A generalized DEA model with imprecise data

Data envelopment analysis (DEA) has excellent efficiency evaluation performance and is extensively employed in measuring efficiency of decision-making units (DMUs). At present, there exist fundamental models such as the DEA model for assessing DMU's technical efficiency, the DEA model for evaluating DMU's scale efficiency, and the model for measuring DMU's efficiency without assuming convexity. In practical production life, the actual statistical data is usually imprecise, as it is affected by various uncontrollable factors and is difficult to collect. In this paper, the expected value method of uncertainty theory is used to deal with these models in order to extend the traditional DEA models which can only deal with precise data to uncertain DEA models which can deal with imprecise data. To simplify the solution and representation of uncertain DEA models and optimize their performance, the uncertain generalized DEA model is further proposed to unify these three basic uncertain DEA models. Furthermore, to further make a clear ranking of DMUs, the super-efficiency method is introduced. Then, this paper applies the basic uncertain DEA models and uncertain generalized DEA model to two numerical examples. The results are analyzed and compared to illustrate the rationality and superiority of the new proposed model.