Ranking of decision making units based on cross efficiency by undesirable outputs and uncertainity

Cross efficiency is one of the useful methods for ranking of decision making units (DMUs) in data envelopment analysis (DEA). Since the optimal solutions of inputs and outputs weights are not unique so the selection of them are not simple and the ranks of DMUs can be changed by the difference weights. Thus, in this paper, we introduce a method for ranking of DMUs which does not have a unique problem. In the real life, the outputs can be shown as desirable and undesirable outputs. So it is important to provide models for the ranking of DMUs in present of desirable and undesirable outputs. The classic DEA models deals with certain data. But, in the real word, all data are not necessarily certain. For solve of this problem, we present a new method that compute the ranks of all DMUs by uncertain data and calculate the lower and upper bounds for the ranks of DMUs. Finally, the results of a simple example are given.