Reserch On The Solutions Of Fuzzy Games With Interval Fuzzy Coalitions

In game theory, cooperative game have been always a research focus. The mostextensively concerned problem in cooperative game theory is how to allocate the profitsof the grand coalition with fair and reasonable. Various solution concepts have beenproposed to handle this problem, including core, stable set, Shapley value, nucleolus andso on. As a emerging branch of game theory, fuzzy cooperative game theory has attractedmany scholars’ interests and some research results have been achieved. The purpose ofthis paper is to extend crisp games, through modify and improve them, to convex fuzzygames through and further to fuzzy cooperative games with interval fuzzy coalition. Thus,it provide theoretical bases for players to select coalitions in the game. This has greatpractical value in real life.First of all, this paper proposes convex fuzzy game and some of its properties, then,through defining the excess of the fuzzy game it proposes the lexicographic order for thefuzzy game, then the definition of the fuzzy nucleolus for the fuzzy cooperative game isobtained. And then the properties of the fuzzy nucleolus for convex fuzzy cooperativegame, such as the existence and uniqueness, are discussed. Moreover, it gives the proofs.Secondly, in this paper, bases of multilinear extension form, n-persons games withinterval fuzzy coalitions with multilinear extension form is defined. Then, the generalizedforms of the core and Shapley value for this n-persons game are given. And, the existenceof this core and the relationship between it and its corresponding core of crisp game areshown. According to axioms system, this paper also investigates the properties of thisShapley value, such as the existence and uniqueness, are discussed and proved. Then, theShapley is applied to an example of profit allocation scheme among company in supplychain coordination.Finally, the model of the fuzzy games with interval fuzzy coalitions on matroids areproposed. Then, we pay more attention to study the Shapley function for static anddynamic fuzzy games with interval fuzzy coalitions on matroids, and the existence anduniqueness of the Shapley functions for these two kinds of matroids are studied and proved by the corresponding axiomatic systems.