This paper proposes the H-average tree solution based on a graph game with fuzzy characteristic function. This solution is a generalization of the classical average tree solution, and is an imputation of a graph game with fuzzy characteristic function. When the game is cycle-free the H-average tree solution is the unique solution that satisfies component efficiency and component fairness. The interval average tree solution is introduced. Furthermore, we show the relationship between the H-average tree solution and the interval average tree solution. A practical application of the proposed model in outsource production is given.
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