Abstract: Basing on the asymmetric duopoly option-game model with investment cost asymmetry,this research discusses the present value of profit flows and the sunk investment costs for the trapezoidal fuzzy number,and Firms'technology innovation investment strategy is analyzed.It constructs followers,leaders of investment value and investment threshold of fuzzy expressions under the fuzzy environment to conduct numerical analysis.And it is concluded that there is still existing the best increasing investment strategy under fuzzy environment,with the development of the trapezoidal fuzzy number of the sunk cost of expected investment,the investment value of business declines,but the critical value for the investment ascends.This offers a kind of explanation to the investment strategies under the fuzzy environment.

Key words: option-game, trapezoidal fuzzy numbers, technological innovation, duopoly