Plithogenic Hesitant Fuzzy Soft Topological Spaces

J. Jayasudha; R.Nishanthi

doi:https://doi.org/10.14445/22315373/IJMTT-V72I6P104

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 6 | Year 2026 | Article Id. IJMTT-V72I6P104 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I6P104

Plithogenic Hesitant Fuzzy Soft Topological Spaces

J. Jayasudha, R.Nishanthi

Received	Revised	Accepted	Published
23 Apr 2026	29 May 2026	15 Jun 2026	29 Jun 2026

Citation :

J. Jayasudha, R.Nishanthi, "Plithogenic Hesitant Fuzzy Soft Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 6, pp. 31-39, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I6P104

Abstract

This present study introduces Plithogenic hesitant fuzzy soft (P-HFS) topological spaces, a new framework that combines Plithogenic sets, hesitant fuzzy sets, and soft set theory to model uncertainty with attribute-based contradictions. The authors define the basic structure of a Plithogenic hesitant fuzzy soft topological space and develop their topological properties. Additionally, several classical topological concepts are extend to this setting, including P-HFS open sets, P-HFS closed sets, P-HFS interior, P-HFS closure, P-HFS subspace topology, P-HFS basis, and P-HFS product topology. Furthermore, a number of theorems are established to demonstrate the theoretical consistency, validity, and robustness of the proposed framework.

Keywords

Hesitant Fuzzy Soft Set, Hesitant Fuzzy Soft topological space, Plithogenic Hesitant Fuzzy Soft Set, Plithogenic Hesitant Fuzzy Soft topological space.

References

[1] Lotfi A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
[CrossRef] [Google Scholar] [Publisher Link]

[2] C.L. Chang, “Fuzzy Topological Spaces,” Journal of Mathematical Analysis and Applications, vol. 24, no. 1, pp. 182-190, 1968.
[CrossRef] [Google Scholar] [Publisher Link]

[3] Krassimir T. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
[CrossRef] [Google Scholar] [Publisher Link]

[4] D. Molodtsov, “Soft Set Theory - First Results,” Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31, 1999.
[CrossRef] [Google Scholar] [Publisher Link]

[5] P.K. Maji, R. Biswas, and A.R. Roy, “Fuzzy Soft Sets,” Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 589-602, 2001.
[Google Scholar]

[6] P.K. Maji, R. Biswas, and A.R. Roy, “Soft Set Theory,” Computers and Mathematics with Applications, vol. 45, no. 4-5, pp. 555-562, 2003.
[CrossRef] [Google Scholar] [Publisher Link]

[7] Florentin Smarandache, “Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Sets,” International Journal of Pure and Applied Mathematics, vol. 24, pp. 287-297, 2005.
[Google Scholar]

[8] Vicenc Torra, and Yasuo Narukawa, “On Hesitant Fuzzy Sets and Decision,” 2009 IEEE International Conference on Fuzzy Systems, Jeju, Korea, pp. 1378-1382, 2009.
[CrossRef] [Google Scholar] [Publisher Link]

[9] Vicenç Torra, “Hesitant Fuzzy Sets,” International Journal of Intelligent Systems, vol. 25, no. 6, pp. 529-539, 2010.
[CrossRef] [Google Scholar] [Publisher Link]

[10] Meimei Xia, and Zeshui Xu, “Hesitant Fuzzy Information Aggregation in Decision Making,” International Journal of Approximate Reasoning, vol. 52, no. 3, pp. 395-407, 2011.
[CrossRef] [Google Scholar] [Publisher Link]

[11] Sujit Das, and Samarjit Kar, “The Hesitant Fuzzy Soft Sets and Its Application in Decision-Making,” Facts of Uncertainties and Applications, pp. 235-247, 2015.
[CrossRef] [Google Scholar] [Publisher Link]

[12] A. Sreedevi, and N.R. Shankar, “Key Properties of Hesitant Fuzzy Soft Topological Spaces,” International Journal of scientific Engineering and Research, vol. 7, no. 2, pp. 149-156, 2016.
[Google Scholar]

[13] Florentin Smarandache, Plithogeny, Plithogenic Set, Logic, Probability, and Statistics, Pons Editions, Brussels, Belgium, 2017.
[Google Scholar] [Publisher Link]

[14] D. Deepak et al., “A Topological Structure Involving Hesitant Fuzzy Sets,” Journal of Intelligent Fuzzy Systems, vol. 36, no. 6, pp. 6401-6412, 2019.
[CrossRef] [Google Scholar] [Publisher Link]

[15] Muhammad Riaz et al., “Hesitant Fuzzy Soft Topology and its Applications to Multi-Attribute Group Decision-Making,” Soft Computing, vol. 24, pp. 16269-16289, 2020.
[CrossRef] [Google Scholar] [Publisher Link]

[16] Shawkat Alkhazaleh, “Plithogenic Soft Set,” Neutrosophic Sets and Systems, vol. 33, no. 1, pp. 256-274, 2020.
[Google Scholar] [Publisher Link]