Hybrid fuzzy optimistic and pessimistic data envelopment analysis models for evaluating decision-making units in the presence of vague data

Data envelopment analysis (DEA) is a vital managerial tool employed to assess the performance of decision-making units (DMUs). However, conventional DEA models predominantly operate in a static environment utilizing crisp data for input and output parameters. In real-world scenarios, the accuracy of obtaining input and output data is often hindered by vagueness caused by fluctuating market conditions. This issue can be effectively addressed by incorporating fuzzy numbers. This research presents the development of novel optimistic and pessimistic fuzzy data envelopment analysis models that enable the measurement of DMU performance. The proposed approach integrates fuzzy optimistic and pessimistic DEA efficiencies using the alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-cut method, resulting in a hybrid model. Furthermore, a ranking approach is introduced that simultaneously incorporates optimistic and pessimistic efficiencies. To validate the efficacy of the proposed hybrid model, a real-life application to the education sector is provided. The proposed methodology is capable of evaluating the performances of DMUs in uncertain environments.