Abstract: Based on triangular fuzzy number, the game model is constructed to solve the problem of can not making accurate judements on both government supervision and enterprises taking part in the third party international environmental audit payoffs in game analysis. The payoffs are expressed with triangular fuzzy numbers,which are better to be described with inaccurate information. The influencing factors and the mechanism of the game strategy are discussed between the government and the polluting enterprises.The conditions of the pure strategy Nash equilibrium and the mixed strategy equilibrium are pointed out and some advice is given for the implementation of game mode. Then, a numerical example is given to verify the correctness and feasibility of the conclusion by the means of structural element method, introducing the concept of the triangular fuzzy number facilitates suiting the applications and extending the application background of the third party international environmental audit. The results show that the government's guidance to consumer consumption and the punishment to polluting enterprises play an important role in deciding whether to join the third party international environmental audit for enterprises.

Key words: triangular fuzzy number, government participation in supervision behavior, third party international environmental audit, triangular element method