Abstract

In this chapter, the model of graph games with fuzzy coalitions is proposed based on graph games and cooperative games with fuzzy coalitions. The fuzzy average tree solution of graph games with fuzzy coalitions is given, which can be regarded as the generalization of crisp graph games. It is shown that the fuzzy average tree solution is equal to the fuzzy Shapley value for complete graph games with fuzzy coalitions. We extend the notion of link-convexity, under which the fuzzy core is non-empty and the fuzzy average tree solution lies in this core.

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