The Research On The Solution To Fuzzy Matrix Game

Matrix game is based on the game theory and it is also one of the most hotest researches. Because of the advance in technology and changing environment in the real life, strategic value or the payment of the players is not a precise numerical.The fuzzy set theory is proposed in 1965 and it provides a powerful tool to deal with the uncertainty phenomenon in real life. With the introduction of fuzzy sets, fuzzy game is generated. Fuzzy matrix game is also liked by many researchers.Fuzzy number is the most basic concept of fuzzy analysis and its operations are based on the form of extension principle. In the use of the extension principle, the most difficulty is its ergodic, that is to say, the difficulty is about the set operations corresponding toλ∈[0,1]. This ergodic in the operation has brought great inconvenience, so the actual operation can not proceed. The introduction of the structured element to the game theory makes the matrix game more and more simple to solving.By the structured element, this article studies the following areas:Firstly, the article focuses on the fuzzy matrix game and by the structured element-weighted sequence it shows the the equivalence theorem of Nash equilibrium solution and gives a detailed proof.Secondly, it focuses on the fuzzy matrix game whose payment values and the strategy value are fuzzy numbers. For different fuzzy numbers this paper derives some theorems and inferences, and summarizes the problem-solving steps for solving the equilibrium solution, finding a shortcut to solve the Nash equilibrium in the future.Finally, it focuses on the fuzzy constraints matrix game whose payment value is fuzzy.And it also draw the same useful conclusions.In addition, the discussion in each case of the matrix game, this paper gives a specific example to verify the feasibility and effectiveness of the corresponding algorithm.