Cross efficiency evaluation of data envelopment analysis (DEA) is an effective tool in measuring the performance of decision-making units. In general, in cross efficiency evaluation models, it is assumed that decision makers are completely rational, in which case they refrain from considering the risk attitude that plays an important role in the evaluation process. In order to fill this gap, cross efficiency evaluation in DEA was performed based on prospect theory. In the real world, many inputs and outputs are not known, which are called inaccurate data; what is expected is that even if one of the data is not accurate, the answer will probably not be accurate. To solve this problem, the present study presents models that are able to evaluate the prospect cross efficiency with interval data and proves the feasibility of the models by proving the theorems.