In this paper, a game with coalition structure and fuzzy coalitions is introduced, which can be regarded as an extension of the game with coalition structure. Firstly, an Owen function is defined. Then, the unique explicit form of the Owen function is given by extending the Owen value. Secondly, as an extension of Owen function, a fuzzy Owen function is proposed. In addition, an explicit form of the fuzzy Owen function is given by considering the fuzzy intermediate game with Owen extension form. Finally, an illustrate example is provided to illustrate the allocation method of gains.
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