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Journal of Applied Mathematics
Volume 2014, Article ID 231508, 13 pages
Research Article

The Shapley Values on Fuzzy Coalition Games with Concave Integral Form

1Library, Beijing Institute of Technology, Beijing 100081, China
2Patent Examination Cooperation Center of the Patent Office, State Intellectual Property Office of P.R.C, Beijing 100088, China
3Department of Information Management, The Central Institute for Correctional Police, Baoding 071000, China

Received 15 November 2013; Accepted 15 December 2013; Published 27 January 2014

Academic Editor: Pu-yan Nie

Copyright © 2014 Jinhui Pang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.