On the importance of perspective and flexibility for efficiency measurement: effects on the ranking of decision-making units

The efficiency of a firm can be assessed from several perspectives and using a variety of methodologies. Data envelopment analysis (DEA) is one of the most commonly used methodologies. Conventional DEA analyses or models allow one to classify decision-making units (DMUs) into efficient and inefficient ones based on their efficiency scores, which could also be used for ranking DMUs; however, such rankings generally show many ties. Super-efficiency DEA analyses have been proposed to address the tie issue. On the other hand, conventional DEA analyses only take account of a single perspective in estimating efficiency scores. Cross-efficiency DEA analyses provide an alternative that takes account of the perspectives or perceptions of different DMUs. Conventional DEA analyses designed for handling crisp data have also been extended to deal with fuzzy data. In this paper, we propose a fuzzy version of cross-efficiency DEA analysis along with a method for ranking DMUs. We illustrate our proposal with a real example from the Spanish banking sector. In order to assess the robustness of our proposal, we compared our results with those obtained with three different approaches based on the perspective from which efficiency aims to be evaluated: a fuzzy DEA approach, a cross-efficiency-based approach and a TOPSIS-based approach.