Core of cooperative fuzzy games with coalition structures

This paper develops an extended model of cooperative fuzzy games with coalition structures, where fuzzy coalitions are characterized by real-valued functions. Moving beyond existing studies on crisp coalition structures, our framework integrates fuzzy set principles with coalitional cooperation to model partial participation in structured games. Our contributions are fourfold: (1) a formal core definition for such games, extending the Aubin core; (2) construction of the superadditive cover and establishment of core non-emptiness conditions; (3) an axiomatic characterization showing the core is the unique solution that satisfies non-emptiness, individual rationality, weak reduced game property, and superadditivity; and (4) a domination-core concept proven equivalent to the conventional core under specific conditions. A concise numerical example validates these theoretical findings, illustrating core allocation, non-emptiness, and the core-cover equivalence in scenarios of partial cooperation. These results unify fuzzy games with structured coalitions, offering new insights into the stability and allocation in games with graded participation and advancing the theory of cooperative decision-making under uncertainty.