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International Journal of Neutrosophic Science
Volume 8 , Issue 2, PP: 110-117 , 2020 | Cite this article as | XML | Html |PDF

Title

NEUTRO-BCK-ALGEBRA

  Mohammad Hamidi 1 * ,   Florentin Smarandache 2

1  Department of Mathematics, University of Payame Noor, Tehran, Iran
    (m.hamidi@pnu.ac.ir)

2  Mathematics & Science, University of New Mexico, Gallup Campus, USA
    (smarand@unm.ed)


Doi   :   https://doi.org/10.54216/IJNS.080204


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,


Cite this Article as :
Style #
MLA Mohammad Hamidi, Florentin Smarandache. "NEUTRO-BCK-ALGEBRA." International Journal of Neutrosophic Science, Vol. 8, No. 2, 2020 ,PP. 110-117 (Doi   :  https://doi.org/10.54216/IJNS.080204)
APA Mohammad Hamidi, Florentin Smarandache. (2020). NEUTRO-BCK-ALGEBRA. Journal of International Journal of Neutrosophic Science, 8 ( 2 ), 110-117 (Doi   :  https://doi.org/10.54216/IJNS.080204)
Chicago Mohammad Hamidi, Florentin Smarandache. "NEUTRO-BCK-ALGEBRA." Journal of International Journal of Neutrosophic Science, 8 no. 2 (2020): 110-117 (Doi   :  https://doi.org/10.54216/IJNS.080204)
Harvard Mohammad Hamidi, Florentin Smarandache. (2020). NEUTRO-BCK-ALGEBRA. Journal of International Journal of Neutrosophic Science, 8 ( 2 ), 110-117 (Doi   :  https://doi.org/10.54216/IJNS.080204)
Vancouver Mohammad Hamidi, Florentin Smarandache. NEUTRO-BCK-ALGEBRA. Journal of International Journal of Neutrosophic Science, (2020); 8 ( 2 ): 110-117 (Doi   :  https://doi.org/10.54216/IJNS.080204)
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)