no.1, pp.8-17,
| Style | # |
|---|---|
| MLA | Mohammad Hamidi,Florentin Smarandache. "NEUTRO-BCK-ALGEBRA." International Journal of Neutrosophic Science, Vol. 8, No. 2, 2020 ,PP. 110-117. |
| APA | Mohammad Hamidi,Florentin Smarandache. (2020). NEUTRO-BCK-ALGEBRA. Journal of International Journal of Neutrosophic Science, 8 ( 2 ), 110-117. |
| Chicago | Mohammad Hamidi,Florentin Smarandache. "NEUTRO-BCK-ALGEBRA." Journal of International Journal of Neutrosophic Science, 8 no. 2 (2020): 110-117. |
| Harvard | Mohammad Hamidi,Florentin Smarandache. (2020). NEUTRO-BCK-ALGEBRA. Journal of International Journal of Neutrosophic Science, 8 ( 2 ), 110-117. |
| Vancouver | Mohammad Hamidi,Florentin Smarandache. NEUTRO-BCK-ALGEBRA. Journal of International Journal of Neutrosophic Science, (2020); 8 ( 2 ): 110-117. |
| IEEE | Mohammad Hamidi,Florentin Smarandache, NEUTRO-BCK-ALGEBRA, Journal of International Journal of Neutrosophic Science, Vol. 8 , No. 2 , (2020) : 110-117 (Doi : https://doi.org/10.54216/IJNS.080204) |