N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems

Nuray Gul; Cemal Sarı

doi:10.17798/bitlisfen.1699048

N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems

Abstract

This study explores the topological structure of N-soft sets and introduces the concept of N-soft homeomorphism as a formal mechanism for preserving structural integrity in multi-criteria decision-making systems. Building upon the theoretical foundations of N-soft topology, we rigorously define continuity, interior, closure, and establish equivalences for N-soft continuity and homeomorphism. We further present a novel application of N-soft homeomorphism in the context of healthcare prioritization, using BRFSS data for U.S. adults aged 35–44. By constructing N-soft topological spaces under both equal-weighted and priority-weighted scoring models for indicators such as fruit intake, vegetable intake, physical activity, and obesity, we demonstrate that the resulting decision spaces are N-soft homeomorphic. This topological equivalence ensures that consistent decision structures are maintained even as evaluation priorities shift. The findings underscore the robustness and flexibility of N-soft topology-based frameworks for dynamic decision-making environments.

Keywords

Ethical Statement

The study is complied with research and publication ethics.

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Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Authors

Nuray Gul ^*
0000-0003-3382-2310
Türkiye

Cemal Sarı
0009-0004-7451-7325
Türkiye

Publication Date

December 31, 2025

Submission Date

May 14, 2025

Acceptance Date

December 7, 2025

Published in Issue

Year 2025 Volume: 14 Number: 4

DOI

https://doi.org/10.17798/bitlisfen.1699048

IZ

https://izlik.org/JA78ZM89ZC

Cite

RIS / Bibtex

APA

Gul, N., & Sarı, C. (2025). N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 14(4), 2081-2100. https://doi.org/10.17798/bitlisfen.1699048

AMA

1.Gul N, Sarı C. N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2025;14(4):2081-2100. doi:10.17798/bitlisfen.1699048

Chicago

Gul, Nuray, and Cemal Sarı. 2025. “N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 14 (4): 2081-2100. https://doi.org/10.17798/bitlisfen.1699048.

EndNote

Gul N, Sarı C (December 1, 2025) N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 14 4 2081–2100.

IEEE

[1]N. Gul and C. Sarı, “N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 14, no. 4, pp. 2081–2100, Dec. 2025, doi: 10.17798/bitlisfen.1699048.

ISNAD

Gul, Nuray - Sarı, Cemal. “N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 14/4 (December 1, 2025): 2081-2100. https://doi.org/10.17798/bitlisfen.1699048.

JAMA

1.Gul N, Sarı C. N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2025;14:2081–2100.

MLA

Gul, Nuray, and Cemal Sarı. “N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 14, no. 4, Dec. 2025, pp. 2081-00, doi:10.17798/bitlisfen.1699048.

Vancouver

1.Nuray Gul, Cemal Sarı. N-Soft Topological Structures and Homeomorphisms: A Framework for Uncertainty in Multi-Criteria Systems. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2025 Dec. 1;14(4):2081-100. doi:10.17798/bitlisfen.1699048