## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2014, Special Issue (2013), Article ID 639684, 9 pages.

### Integral Representations of Cooperative Game with Fuzzy Coalitions

#### Abstract

Classical extensions of fuzzy game models are based on various integrals, such as Butnariu game and Tsurumi game. A new class of symmetric extension of fuzzy game with fuzzy coalition variables is put forward with Concave integral, where players’ expected values are on a partial set of coalitions. Some representations and properties of some limited models are compared in this paper. The explicit formula of characteristic function determined by coalition variables is given. Moreover, a calculation approach of imputations is discussed in detail. The new game could be regarded as a general form of cooperative game. Furthermore, the fuzzy game introduced by Tsurumi is a special case of the proposed game when game is convex.

#### Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 639684, 9 pages.

Dates
First available in Project Euclid: 1 October 2014

https://projecteuclid.org/euclid.jam/1412177643

Digital Object Identifier
doi:10.1155/2014/639684

Mathematical Reviews number (MathSciNet)
MR3178966

Zentralblatt MATH identifier
07010706

#### Citation

Pang, Jinhui; Chen, Xiang. Integral Representations of Cooperative Game with Fuzzy Coalitions. J. Appl. Math. 2014, Special Issue (2013), Article ID 639684, 9 pages. doi:10.1155/2014/639684. https://projecteuclid.org/euclid.jam/1412177643

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