Abstract
In this paper, by introducing a degree of satisfaction represented by a fuzzy set for an n-person cooperative game, the game is defined by a three-tuple(N, μ, G), where N is a set of players, μis a membership function of a fuzzy set representing a degree of satisfaction with respect to a payoff and G is the amount of payoff. For the game(N, μ, G)we propose a new solution concept on the basis of the fuzzy decision by Bellman & Zadeh. Then we further consider how to construct the membership functions through characteristic functions υ in a traditional game(N, υ). This means that the game(N, υ)is extended to the game(N, μ, G). When all of the membership functions are linear functions or hyperbolic functions, the proposed solution can be obtained through the formulated linear programming problems respectively. We also consider to adopt one of the five types of membership functions, which include linear, hyperbolic, exponential, hyperbolic inverse and piecewise linear functions, to each coalition. In this case, the proposed solution can be obtained by combined use of the bisection method and the phase one of linear programming. An illustrative numerical example is presented and the proposed solution and the nucleolus which is a related solution concept are compared.
