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

Abstract

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.