A Fuzzy-SNA Computational Framework for Quantifying Intimate Relationship Stability and Social Network Threats

Intimate relationship stability is fundamental to human wellbeing, yet its quantitative assessment faces dual challenges: the inherent subjectivity of psychological constructs and the complexity of social ecosystems. Symmetry, as a fundamental structural feature of social interaction, plays a pivotal role in shaping relational dynamics. To address these limitations, this study proposes an innovative computational framework that integrates Fuzzy Set Theory with Social Network Analysis (SNA). The framework consists of two complementary components: (1) a psychologically grounded fuzzy assessment model that employs differentiated membership functions to transform discrete subjective ratings into continuous and interpretable relationship quality indices and (2) an enhanced Fuzzy C-Means (FCM) threat detection model that utilizes Weighted Mahalanobis Distance to accurately identify and cluster potential interference sources within social networks. Empirical validation using a simulated dataset—comprising typical characteristic samples from 10 couples—demonstrates that the proposed framework not only generates interpretable relationship diagnostics by correcting biases associated with traditional averaging methods, but also achieves high precision in threat identification. The results indicate that stable relationships exhibit greater symmetry in partner interactions, whereas threatened nodes display structural and behavioural asymmetry. This study establishes a rigorous mathematical paradigm—“Subjective Fuzzification → Multidimensional Feature Engineering → Intelligent Clustering”—for relationship science, thereby advancing the field from descriptive analysis toward data-driven, quantitative evaluation and laying a foundation for systematic assessment of relational health.