摘要：Due to the uncertainty of the financial market and insufficient knowledge of investors, it is very difficult for investors to determine the investment proportion. Therefore, we do some research on uncertain portfolio when the investment proportion is regarded as a fuzzy number. First, we discuss the two cases where the return and the investment proportion are either triangular fuzzy numbers or trapezoidal fuzzy numbers. Then, based on possibilistic theory and fuzzy theory, we derive the mathematical expressions of the possibilistic returns and variances of portfolio with fuzzy investment proportions. Later, a tri-objective model is constructed with liquidity and fuzzy constraints. It istransformed into a single objective model with parameters by the fuzzy linear programming. Finally, the feasibility of themodel is illustrated. We explore the effects of variable parameter values by a numerical example. In fact, our proposed model in this paper can guide investors to make proper investment decisions when the economy is in recession and the investment information is not comprehensive.
