## International Journal of Neutrosophic Science

##### Journal DOI

https://doi.org/10.54216/IJNS

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

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.