中文摘要：

考虑交易成本、借款限制、阀值约束和基数约束，提出多阶段均值-半方差模糊投资组合模型。在该模型中，收益水平被定义为可能的平均回报，风险水平被定义为回报的半方差。由于交易成本和基数约束，多阶段投资组合模型为具有路径依赖性的混合整数动态优化问题。文章提出了前向动态规划方法求解。最后，以一个具体的算例比较了不同的基数约束投资组合的最优投资策略。

英文摘要：

This paper discusses a multi-period portfolio selection problem in fuzzy environment. A possibilistic mean semivariance model for multi-period portfolio selection is presented by taking into account the transaction costs, borrowing constraints, threshold constraints and cardinality constraints. In the proposed model, the return level is quantified by the possibilistic mean of return, and the risk level is characterized by the possibilistic semivafiance of return. Because of the transaction costs and cardinality constraints, the multi-period portfolio selection is the mix integer dynamic optimization problem with path dependence. Furthermore, the forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of the different cardinality constraints is provided by a numerical example to illustrate the efficiency of the proposed approaches and the designed algorithm.