Abstract: In the fuzzy uncertainty environment,we use the fuzzy AR time series in which the security price is trapezoid fuzzy number to forecast the security price and to describe the market movement trend,and also adjust the semi-absolute deviation risk to the fuzzy relaxation constraint. In the framework of the mean semi-absolute deviation,we establish a fuzzy investment programming in which the objective function subjects to the possibility distributing and the risk constraint is the fuzzy relaxation constraint,then obtain the efficient frontier. Using the 15 securities of the SEE 50 to empirically analyze,it shows that the programming can give the investor a higher level of investment satisfaction;the programming considers the market trend and possesses the decision-making pertinence;the risk tolerance level reflects the degree of the investors assessing themselves,and the risk tolerance level has the different effects in the different market;compared with the model of the mean-semi-absolute deviation,the programming owns the higher efficient frontier,and has more investment pertinence.

Key words: fuzzy time series, trapezoidal fuzzy number, semi-absolute deviation function, tolerance, efficient frontier, satisfaction