International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 19 , Issue 3 , PP: 08-15, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

Neutrosophic BCK-algebra and Ω-BCK-algebra

Saad H. Zail 1 * , Majid Mohammed Abed 2 , Faisal AL-Sharqi 3

  • 1 General Directorate of Education in Anbar, Ministry of Education, Ramadi, Anbar, Iraq - (SaadHaif50@gmail.com)
  • 2 Department of Mathematics, Faculty of Education For Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq - (Majid_math@uoanbar.edu.iq)
  • 3 Department of Mathematics, Faculty of Education For Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq - ( Faisal.Sharqi@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.190301

    Received: April 20, 2021 Accepted: October 04, 2022
    Abstract

    In this paper, we study neutrosophic of one important types of algebra namely BCK-algebra.  Some new results of a generalization of BCK-algebra (Ω-BCK-algebra) have been introduced. Several facts about neutrosophic Ω-BCK-algebra are presented such as neutrosophic of homomorphic image and neutrosophic of kernel homomorphism.  Finally, some definitions, examples, and other properties of neutrosophic BCK-algebra and neutrosophic Ω-BCK-algebra are given.

    Keywords :

    Neutrosophic set , Neutrosophic algebra , BCK-algebra , BCI-algebra , Fuzzy set

    References

    [1] Smarandache, F. Neutrosophy: Neutrosophic probability, set and logic; American Research Press:

    Rehoboth, IL, USA, 1998.

    [2] Smarandache, F. Neutrosophic set, a generalisation of the intuitionistic fuzzy sets. International Journal

    of Pure and Applied Mathematics, 2005, 24, 287-297.

    [3] Zadeh, L.A. Fuzzy sets. Information and Control, 1965, 8, 331–352.

    [4] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87–96.

    [5] Chang, C. L. (1968). Fuzzy topological spaces. Journal of mathematical Analysis and Applications,

    24(1), 182-190.

    [6] Youssef, N. L., & Dib, K. A. (1992). A new approach to fuzzy groupoids. Fuzzy sets and systems,

    49(3), 381-392.

    [7] Fathi, M., & Salleh, A. R. (2009). Intuitionistic fuzzy groups. Asian Journal of Algebra, 2(1), 1-10.

    [8] A. A. Agboola, A. D. Akwu, and Y. T. Oyebo, “Neutrosophic groups and subgroups,” International

    Journal of Mathematical Combinatorics, vol. 3, pp. 1–9, 2012.

    [9] Yuan, X. H., Li, H. X., & Lee, E. S. (2010). On the definition of the intuitionistic fuzzy subgroups.

    Computers & Mathematics with Applications, 59(9), 3117-3129.

    [10] Smarandache, F., & Ali, M. (2018). Neutrosophic triplet group. Neural Computing and Applications,

    29(7), 595-601.

    [11] Shabir, M., Ali, M., Naz, M., & Smarandache, F. (2013). Soft neutrosophic group. Neutrosophic Sets

    and Systems, 1, 13-25.

    [12] Abobala, M., & Lattakia, S. (2019). n-refined neutrosophic groups I. International Journal of

    Neutrosophic Science, Vol. 0, (1), 27-34.

    [13] Zhang, X., Smarandache, F., & Liang, X. (2017). Neutrosophic duplet semi-group and cancellable

    neutrosophic triplet groups. Symmetry, 9(11), 275.

    [14] Mohammed Abed, M., Hassan, N., & Al-Sharq, F. (2022). On Neutrosophic Multiplication Module.

    Neutrosophic Sets and Systems, 49(1), 12.

    [15] Abuqamar, M., & Hassan, N. (2022). The Algebraic Structure of Normal Groups Associated with QNeutrosophic

    Soft Sets. Neutrosophic Sets and Systems, 48, 328-338.

    [16] Salama, AA & Alblowi, SA 2012, Neutrosophic set and neutrosophic topological space, ISOR J.

    mathematics, vol. (3), Issue (4), pp. 31 - 35.

    [17] Al-Sharqi, F. G., Abed, M. M., & Mhassin, A. A. (2018). On Polish Groups and their Applications.

    Journal of Engineering and Applied Sciences, 13(18), 7533-7536.

    [18] Abed, M. M., Al-Jumaili, A. F., & Al-sharqi, F. G. (2018). Some mathematical structures in a

    topological group. J. Algab. Appl. Math, 16(2), 99-117.

    [19] Jun, Y. B., Al-Masarwah, A., & Qamar, M. A. (2022). Rough Semigroups in Connection with Single

    Valued Neutrosophic ( , )-Ideals. Neutrosophic Sets & Systems, 51.

    [20] Akinleye, S. A., Smarandache, F., & Agboola, A. A. A. (2016). On neutrosophic quadruple algebraic

    structures. Neutrosophic Sets and Systems, 12(1), 16.

    [21] Al-Obaidi, A. H., Imran, Q. H., & Broumi, S. (2022). On New Concepts of Weakly Neutrosophic

    Continuous Functions. Journal of Neutrosophic and Fuzzy Systems (JNFS) Vol, 4(01), 08-14.

    [22] Abdulkadhim, M. M., Imran, Q. H., Al-Obaidi, A. H., & Broumi, S. (2022). On Neutrosophic Crisp

    Generalized Alpha Generalized Closed Sets. International Journal of Neutrosophic Science, 19(1), 107-

    115.

    [23] Saeid, A.B.; Jun, Y.B. Neutrosophic subalgebras of BCK/BCI-algebras based on neutrosophic points.

    Ann. Fuzzy Math. Inform. 2017, 14, 87–97.

    [24] Jun, Y. B., Kim, S. J., & Smarandache, F. (2018). Interval neutrosophic sets with applications in

    BCK/BCI-algebra. Axioms, 7(2), 23.

    [25] Khan, M.; Anis, S.; Smarandache, F.; Jun, Y.B. Neutrosophic N N -structures and their applications in

    semigroups. Ann. Fuzzy Math. Inform. 2017, 14, 583–598.

    [26] Öztürk, M.A.; Jun, Y.B. Neutrosophic ideals in BCK/BCI-algebras based on neutrosophic points. J.

    Inter. Math. Virtual Inst. 2018, 8, 1–17.

    [27] Al-Masarwah, A., & Ahmad, A. G. (2022). A New Interpretation of Multi-Polarity Fuzziness

    Subalgebras of BCK/BCI-Algebras. Fuzzy Information and Engineering, 1-12.

    [28] Al-Masarwah, A., & Alshehri, H. (2022). Algebraic Perspective of Cubic Multi-Polar Structures on

    BCK/BCI-Algebras. Mathematics, 10(9), 1475.

    [29] Al-Masarwah, A., Ahmad, A. G., Muhiuddin, G., & Al-Kadi, D. (2021). Generalized m-polar fuzzy

    positive implicative ideals of BCK-algebras. Journal of Mathematics, 2021.

    Cite This Article As :
    H., Saad. , Mohammed, Majid. , AL-Sharqi, Faisal. Neutrosophic BCK-algebra and Ω-BCK-algebra. Journal of International Journal of Neutrosophic Science, vol. 19, no. 3, 2022, pp. 08-15. DOI: https://doi.org/10.54216/IJNS.190301
    H., S. Mohammed, M. AL-Sharqi, F. (2022). Neutrosophic BCK-algebra and Ω-BCK-algebra. Journal of International Journal of Neutrosophic Science, 19( 3), 08-15. DOI: https://doi.org/10.54216/IJNS.190301
    H., Saad. Mohammed, Majid. AL-Sharqi, Faisal. Neutrosophic BCK-algebra and Ω-BCK-algebra. Journal of International Journal of Neutrosophic Science 19, no. 3 (2022): 08-15. DOI: https://doi.org/10.54216/IJNS.190301
    H., S. , Mohammed, M. , AL-Sharqi, F. (2022) . Neutrosophic BCK-algebra and Ω-BCK-algebra. Journal of International Journal of Neutrosophic Science , 19( 3) , 08-15 . DOI: https://doi.org/10.54216/IJNS.190301
    H. S. , Mohammed M. , AL-Sharqi F. [2022]. Neutrosophic BCK-algebra and Ω-BCK-algebra. Journal of International Journal of Neutrosophic Science. 19( 3): 08-15. DOI: https://doi.org/10.54216/IJNS.190301
    H., S. Mohammed, M. AL-Sharqi, F. "Neutrosophic BCK-algebra and Ω-BCK-algebra," Journal of International Journal of Neutrosophic Science, vol. 19, no. 3, pp. 08-15, 2022. DOI: https://doi.org/10.54216/IJNS.190301