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

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.

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