Theory Study Of Several Solutions On Compound Fuzzy Cooperative Games

In game theory, The research of cooperative game have been always favored byscholars. The most extensively concerned problem in cooperative game theory is howto divide the total earnings with fair and reasonable. Various solution concepts havebeen proposed to handle this problem, including core, stable set, Shapley value and soon, each kind of which satisfies a certain rational behavior and reasonable principle.As an emerging branch of game theory, fuzzy game theory has attracted manyscholars' interests to research and some research results appeared one after another.The purpose of this paper is to extend mature theories of classic cooperative games tofuzzy cooperative games and convex compound fuzzy games by revising andperfecting, It afford theoretic bases for players to select coalitions in the game. So ithas biggish applied value and it avoid unnecessary loss because of failure in selectingcoalition.Firstly, a new generalization for τ value of the fuzzy cooperative games isdefined, on the base of two kinds of models of fuzzy cooperative games withgenerlized characteristic functions which are defined by Nowak and Radzik. It is basedon the coalition of fuzzy game and τ value. The new generalization for τ valuecontains the efficiency property, restricted proportionality property and so on. Thenaxiomatic characterizations are found for τ value using characteristical of the abovementioned.Secondly, the definition for interval compound cooperative fuzzy game on convexgeometries and the interval Shapley on convex geometries satisfies axiomatic systemis given. The existence and uniqueness of interval Shapley on convex geometries isstudied and proved by mentioned above axiomatic system.Finally, a new model of convex compound fuzzy game that the characteristicfunction and player involvement are based on triangular fuzzy number is given.On thebase of this model, the triangular core and triangular stable set of convex compoundfuzzy game is given and proved them can be expressed by their corresponding subgame.