A simplified expression of the Shapley function for fuzzy game |
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Authors: | Shujin Li Qiang Zhang |
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Institution: | 1. The Central Institute for Correctional Police, Baoding 071000, China;2. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China |
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Abstract: | In this paper, a simplified expression of the Shapley function for games with fuzzy coalition is proposed, which can be regarded as the generalization of Shapley functions defined in some particular games with fuzzy coalition. The simplified expression of the Shapley function is compared with two definitions established by Butnariu, Tsurumi et al. A conclusion is drawn that the simplified expression of the Shapley function is equivalent to Butnariu’s definition when characteristic function is a game with proportional values, and is equivalent to Tsurumi’s definition when characteristic function is a game with Choquet integral forms. Furthermore, from an angle of interaction between two participation levels, the properties of the two games defined by Butnariu and Tsurumi are respectively studied. |
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Keywords: | Cooperative game Fuzzy coalition Interaction Shapley function |
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