Profit Allocations for Restricted Coalition With Hesitation Degrees in Cooperative Game Theory

Profit allocation plays an important role in the decision-making field. In this paper, we study an allocation method on restricted coalition cooperation with intuitionistic fuzzy coalitions, in which the partners have some hesitation degree and different risk preferences when they participate in a limited communication structure game. In order to sufficiently analyze the profit allocation strategy, an average tree solution (A-T solution) with Choquet integrals and hesitation degrees is studied. In particular, a simple solving method for the A-T solution is proposed by proving that the characteristic functions of the cooperative game satisfy the monotonicity condition. Using this method, the upper and lower bounds of the A-T solution can be calculated directly from the upper and lower bounds of the interval characteristic functions. This method avoids the subtraction of interval numbers. Furthermore, the properties of the A-T solution according to an axiomatic system are proved in this paper. Finally, the applicability and superiority of the proposed approach are demonstrated through comparison with other methods.