Dual-Weighted Neighborhood Rough Sets for Minimal Winning Coalition Discovery in Online Social Networks

Online social networks increasingly serve as platforms for collective action, yet identifying minimal winning coalitions remains challenging due to heterogeneous user features, noisy behavioral traces, and the strategic ambiguity of swing members. Traditional neighborhood rough set models effectively handle numerical data but typically weight either attributes or objects in isolation, neglecting the joint influence of feature importance and user reliability. Moreover, boundary-region users, often critical for tipping coalition outcomes, are frequently discarded or misclassified by hard-thresholding mechanisms. To bridge these gaps, we propose a Dual-Weighted Neighborhood Rough Set framework, called DWNRS, that combines attribute-weighted neighborhood construction with object-reliability-weighted rough-membership estimation. In this formulation, attribute weights determine the geometry of distance-based neighborhoods, while object weights determine how reliably neighboring users contribute to membership estimation and coalition strength. We formalize dual-weighted rough membership, define lower, boundary, outside, and candidate approximation regions, and introduce a dependency-guided reduction algorithm that extracts coalitions that are winning and inclusion-wise minimal under the induced DWNRS strength function, whenever a winning coalition exists within the allowed candidate pool. Theoretically, we prove that DWNRS generalizes classical neighborhood rough sets and Pawlak rough sets, preserves the monotonicity required by simple games, and provides precise conditions under which boundary recruitment and inclusion-wise minimality hold. We further establish a boundary-change accounting identity that characterizes when and how the boundary region contracts, showing that contraction is a data-dependent empirical effect rather than a universal guarantee. Empirically, we validate the framework on a controlled synthetic benchmark and a semi-real US Congress Twitter interaction network under a fair common-strength evaluation protocol. Against the original non-hybrid baselines, DWNRS is the only method that consistently returns coalitions that are both winning and inclusion-wise minimal. A new GWNRS-style hybrid experiment shows that object-weighted geometric denoising can also produce winning and inclusion-wise minimal coalitions; on the synthetic benchmark, the hybrid obtains a slightly higher mean F1 than DWNRS under the fixed-quota protocol, while on the Congress benchmark both methods bypass boundary recruitment because the core alone is sufficient. These results clarify DWNRS’s distinct role without claiming universal classification superiority over the hybrid: DWNRS preserves a regulated boundary region and the strategic option value of swing-user recruitment in regimes where the core alone may be insufficient. Among the original non-hybrid baselines, DWNRS leads all classification metrics on the Congress topology and produces coalitions 23–35% smaller than the original winning baselines.