Abstract: In this paper,by defining the security price as trapezoidal fuzzy number,we establish a longshort portfolio selection model with liquidity constraints,margin,transaction costs and different borrowing and lending interests.By using the theory of nonlinear programming and maximum entropy methods, we give an algorithm to solve this model.Finally,an example is given to illustrate our main results and analysis of the interaction of the portfolio efficient frontier with liquidity constraints,margin,transaction costs and different borrowing and lending interests.

Key words: trapezoidal fuzzy number, liquidity, possibilistic mean value, possibilistic variance, transaction costs, marginpurchase, maximum entropy