The credibility-based cores in games with fuzzy coalitions

In an uncertain game environment, it is usually difficult to solve the least core because the rates of players´ participation must hold for some real number which belong to [0,1]. In addition, available characteristic function sometimes cannot be accurately given either when the rates are allowed to be fuzzy variables. In this paper, fuzzy coalitions, fuzzy characteristic function and fuzzy cores are studied based on the Choquet integral and the credibility measure. A new fuzzy chance-constrained programming model is proposed for solving the least core under a predetermined confidence level, which is also a game decision procedure for generating cores converging to elements of the fuzzy core to meet different confidence level. It is shown that the least core gained by the presented model coincides with Aubin´s core for a specific class of games with fuzzy coalition and reflect the influence rooted in players´ preference. A numerical example is presented to show the model idea and its rational property.