N-SOFT TOPOLOGICAL STRUCTURES AND HOMEOMORPHISMS: A FRAMEWORK FOR UNCERTAINTY IN MULTI-CRITERIA SYSTEMS

Abstract

This study investigates the topological structure of N-soft sets and introduces the notion of N-soft homeomorphism, which serves as a formal tool for preserving structural consistency in multi-criteria decision-making systems. Building upon the existing framework of N-soft topology, the study extends previously established notions such as continuity, interior, and closure to define topological equivalence within this context. We present a novel application of N-soft homeomorphism in the context of healthcare prioritization, using Behavioral Risk Factor Surveillance System data for US 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 decisionmaking environments.