Theory Study And Application Of The Solutions Of Fuzzy Games With Fuzzy Payoffs

In game theory, solutions of cooperative game have been always a research focus.The most extensively concerned problem in cooperative game theory is how to divide thetotal earnings of the grand coalition if all players cooperate. Various solution conceptshave been proposed to handle these problems, including core, stable set, Shapley value,and so on, each kind of which satisfies a certain rational behavior and reasonable principle.As an emerging modle of game theory, fuzzy cooperative game theory has attracted manyscholars' interests since since it emerged, some research results appeared one after another.The purpose of this paper is to extend mature theories of classic cooperative games tointerval convex compound fuzzy games, interval fuzzy cooperative games with Choquetintegral form, and n-persons games with interval worth based on Choquet extension, Itafford theoretic bases for players to select coalitions in the game.Firstly, this paper proposes the Shapley function for fuzzy cooperative games withmultilinear extension, then it defines interval convex compound fuzzy games, andobtained the interval fuzzy stable set and interval strong ε fuzzy core, and it proves thatthe interval fuzzy stable set and interval strong ε fuzzy core of interval convexcompound fuzzy can be expressed by their corresponding sub-games, then the intervalBanzhaf-Coleman index of the interval fuzzy game is gained.Secondly, by means of Choquet integral, a class of fuzzy cooperative game withinterval payoffs and interval fuzzy coalitions-fuzzy cooperative game is defined, then theinterval fuzzy payoff of it is given. When the game is fuzzy convex, we obtained that theinterval fuzzy core is non-empty. Furthermore, an explicit formula of the interval fuzzycore is given. Furthermore, the Shapley value of the interval fuzzy games with Choquetintegral is studied.Finally, we introduce the three axioms and the formula of the Shapley value for fuzzycooperative games with Choquet integral. Meanwhile, according to axioms system, thepaper investigated and proved the existence and uniqueness of the Shapley value ofn-persons games with interval worth based on Choquet extension from another perspective, then an explicit formula of the Shapley value is gained.