A simplified expression of the Shapley function for fuzzy game

Shujin Li and Qiang Zhang

European Journal of Operational Research, 2009, vol. 196, issue 1, 234-245

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.

Keywords: Cooperative; game; Fuzzy; coalition; Interaction; Shapley; function (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (17)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:196:y:2009:i:1:p:234-245

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