Portfolio Selection Using Data Envelopment Analysis Cross-Efficiency Evaluation with Undesirable Fuzzy Inputs and Outputs

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.