International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 8 , Issue 2 , PP: 110-117, 2020 | Cite this article as | XML | Html | PDF | Full Length Article

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

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    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

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

    Cite This Article As :
    Hamidi, Mohammad. , Smarandache, Florentin. NEUTRO-BCK-ALGEBRA. International Journal of Neutrosophic Science, vol. , no. , 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, (), 110-117. DOI: https://doi.org/10.54216/IJNS.080204
    Hamidi, Mohammad. Smarandache, Florentin. NEUTRO-BCK-ALGEBRA. International Journal of Neutrosophic Science , no. (2020): 110-117. DOI: https://doi.org/10.54216/IJNS.080204
    Hamidi, M. , Smarandache, F. (2020) . NEUTRO-BCK-ALGEBRA. International Journal of Neutrosophic Science , () , 110-117 . DOI: https://doi.org/10.54216/IJNS.080204
    Hamidi M. , Smarandache F. [2020]. NEUTRO-BCK-ALGEBRA. International Journal of Neutrosophic Science. (): 110-117. DOI: https://doi.org/10.54216/IJNS.080204
    Hamidi, M. Smarandache, F. "NEUTRO-BCK-ALGEBRA," International Journal of Neutrosophic Science, vol. , no. , pp. 110-117, 2020. DOI: https://doi.org/10.54216/IJNS.080204