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. Unfortunately, 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 put forward a fuzzy DEA model with the fuzzy inputs and fuzzy outputs to obtain the interval efficiency using a common set of weights approach. First, we construct a fuzzy anti-ideal DMU and its best relative efficiency is measured. Second, we propose a pair of the models to acquire the upper and lower bounds of the efficiency. Third, we use a method to rank the interval efficiency of the DMUs. Finally, we present a numerical example to demonstrate the applicability of the proposed model.