Artificial Intelligence Enhanced Framework for Complex Double Valued Neutrosophic Soft Sets and Emotional Affinity Evaluation via Cotangent Similarity

Abstract

This work introduces a novel hybrid emotion signal/template mapping system that combines the artificial intelligence (AI) validation layer with complex two-valued neutrosophic soft sets (DNSS). Next, by describing a comprehensive DNSS topology, fundamental operations, and properties, we create a rigorous mathematical foundation. Its analytical center measures emotional alignment using a Cotangent Similarity Measure (Cot SM), which shows a discernible hierarchy of connectedness between signal channels (S1 − S4) and emotional foci (T1 − T4). The multi-method visualization displays a hierarchy between cases of absolute dissonance (T2S4: 0.1431) and strong and stable pairs (e.g., T2S3: 0.3776). To guarantee the consistency of the paradigms, a nonlinear verification technique was implemented using an Artificial Neural Network (ANN). Strong performance metrics (Precision = 0.86, Recall = 0.83, F1-Score = 0.84, ROC-AUC = 0.91) verified that ANN was able to replicate the analytical hierarchy. The integration of the symbolic cotangent model with numerical ANN validation demonstrates statistical consistency and structural harmony across computation domains. In order to establish a repeatable paradigm of affective computing and quantification of uncertainty in emotional connections, this research presents a theoretically and AI-checkable model of emotional analytic.