Evaluating the Efficiency of Decision Making Units in Fuzzy two-stage DEA Models

Data envelopment analysis (DEA) is an optimization method to assess the efficiency of decision-making units with multiple-inputs/multiple-outputs assumption. Most real-life issues contain more than one stage unit which needs multiple-stage data envelopment analysis models to be solved. Moreover, the inputs and outputs of the units are rarely measured accurately in real-life problems, hence fuzzy data envelopment analysis approaches can be significantly helpful in calculating efficiency scores. In this study, an approach for evaluating the performance of decision-making units (DMUs) in fuzzy two-stage DEA models is developed. The developed model is a parametric program based on alpha-cuts. The dependence on alpha allows the manager to compare and rank DMUs based on his/her degree of certainty and after the selection of alpha, our proposed model becomes linear. Furthermore, a theorem is proposed and proved for conventional multiplicative two-stage DEA models with the assumption of Variable Returns to Scale. This theorem can be used to evaluate the correctness of the results. Finally, by two illustrative examples, the ability of the proposed approach to solve fuzzy two-stage DEA models is shown, and the obtained results are compared to that of some other methods in this field.