Multiobjective N-Players' Partly Cooperation Fuzzy Game With Fuzzy Goals

As a branch of game theory, fuzzy game theory has attracted quite a few scholars' interest since the last 70s' . A few research achievements appeared and mainly introduced fuzzy concepts to strategy sets, payoff matrix, solutions of game, coalition, multiobjects and so on. However, there are few papers that comprehensively involve all the above aspects. A case in point is the problem of some players' partly cooperation fuzzy game with fuzzy multiobjects and fuzzy payoff. Therefore, this paper tries to discuss the problem of some players' partly cooperation with fuzzy multiobjects and fuzzy payoff in the method of fuzzy set theory.For convenience, suppose that each player has the same objects to consider. Firstly, this paper brings forward the concept of N-players' partly cooperation fuzzy matrix game with r-object determined by some of the players. n players turned into two coalitions, thus N-players' partly cooperation fuzzy game turns into two-players' noncooperation fuzzy game. By extension theory of fuzzy set, definitions of fuzzy expect payoff and fuzzy goal of each player are given to introduce the concept of the attainment degree of fuzzy goal. Furthermore, attainment degree of aggregated fuzzy goal is introduced as a commensurable measure. There are two methods in this paper to aggregate fuzzy goals: aggregation by weighting coefficients and aggregation by aminimum component.Secondly, this paper gives the concept of the equilibrium solution of coalition by using Nash equilibrium theory. According to the real situation, the method to refine equilibrium solution is discussed, which includes the definition of (ε)-coordinative solution. Consequently, this paper brings forward the definition of refined equilibrium solution of coalition. Next, on the basis of the set of it, this paper respectively discusses properties of refined equilibrium solution sets, by defining the super refined equilibrium solution, refined equilibrium solution above (α)-level, stable number, (δ)-similar super refined equilibrium solution, etc. Consequently, player k can obtain the attainment degree of aggregated fuzzy goals at least dkp in the fuzzy gamedetermined by P. Finally, by comparing dkp , player k candetermines his super optional coalition. Therefore, this theory offers a method for players to select their coalitions. In conclusion, it has some practical value in reality.At last, a concrete case is discussed by using the theory of this paper, and more explanations can be found in the part of conclusion and expectation.