Abstract
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.
Highlights
Research into cooperative games is based mainly on the hypothesis of arbitrary coalitions being formed
We study the restricted coalition cooperative game with intuitionistic fuzzy coalitions which satisfies the monotonicity condition and proposes a corresponding A-T solution based on Choquet integrals
There are two important contributions: (1) we combining the idea of intuitionistic fuzzy coalitions and the restricted coalition cooperative games to study the fuzzy profit allocation problem. (2) due to the interval subtraction is complex, and is not invertible in the compute process, we propose a simple method for the A-T solution by proving that the characteristic functions of the cooperative game satisfy the monotonicity condition
Summary
Research into cooperative games is based mainly on the hypothesis of arbitrary coalitions being formed. We study the restricted coalition cooperative game with intuitionistic fuzzy coalitions which satisfies the monotonicity condition and proposes a corresponding A-T solution based on Choquet integrals. ΜS (i) describes a real number in the interval [0, 1], and the cooperative game with fuzzy coalitions [0, 1]n, the essence is still a crisp number It shows that there is no uncertain information, let alone players’ hesitation degrees. The restricted coalition cooperative games with intuitionistic fuzzy coalitions is denoted G , and the entirety of Gis denoted Gn. This paper discusses the most common cooperative game, which satisfies general properties of convexity and super additivity. Definition 6: Let (N , v, L) be a restricted coalition cooperative game with intuitionistic fuzzy coalitions, it is called super-additive if it satisfies v(S ∪ T ) ≥ v(S ) + v(T ). It is clear that the participation degree of player i is ηS (i) ⊆ [0, 1]
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