Evaluating The Performance and Ranking of DMUs: A Fuzzy Bounded DEA Approach

Data envelopment analysis (DEA) is a common technique in measuring the relative efficiency of a set of decision making units (DMUs) with multiple inputs and multiple outputs. The existing DEA models are limited to crisp parameters. To deal with data uncertainty in real-life problems, the notion of fuzziness has been often utilizing in the context of decision sciences such as DEA. In this study, we propose a fuzzy DEA model with the fuzzy inputs and fuzzy outputs to obtain the interval efficiency using a common set of weights approach. To do so, we first construct a fuzzy anti-ideal DMU and obtain its best relative efficiency. Second, we propose a pair of models to acquire the upper and lower bounds of the efficiency. Third, we use a simple method to rank the interval efficiency of the DMUs. Finally, we present a numerical example to demonstrate the applicability of the proposed model.