International Journal of Mathematics Trends and Technology
Volume 71 | Issue 4 | Year 2025 | Article Id. IJMTT-V71I4P106 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I4P106
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 01 Mar 2025 | 30 Mar 2025 | 18 Apr 2025 | 30 Apr 2025 |
Separation axioms are fundamental, widely used and highly influential concepts in classical topology. They play a crucial role in addressing problems in digital topology and establishing more restricted families of topological spaces. These concepts were extended to soft, fuzzy, and binary soft (BS) topology. Fuzzy binary soft topological spaces (FBS topological spaces) emerge as a more powerful tool than fuzzy soft topological spaces. However, the separation axioms must be explored in the FBS topological spaces. This paper introduces and investigates the separation axioms within the framework of FBS topological spaces. Fuzzy binary soft points and their corresponding neighbourhoods were defined in this article, laying the foundation for the development of fuzzy binary soft. 𝑇0 , 𝑇1 and 𝑇2 spaces. Furthermore, characterizations of regularity, normality, and FBS-connectedness are provided.
Fuzzy soft set, Binary soft set, Fuzzy soft set, Fuzzy binary soft topology, Fuzzy binary soft point, Separation axioms.
[1] D. Molodtsov, “Soft Set Theory-First Results,” Computers and Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31, 1999.
[CrossRef] [Google Scholar] [Publisher Link]
[2] L.A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Zdzisław Pawlak, “Rough Sets,” International Journal of Computer and Information sustem, vol. 11, pp. 341-356, 1982.
[CrossRef] [Google Scholar] [Publisher Link]
[4] P. K. Maji, R. K. Biswas and A.Roy, “Fuzzy Soft Sets,” Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 589-602, 2001.
[5] Athar Kharal, and B. Ahmada, “Mappings on Fuzzy Soft Classes,” Advances in Fuzzy Systems, vol. 2009, pp. 1-6, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[6] Bekir Tanay, and M. Burç Kandemir, “Topological Structure of Fuzzy Soft Sets,” Computers and Mathematics with Applications, vol.
61, no. 10, pp. 2952-2957, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Cigdem Gunduz, and Sadi Bayramov, “Some Results on Fuzzy Soft Topological Spaces,” Mathematical Problems in Engineering, vol.
2013, no. 1, pp. 1-10, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Tugbahan Simsekler, and Saziye Yuksel, “Fuzzy Soft Topological Spaces,” Annals of Fuzzy Mathematics Informatics, vol. 5, no. 1, pp.
87-96, 2013.
[Google Scholar] [Publisher Link]
[9] Serkan Atmaca, and Idris Zorlutuna, “On Fuzzy Soft Topological Spaces,” Annals of Fuzzy Mathematics and Informatics, vol. 5, no. 2,
pp. 377-386, 2013.
[Google Scholar] [Publisher Link]
[10] J. Mahanta, and P.K. Das, “Results on Fuzzy Soft Topological Spaces,” arXiv, pp. 1-11, 2012.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Alaa Mohamed Abd El-latif, “Characterizations of Fuzzy Soft Pre Separation Axioms,” Journal of New Theory, no. 7, pp. 47-63, 2015.
[Google Scholar] [Publisher Link]
[12] Ahu Açıkgöz, and Nihal Taş, “Binary Soft Set Theory,” European Journal of Pure and Applied Mathematics, vol. 9, no. 4, pp. 452-463,
2016.
[Google Scholar] [Publisher Link]
[13] Shivanagappa S. Benchalli et al., “On Binary Soft Topological Spaces,” International Journal of Applied Mathematics, vol. 30, no. 6, pp.
437-453, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[14] P.G. Patil, and Nagashree N. Bhat, “New Separation Axioms in Binary Soft Topological Spaces,” Italian Journal of Pure and Applied
Mathematics, vol. 44, pp. 775-783, 2020.
[Google Scholar] [Publisher Link]
[15] Sabir Hussain, “Binary Soft Connected Spaces and an Application of Binary Soft Sets in Decision Making Problem,” Fuzzy Information
and Engineering, vol. 11, no. 4, pp. 506-521, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[16] P.G. Metilda, and D.J. Subhashini, “Remarks on Fuzzy Binary Soft Set and Its Characters,” Proceedings of International Conference on
Materials And Mathematical Sciences, 2020.
[Google Scholar]
[17] P. Gino Metilda, and J. Subhashini, “Fuzzy Binary Soft Topological Spaces,” GIS Science Journal, vol. 8, no. 1, pp. 455-465, 2021.
[Publisher Link]
[18] P.G. Patil, Vyshakha Elluru, and S. Shivashankar, “A New Approach To MCDM Problems by Fuzzy Binary Soft Sets,” Journal of Fuzzy
Extension and Applications, vol. 4, no. 3, pp. 207-216, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
P.G. Patil, C Jaya Subba Reddy, Rani Teli, Vyshakha Elluru, "New Structures in Fuzzy Binary Soft Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 4, pp. 55-60, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I4P106
PDF 
Abstract 
Keywords 
References 
Citation