Efficiency distribution and expected efficiencies in DEA with imprecise data

Several methods have been proposed for ranking the decision making units (DMUs) in data envelopment analysis (DEA) with imprecise data. Some methods have only used the upper bound efficiencies to rank DMUs. However, some other methods have considered the both of the lower and upper bound efficiencies to rank DMUs. The current paper shows that these methods did not consider the DEA axioms and may be unable to produce a rational ranking. We show that considering the imprecise data as stochastic and using the expected efficiencies to rank DMUs give better results. Indeed, we propose a new ranking approach, based on considering the DEA axioms for imprecise data that removes the existing drawbacks. Some numerical examples are provided to explain the content of the paper.