Volume 19 • Issue 3 • PP: 08-15 • 2022
Neutrosophic BCK-algebra and Ω-BCK-algebra
Open Access & Copyright
© 2022 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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
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
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.