Fuzzy interpretation of efficiency in data envelopment analysis and its application in a non-discretionary model

Data envelopment analysis (DEA) is a nonparametric model which evaluates the relative efficiencies of decision-making units (DMUs). These DMUs produce multiple outputs by using multiple inputs and the relative efficiency is evaluated using a ratio of total weighted output to total weighted input. In this paper an alternative interpretation of efficiency is first given. The interpretation is based on the fuzzy concept even though the inputs and outputs data are crisp numbers. With the interpretation, a new model for ranking DMUs in DEA is proposed and a new perspective of viewing other DEA models is now made possible. The model is then extended to incorporate situations whereby some inputs or outputs, in a fuzzy sense, are almost discretionary variables.