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

Year 2025, Volume: 14 Issue: 4, 2081 - 2100, 31.12.2025

Nuray Gul , Cemal Sarı

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

https://izlik.org/JA78ZM89ZC

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

N-soft set , N-soft homeomorphism , healthcare prioritization , topological decision model , BRFSS , multi-criteria decision-making.

Ethical Statement

The study is complied with research and publication ethics.

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