Theory Study Of Solutions On Interval Fuzzy Cooperative Game

In game theory, the research of cooperative game has been always favored by thetheory scholars. The most extensively concerned problem in cooperative game theory ishow to divide the total earnings of the grand coalition if all players cooperate. Varioussolution concepts have been proposed to handle these problems, including core, stable set,Shapley value, and so on, each kind of which satisfies a certain rational behavior andreasonable principle. As an emerging branch of game theory, fuzzy game theory hasattracted many scholars’ interests to research and some research results appeared oneafter another. The purpose of this paper is to extend mature theories of classiccooperative games to fuzzy cooperative games and interval convex compound fuzzygames. It afford theoretic bases for players to select coalitions in the game.Firstly, based on the fuzzy mathematics’s relevant theory, this paper defines core andstable sets of fuzzy cooperative games under fuzzy strategy sets, promotes a series ofproperties if the classic cooperative games, and gives specific proofs.Secondly, combing interval number with fuzzy coopertative game, this paper definesinterval convex compound fuzzy games, and obtained the interval fuzzy stable set andinterval strong ε fuzzy core, and it proves that the interval fuzzy stable set and intervalstrong ε fuzzy core of interval convex compound fuzzy can be expressed by theircorresponding sub-games, finally, some characters and properties of this kinds of stablesets and scores are given.Thirdly, the definition for interval compound cooperative fuzzy game on convexgeometries and the interval Shapley on convex geometries satisfies axiomatic system isgiven. The existence and uniqueness of interval Shapley on convex geometries is studiedand proved by mentioned above axiomatic system.