Integral Representations of Cooperative Game with Fuzzy Coalitions

Abstract EN

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.