Abstract: When multiple performance measures are used to evaluate the effectiveness of the decision-making units, the decision makers often compare these decision units with the pre-specified criteria (sample units). Because of the complexity and uncertainty of the objective things, the index information of sample units and decision unit must be given in the form of interval numbers. According to the three cases of the interval number of the evaluation index value of the sample unit or the decision unit, or the evaluation index values of both of them, it is established respectively that the generalized interval DEA model with only output (IS-DEA model, S-IDEA model and IS-IDEA model) based on the sample unit to evaluate the effectiveness of the decision making unit,and three types of generalized interval DEA models with output are further given according to the index types-benefit, cost and hybrid. At the same time, the meaning of the model, the solving methods, the related properties, the effectiveness classification and sequencing of decision making units of these models are discussed. Finally, an example of comprehensive performance evaluation of commercial banks is given to verify its feasibility and effectiveness.The method proposed in this paper extends the relative efficiency of the traditional DEA method, which is based on the effective decision unit, to evaluate the relative efficiency of the decision making unit, which is based on the arbitrary reference set, and extends the index value to the interval value. These models have their own advantages and application fields and can be chosen according to practical problems.

Key words: Data Envelopment Analysis, generalized interval DEA, sample unit, decision-making unit, interval number