Neutrosophic Semi-Open and Semi-Closed SuperHyperSoft Sets with Application to MAGDM

A. Saranya; A. Kalavathi

doi:https://doi.org/10.14445/22315373/IJMTT-V72I5P111

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 5 | Year 2026 | Article Id. IJMTT-V72I5P111 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I5P111

Neutrosophic Semi-Open and Semi-Closed SuperHyperSoft Sets with Application to MAGDM

A. Saranya, A. Kalavathi

Received	Revised	Accepted	Published
02 Apr 2026	03 May 2026	18 May 2026	30 May 2026

Citation :

A. Saranya, A. Kalavathi, "Neutrosophic Semi-Open and Semi-Closed SuperHyperSoft Sets with Application to MAGDM," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 5, pp. 113-124, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I5P111

Abstract

Neutrosophic Semi-Open SuperHyperSoft Sets (NSOSHS) and Neutrosophic Semi-Closed SuperHyperSoft Sets (NSCSHS) are two new concepts in Neutrosophic SuperHyperSoft Topological Spaces that this paper introduces. Both of these concepts extend the classes of classical hypersoft and neutrosophic theories to include multi-parameterized semi-topological environments. The fundamental properties, characterizations, and structural relations of NSOSHS and NSCSHS are established, as well as their interactions under union, intersection, interior, and closure operations. Additionally, the authors define and study new operators (namely, neutrosophic semi-interior and neutrosophic semi-closure) and their algebraic and topological properties. A number of theorems are proven in this paper to illustrate the theoretical consistency and robustness of the proposed framework for decision-making. Finally, the authors demonstrate the practical application of the developed theory in a Multi-Attribute Group Decision Making (MAGDM) scenario for resource allocation in a smart hospital. Therefore, neutrosophic uncertainty combined with hierarchical parameterization creates a powerful and flexible tool for exploring undetermined and/or inconsistent information in complex decision-making systems.

Keywords

Neutrosophic Sets, Soft Set Theory, Neutrosophic Semi-Open SuperHyperSoft Set (NSOSHS), Neutrosophic Semi-Closed SuperHyperSoft Set (NSCSHS), Neutrosophic SuperHyperSoft Topological Space (NSHSTS).

References

[1] Mumtaz Ali, and Florentin Smarandache, “Complex Neutrosophic Set,” Neural Computing and Applications, vol. 28, pp. 1817-1834, 2017.
[CrossRef] [Google Scholar] [Publisher Link]

[2] Mumtaz Ali, Irfan Deli, and Florentin Smarandache, “The Theory of Neutrosophic Cubic Sets and their Applications in Pattern Recognition,” Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, vol. 30, no. 4, pp.1957-1963, 2016.
[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. Ajay et al., “Neutrosophic Semiopen Hypersoft Sets with an Application to MAGDM under the COVID-19 Scenario,” Journal of Mathematics, vol. 2021, pp. 1-16, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[5] Said Broumi, and Florentin Smarandache, “Intuitionistic Neutrosophic Soft Sets,” Journal of Information & Computational Science, vol. 8, no. 2, pp. 130-140, 2013.
[Google Scholar] [Publisher Link]

[6] Irfan Deli, and Said Broumi, “Neutrosophic Soft Relations and Some Properties,” Annals of Fuzzy Mathematics and Informatics, vol. 9, no. 1, pp. 169-182, 2015.
[Google Scholar] [Publisher Link]

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

[8] A.R. Roy, and P.K. Maji, “A Fuzzy Soft Set Theoretic Approach to Decision Making Problems,” Journal of Computational and Applied Mathematics, vol. 203, no. 2, pp. 412-418, 2007.
[CrossRef] [Google Scholar] [Publisher Link]

[9] 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]

[10] Florentin Smarandache, Neutrosophy: Neutrosophic Probability, Set, and Logic, American Research Press, 1998.
[Google Scholar] [Publisher Link]

[11] Florentin Smarandache, “Extension of Soft Set to Hypersoft Set, and Then to Plithogenic Hypersoft Set,” Neutrosophic Sets and Systems, vol. 22, pp. 168-170, 2018.
[Google Scholar] [Publisher Link]

[12] Haibin Wan et al., Interval Neutrosophic Sets and Logic,Theory and Applications, Hexis, 2010.
[Google Scholar] [Publisher Link]

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