INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS

R. Narmada Devi; Yamini Parthiban; Raman Sundareswaran

INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS

Abstract

The significance of Neutrosophic environments continues to grow across various disciplines through ongoing advancements. A notable recent development is the Neutrosophic Over Soft Modal Topological Structure ($\mathcal{N}_{\mathfrak{s}}^{\mathfrak{o}}$-topology), which integrates Neutrosophic topological operations $\boxplus$ (closure) and $\boxdot$ (interior) with modal operations $\logof$ (modal closure) and $\astrosun$ (modal interior). This work introduces two such structures for the first time, detailing their core properties and addressing challenges related to uncertainty and indeterminacy. Key concepts developed include Neutrosophic Over Soft Modal $\alpha$ closed, $\alpha g$ closed, and $\alpha^{\mathfrak{m}}$ closed sets, along with various forms of continuity such as modal $\alpha^{\mathfrak{m}}$ and strong continuity. A real-life application is presented for selecting the best cancer hospital using cosine correlation on Neutrosophic Over Sets, demonstrating the practicality and strength of the proposed framework.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Logic, Set Theory, Lattices and Universal Algebra, Topology

Journal Section

Research Article

Authors

R. Narmada Devi ^*
0000-0001-6472-3003
India

Yamini Parthiban
0009-0001-8802-129X
India

Raman Sundareswaran
0000-0002-0439-695X
India

Publication Date

July 4, 2026

Submission Date

April 11, 2025

Acceptance Date

August 5, 2025

Published in Issue

Year 2026 Volume: 16 Number: 7

IZ

https://izlik.org/JA49XP55ZS

Cite

RIS / Bibtex

APA

Devi, R. N., Parthiban, Y., & Sundareswaran, R. (2026). INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS. TWMS Journal of Applied and Engineering Mathematics, 16(7), 837-852. https://izlik.org/JA49XP55ZS

AMA

1.Devi RN, Parthiban Y, Sundareswaran R. INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS. JAEM. 2026;16(7):837-852. https://izlik.org/JA49XP55ZS

Chicago

Devi, R. Narmada, Yamini Parthiban, and Raman Sundareswaran. 2026. “INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS”. TWMS Journal of Applied and Engineering Mathematics 16 (7): 837-52. https://izlik.org/JA49XP55ZS.

EndNote

Devi RN, Parthiban Y, Sundareswaran R (July 1, 2026) INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS. TWMS Journal of Applied and Engineering Mathematics 16 7 837–852.

IEEE

[1]R. N. Devi, Y. Parthiban, and R. Sundareswaran, “INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS”, JAEM, vol. 16, no. 7, pp. 837–852, July 2026, [Online]. Available: https://izlik.org/JA49XP55ZS

ISNAD

Devi, R. Narmada - Parthiban, Yamini - Sundareswaran, Raman. “INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS”. TWMS Journal of Applied and Engineering Mathematics 16/7 (July 1, 2026): 837-852. https://izlik.org/JA49XP55ZS.

JAMA

1.Devi RN, Parthiban Y, Sundareswaran R. INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS. JAEM. 2026;16:837–852.

MLA

Devi, R. Narmada, et al. “INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 7, July 2026, pp. 837-52, https://izlik.org/JA49XP55ZS.

Vancouver

1.R. Narmada Devi, Yamini Parthiban, Raman Sundareswaran. INCORPORATION OF $\alpha^{\mathfrak{m}}$ CLOSED SETS OF NEUTROSOPHIC OVER SOFT MODAL TOPOLOGICAL STRUCTURES FOR REVOLUTIONIZING HOSPITAL RANKING WITH NUMERICAL INSIGHTS. JAEM [Internet]. 2026 Jul. 1;16(7):837-52. Available from: https://izlik.org/JA49XP55ZS