Research On Income Distribution Of Cooperative Game Based On Vague Payment

At the same time of social development and economic growth,limited resources become the fundamental reason for the cooperation and competition in many areas.Win-win cooperation has gradually become the theme of the times,and some problems have been exposed in the cooperative game.Firstly,due to the existence of a variety of external uncertainties,the payoff of the players become uncertain,then how to find a proper income distribution becomes a puzzle.Secondly,for the representation of uncertain payoff,the classical fuzzy set theory is insufficient in maintaining information completeness.In order to solve these problems,based on the condition of uncertain payoff may appear in practical cooperative games,this thesis introduces the vague set theory which can express the support,objection and hesitation in the fuzzy information into the problem to express the payoff in the cooperative games.With the help of vague set theory,classical cooperative game theory and fuzzy cooperative game theory,this thesis constructs the model of vague payoff cooperative games.In order to avoid the problem of fuzzy degree amplification may be caused by fuzzy value calculation,with the help of the theory of vague level set,this thesis gives the form,determination method and exist conditions of Shapley value in vague payoff cooperative game,then verifies these methods by an example.To find a more applicable solution to the cooperative game of vague payoff,based on one shape of vague value-triangular vague value and the definition of excess,this thesis constructs a method of the maximum satisfaction of the player in the vague payoff cooperative game,and then gives the solution model and solution method of the triangular fuzzy number contained in the value of triangular vague and its corresponding supporting membership degree and opposing membership degree respectively.The feasibility of this method is verified by an example.Finally,taking the cost sharing problem in cross regional water pollution control as an example,this thesis studies the uncertain information in the problem,transforms the extracted data,and then obtains the Shapley value of vague payoff and the maximum satisfactory solution of the problem,then verifies the rationality of the solution.The results of this thesis have practical means for promoting regional cooperative water pollution control,and can be used as a reference for cost sharing in cooperative water pollution control.