Bi-coalitions analysis in the rough sets conflict model

This paper introduces a novel framework for conflict analysis based on rough set theory, extending Pawlak’s classical model. We introduce the concept of bi-coalitions, defined as groups of agents that fully agree on a subset of issues. Unlike traditional alliance relations, bi-coalitions are constructed without reliance on numerical thresholds, enabling a crisp and interpretable representation of consensus. The paper proposes an algorithm for identifying bi-coalitions using an indiscernibility matrix. To quantify coalition coherence, we introduce two strength measures with optional weighting of issues to reflect domain-specific relevance. Furthermore, we develop a negotiation algorithm guiding the system toward consensus or stable partitions. The proposed model is empirically validated on two real-world conflict scenarios: the 2023 parliamentary elections in Poland and the Middle East geopolitical situation. These case studies demonstrate the model’s ability to uncover interpretable coalition structures and support dynamic consensus-building. • A novel definition of coalitions (bi-coalitions) and coalition strength evaluation. • An algorithm to infer bi-coalitions based on indiscernibility matrix. • The negotiation algorithm for finding the consensus in the conflict situation based on the conflict value between bi-coalitions. • Practical examples demonstrating the application of the proposed solutions.