Optimized Formula for Distributing Coalition Worth in n-Person Fuzzy Cooperative Games

Marwa Mostafa Sabry, Assem Tharwat and Ihab El-Khodary

In this paper, an optimized general formula for distributing gains of fuzzy cooperative players, fuzzy coalitions, is proposed. The game is characterized by a fuzzy characteristic function. The formula is derived from a linear multi-objective optimization model for fuzzy cooperative games developed earlier. In the developed model, players do not need to know precise information about the payoff value or even to form a crisp coalition. The optimality of the proposed formula is proved and the properties are verified. The formula is applied to a joint production problem for the purpose of validation and the obtained results are compared with Shapley value for solving fuzzy games. The proposed formula has the advantage of being easier and of less computational effort when compared to applying Shapley value.

DOI : https://doi.org/10.21102/wjm.2017.03.81.07