Complex Neutrosophic Soft Topology with Multivariate Analysis: A Unified Framework for Signal-Template Relationships

Abstract

A novel theoretical method based on the topological formulation of complex neutrosophic soft sets (CNSS) is presented in this work. We go on to provide a thorough one-value complex neutrosophic soft topology, defining the most important topological properties such as interior, closure, and other related theoretical concerns, in order to give a strong mathematical foundation. An example is then provided to illustrate this frameworks analytical capabilities. To ensure a thorough empirical validation  of this paradigm, we employ a multifaceted approach that combines PCA, clustering, and manifold learning. Everyone agreed that a clear target hierarchy should be established, even though we employed a variety of analytical methodologies. In this hierarchy, T1 was consistently described as the most stable and representative target, T2 as a transitional outlier, and T3 as the most divergent target. In its most basic form, multivariate analysis and topological theory o er a versatile framework for clarifying the connections between templates and signals while avoiding the drawbacks of over-methodologization.