The Solutions On A Class Of Interval Fuzzy Cooperative Game

In the game theory, cooperative game became a research focus inacademia since it was put forward. The most extensively concerned problemin cooperative game theory is how to divide the total earnings with fair andreasonable. Various solution concepts have been proposed to handle thisproblem, including core, stable set, Shapley value and so on, each kind ofwhich satisfies a certain rational behavior and reasonable principle. As anemerging branch of game theory, fuzzy game theory has attracted manyscholar’s interests since the last70’s. Recently interval fuzzy cooperationgame as a new branch of game theory, scholars also conduct researches onvarious aspects of interval fuzzy cooperation game. Interval fuzzycooperation game has been extensively studied by many scholars, and somesignificant results has obtained.The purpose of this paper is to extend mature theories of classiccooperative games to interval fuzzy cooperative games by expanding thedefinition of classic cooperative games. By the use of Choquet integral, theestablishment of a Choquet integral form of interval fuzzy cooperation gamemodel. It affords theoretic bases for players to select coalitions in the game. This paper firstly established Choquet integral form of the intervalfuzzy cooperation game model, defines the interval strongε core, and givesthis kind of core of some of the characteristics and properties, and this be theproof. To study interval fuzzy game have the certain reference value.Secondly, this paper introduces the interval fuzzy core, interval Shapleyvalue and the relationship between them of interval fuzzy cooperation gameon the convex geometry. By use of Choquet integral, structure Choquetintegral form with the interval value fuzzy cooperation game model on theconvex geometry. This paper gives the definition of the interval fuzzy coreand interval Shapley function, and prove the existence and uniqueness.Finally, this paper based on the classic cooperation game, thepromotion of the nation of Banzhaf function in the classical cooperationgame. The author has define function definition of Banzhaf in Choquetintegral form of interval fuzzy cooperation game, discussed the existenceand the uniqueness of the function of Banzhaf, and discussed some of theirrelated properties.