Double Valued Neutrosophic Soft Topologies with Cotangent Similarity Analytics for Real Time Target Identification

Abstract

In this study, Double Valued Neutrosophic Soft Sets (DNSSs) are examined. Basic operations are provided with examples. Based on this set, Double-Valued Neutrosophic Soft Topological Spaces (DNSTSs) are introduced. Basic operations are studied, and theorems are presented. For better understanding, examples are provided. Additionally, this study examines the analysis of Cotangent Similarity Measure (Cot SM) scores between signal samples (S₁ − S₄) and class templates (T₁ − T₄), focusing on their effectiveness in real-time military target identification. The Cot SM values quantify the alignment between signals and predefined templates, facilitating target classification by indicating the strength of the match. Higher Cot SM values (e.g., > 0.85) suggest a high degree of similarity, implying an immediate engagement decision, while lower values indicate weaker matches, requiring further verification. Various visualization techniques, including Heatmaps, Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), and 3D plots, are used to represent the correlations and patterns within the data. These methods visually showcase the strength and direction of signal-template relationships, with a specific emphasis on identifying strong matches and distinguishing weak correlations. PCA and t-SNE are employed to reduce dimensionality, enabling the clear identification of clusters and outliers. The Elbow Method optimizes clustering, ensuring effective partitioning of the data. The analysis identifies the strongest matches, such as template T₁ with class C₄, and provides a comprehensive view of the data's structure. This framework improves target classification and decision-making by providing a quantitative, visual, and efficient method for prioritizing actions in military contexts. The techniques and tools presented also offer broader applications in fields such as biomedical diagnostics and disaster management.