Abstract: The solution to the cooperative games with fuzzy coalitions is researched based on the uncertainty of the coalition formation in reality. A new imputation method for cooperative games with fuzzy coalitions, namely the equal allocation solution, is defined. The sufficient condition of the equivalence between this solution and Shapley value for cooperative games with fuzzy coalitions is put forward in this paper. Finally, the property of Shapley value is also discussed. Meanwhile, an numerical example for this is given in the paper.

Key words: operational research, cooperative games, Shapley value, fuzzy coalitions

摘要： 针对现实环境中联盟组成的不确定性, 本文研究了具有模糊联盟的合作对策求解问题。提出了模糊联盟合作对策的一种新的分配方式,即平均分摊解,并给出了这种解与模糊联盟合作对策Shapley值一致的充分条件。同时,还提出了模糊联盟合作对策的Shapley值的一个重要性质。最后,结合算例进行了分析论证。

关键词: 运筹学, 合作对策, Shapley值, 模糊联盟