Volume 27 • Issue 2 • PP: 235-249 • 2026
Separation Axioms in Neutrosophic Bipolar Fuzzy Topological Space
Open Access & Copyright
© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
The purpose of this research is to introduce the notion of neutrosophic bipolar Ti – spaces (i = 0, 1, 2, 3, 4) via neutrosophic bipolar fuzzy topological spaces, and investigate their different properties. By defining neutrosophic bipolar Ti – spaces (i = 0, 1, 2, 3, 4), some interesting results on neutrosophic bipolar separation axioms via neutrosophic bipolar fuzzy topological spaces are proved.
Keywords
References
[1] M. Abdel-Basset et al., "An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number," Appl. Soft Comput., vol. 77, pp. 438–452, 2019.
[2] B. Al-Nafee, R. K. Al-Hamido, and F. Smarandache, "Separation axioms in neutrosophic crisp topological spaces," Neutrosophic Sets Syst., vol. 25, pp. 25–32, 2017.
[3] M. Azhagappan and M. Kamaraj, "Notes on bipolar valued fuzzy RW-closed and bipolar valued fuzzy RW-open sets in bipolar valued fuzzy topological spaces," Int. J. Math. Archive, vol. 7, no. 3, pp. 30–36, 2016.
[4] C. L. Chang, "Fuzzy Topological Spaces," J. Math. Anal. Appl., vol. 24, pp. 182–190, 1968.
[5] M. Fatimah, A. Anas, and F. Shaymaa, "Fuzzy Neutrosophic Weakly-Generalised Closed set in Fuzzy Neutrosophic Topological Spaces," Univ. Anbar Pure Sci., vol. 12, pp. 63–73, 2018.
[6] M. Fatimah and W. Sarah, "Generalized b Closed Sets and Generalized b Open Sets in Fuzzy Neutrosophic bi-Topological Spaces," Neutrosophic Sets Syst., vol. 35, pp. 188–197, 2020.
[7] J. Kim, P. K. Lim, J. G. Lee, and K. Hur, "The category of bipolar fuzzy sets," to be published.
[8] J. Kim, P. K. Lim, J. G. Lee, and K. Hur, "Bipolar Fuzzy Topological Spaces," Ann. Fuzzy Math. Inform, vol. 17, no. 3, pp. 205–229, 2019.
[9] R. M. Hashim and M. Gulistan, "Neutrosophic Bipolar Fuzzy Set and its Application in Medicines Preparations," Neutrosophic Sets Syst., vol. 31, 2020.
[10] M. S. A. Alkhateeb and A. A. D. Alsharif, “Neutrosophic Logic-Based Approach for Decision Making in Smart Cities,” Journal of Computational and Theoretical Nanoscience, vol. 18, no. 1, pp. 1-7, 2021.
[11] F. Smarandache, "Neutrosophic Set-A Generalization of the Intuitionistic Fuzzy Logic," vol. 4, pp. 403–409, 2010, ISBN 978-952-67349-2-7.
[12] S. Das, R. Das, and S. Pramanik, "Neutrosophic Separation Axioms," Neutrosophic Sets Syst., vol. 49, 2022.
[13] S. Dey and G. C. Raj, "Separation Axioms in Neutrosophic Topological Spaces," Neutrosophic Syst. Appl., vol. 2, 2023.
[14] N. Yaqoob and M. A. Ansari, "Bipolar–Fuzzy ideals in ternary semigroups," Int. J. Math. Anal., vol. 7, pp. 1775–1782, 2013.
[15] N. Yaqoob et al., "Structures of Bipolar Fuzzy–Hyper ideals in semihyper groups," J. Intell. Fuzzy Syst., vol. 21, pp. 3015–3032, 2014.
[16] W.-R. Zhang, "Bipolar Fuzzy Set," in Proc. IEEE, 1998, pp. 835–840.
[17] L. A. Zadeh, "Fuzzy Sets," Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
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.