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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 8Issue 2PP: 110-117 • 2020

NEUTRO-BCK-ALGEBRA

Mohammad Hamidi 1* ,
Florentin Smarandache 2
1Department of Mathematics, University of Payame Noor, Tehran, Iran
2Mathematics & Science, University of New Mexico, Gallup Campus, USA
* Corresponding Author.

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 -Ideals (-Subalgebras) of Subtraction Algebra. International Journal of
Neutrosophic 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, , no.1, pp. 8–15,2020.

 

[7]   F. Smarandache, Neutro algebra is a generalization of partial algebra,International Journal of Neutrosophic Science, , no.1, pp.8-17,

Cite This Article

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Hamidi, Mohammad, Smarandache, Florentin. "NEUTRO-BCK-ALGEBRA." International Journal of Neutrosophic Science, vol. Volume 8, no. Issue 2, 2020, pp. 110-117. DOI: https://doi.org/10.54216/IJNS.080204
Hamidi, M., Smarandache, F. (2020). NEUTRO-BCK-ALGEBRA. International Journal of Neutrosophic Science, Volume 8(Issue 2), 110-117. DOI: https://doi.org/10.54216/IJNS.080204
Hamidi, Mohammad, Smarandache, Florentin. "NEUTRO-BCK-ALGEBRA." International Journal of Neutrosophic Science Volume 8, no. Issue 2 (2020): 110-117. DOI: https://doi.org/10.54216/IJNS.080204
Hamidi, M., Smarandache, F. (2020) 'NEUTRO-BCK-ALGEBRA', International Journal of Neutrosophic Science, Volume 8(Issue 2), pp. 110-117. DOI: https://doi.org/10.54216/IJNS.080204
Hamidi M, Smarandache F. NEUTRO-BCK-ALGEBRA. International Journal of Neutrosophic Science. 2020;Volume 8(Issue 2):110-117. DOI: https://doi.org/10.54216/IJNS.080204
M. Hamidi, F. Smarandache, "NEUTRO-BCK-ALGEBRA," International Journal of Neutrosophic Science, vol. Volume 8, no. Issue 2, pp. 110-117, 2020. DOI: https://doi.org/10.54216/IJNS.080204
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