Abstract: From the viewpoint of coalition payoff allocation, the definition of T-coalition is employed. The axioms of T-coalition Shapley value have been proposed. The explicit form of T-coalition Shapley value has also been given, which can be served as the payoff of the whole coalition. The fair axioms of T-coalition are an extension of crisp axioms, and the explicit form of T-coalition Shapley value is also an extension of crisp Shapley value. The properties of the T-coalition Shapley function are discussed. The condition that the cooperative game accepts the partnership is also proposed. This allocation method allows the players to participate the grand allocation in partnership form. Hence, the T-coalition Shapley function can help players to choose cooperative form. Finally, an illustrative example has been given in order to show the decision process based on T-coalition Shapley function.

Key words: Cooperative game, Shapley value, Dummy coalition, Partnership coalition, T-coalition