Abstract: In this paper, by means of objective fuzzy frequency statistics, the uncertain returns of securities investment are expressed by fuzzy numbers, and the fuzzy returns are clarified by the possibility mean of fuzzy numbers, and the semi-absolute deviation function is used to measure the risk of securities investment. Considering the constraint of securities turnover rate, a portfolio model based on preference possibility mean-semi-absolute deviation is constructed, and the empirical analysis of the model is carried out.

Key words: Portfolio , Probability Mean , Fuzzy Number