Operations on Complex Neutrosophic Soft Sets and Their Topological Spaces: A New Approach with Applications to Decision-Making

Abstract

This research presents a new theoretical framework and shows how to use it e ectively to  data analysis. First, we introduce a novel method to complex neutrosophic soft sets (CNSS) and ensure the generalize ability of their use by de ning basic operations such as union, intersection, and complement. We go on to construct a complete one-value neutrosophic soft topology, de ning the most important topological properties such as interior, closure, and other related theoretical aspects, to give a strong mathematical foundation. An example is then provided to illustrate this frameworks analytical capabilities. Using a comprehensive visualizing package that includes spline-smoothed functional curves, 3D surface plots, and 2D Heatmaps, we apply our method to address a signal-template alignment problem. The Cotangent Similarity Measure (Cot SM) is used to systematically examine three input signals (S1 S3) and three templates (T1 T3). The ndings are striking and unambiguous: a worldwide maximum indicates a high degree of condence, and the correlation between S2 T1 (CotSM = 06653) is widely recognized as the strongest and most conclusive connection. Subsequent analysis shows that while signal S2 is the most important overall, signals S1 and S3 are helpful for particular targets.