Research On Profit Allocation Of Cooperative Enterprises With Intuitionistic Fuzzy Coalitions

The market competition is becoming increasingly fierce. With limited resources, enterprises can hardly adapt to complex competitive environment on their own. They need cooperation with each other to enhance competitiveness. Enterprise coalitions are formed when enterprises have relation based on the contract to seek profit. The key of the formation for enterprise coalitions is the reasonable allocation of the profit.The profit allocation is the result of games between enterprises in the coalitions. It can be viewed as a kind of cooperative games. Much research has been made to use classical cooperative games or fuzzy cooperative games to allocate profit in the enterprise coalitions. In classical cooperative games, the players either fully participate in a specific coalition or fully out of it, which means that the rate of the participation of each player in a coalition is 1 or 0. In fuzzy cooperative games, the players can partly participate in a specific coalition, which means that the rate of the participation of each player in a coalition is between o and 1. However, in most real-world situations, the players may partly participate in a specific coalition, at the mean time, partly out of the coalition. Namely, players have a degree of hesitancy for participating in a specific coalition.With the observation mentioned above in mind, this paper conducts research on making use of intuitionistic fuzzy cooperative games to allocate profit among partners in enterprise coalitions, including cooperative games with intuitionistic fuzzy coalitions and cooperative games with intuitionistic fuzzy coalitions and fuzzy payoffs.Firstly, this paper studies the profit allocation in the situation that the parters have a degree of membership and a degree of nonmembership of enterprise coalitions, assuming that at the very beginning of the games, the players know exactly the expected profit. This problem can be viewed as a cooperative game with intuitionistic fuzzy coalitions. Based on the analysis of classical cooperative games and fuzzy cooperative games with real number typed payoffs, this paper introduces Shapley value of cooperative games with intuitionistic fuzzy coalitions by the use of intuitionistic fuzzy set theory, Choquet integral and continuous ordered weighted average operator. It is also proven that the defined Shapley value satisfies three axioms, which are similar to those of the Shapley value of the classical cooperative games. Then we apply the defined Shapley value to solve the problem of profit allocation in intuitionistic fuzzy enterprise coalitions. Secondly, on the basis of the aforementioned research, we made a further discussion about cooperative games with intuitionistic fuzzy coalitions and fuzzy payoffs. We transfers cooperative games with intuitionistic fuzzy coalitions and payoffs of interval-valued fuzzy sets (i.e., intervals) to cooperative games with intuitionistic fuzzy coalitions and real number typed payoffs by using the continuous ordered weighted average operator. In some confidence level, we transfers cooperative games with intuitionistic fuzzy coalitions and triangular fuzzy number typed payoffs to cooperative games with intuitionistic fuzzy coalitions and real number typed payoffs by using the continuous ordered weighted average operator and the concept of cut sets. Then, we can obtain the Shapley value for intuitionistic fuzzy cooperative games with fuzzy payoffs, which can be used to allocate profit of enterprise coalitions.