## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2014, Special Issue (2013), Article ID 231508, 13 pages.

### The Shapley Values on Fuzzy Coalition Games with Concave Integral Form

#### Abstract

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.

#### Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 231508, 13 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.jam/1395855225

Digital Object Identifier
doi:10.1155/2014/231508

Mathematical Reviews number (MathSciNet)
MR3166755

Zentralblatt MATH identifier
07010574

#### Citation

Pang, Jinhui; Chen, Xiang; Li, Shujin. The Shapley Values on Fuzzy Coalition Games with Concave Integral Form. J. Appl. Math. 2014, Special Issue (2013), Article ID 231508, 13 pages. doi:10.1155/2014/231508. https://projecteuclid.org/euclid.jam/1395855225

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