N -hypersoft Topology: A Unified Approach for Multi-criteria Group Decision-making

This manuscript introduces N -hypersoft topology ( N -HST), an innovative extension of the established hypersoft topology (HST). Unlike its predecessor, the N -hypersoft ( N -HS) set, N -HST adopts a multi-opinion approach to decision-making, enhancing robustness and adaptability across various domains. In addressing limitations observed in N -soft topology ( N -ST), particularly in handling multi-argument approximate functions, N -HST offers a comprehensive framework. The study delves into various operators within the N -HST framework, including closure, interior, exterior, and boundary operators, elucidating their interrelationships and providing a deeper understanding of the structural components. Furthermore, this manuscript explores the practical implications of N -HST in multi-criteria group decision-making (MCGDM), showcasing its applicability in real-world decision scenarios. In addition to its specific applications in MCGDM, N -HST offers generic aspects that contribute to its versatility and efficacy in decision-making processes. By accommodating multiple opinions and handling complex evaluation factors, N -HST emerges as a superior framework for addressing diverse decision-making challenges. Through a numerical example, this manuscript demonstrates the practical utility and potential impact of N -HST in various domains.