In this paper, we discuss a portfolio selection problem based on fuzzy data envelopment analysis cross-efficiency evaluation wherein both undesirable fuzzy inputs and outputs have been considered. We first propose a data envelopment analysis cross-efficiency model, in which both undesirable inputs and outputs are considered. Furthermore, considering the imprecision of the data, we extend the crisp model to the fuzzy environment and propose a fuzzy data envelopment analysis cross-efficiency model with coexisting undesirable input and output data. We then apply the proposed model to the portfolio selection problem and present a novel mean-semivariance portfolio selection model based on fuzzy data envelopment analysis cross-efficiency scores, in which several realistic constraints are considered, including a budget, cardinality, buy-in thresholds, and no short selling constraints. After that, we employ the genetic algorithm (GA) to solve the proposed model. Finally, a real-life case study is presented to demonstrate the effectiveness of the proposed approaches.

在本文中，我们讨论了基于模糊数据包络分析交叉效率评估的投资组合选择问题，其中考虑了不希望有的模糊输入和输出。我们首先提出一个数据包络分析交叉效率模型，其中同时考虑了不良输入和输出。此外，考虑到数据的不精确性，我们将明快模型扩展到模糊环境，并提出了具有不期望的输入和输出数据共存的模糊数据包络分析交叉效率模型。然后，我们将提出的模型应用于投资组合选择问题，并基于模糊数据包络分析交叉效率得分，提出了一种新颖的均值-半方差投资组合选择模型，其中考虑了一些现实的约束条件，包括预算，基数，买入门槛，而且没有卖空限制。之后，我们采用遗传算法（GA）来求解所提出的模型。最后，提出了一个现实生活中的案例研究，以证明所提出方法的有效性。