Data envelopment analysis is a technique widely used to measure the relative efficiency of a set of decision making units and for ranking alternatives based on the measured efficiency. When there are data that need to be estimated, a group of experts is consulted. The opinions of the experts can be aggregated at either the data level, based on which the efficiency is calculated, or the efficiency level, where the efficiencies calculated from the data provided by individual experts are aggregated. However, the results may not be consistent, which leads to a puzzling situation as which result to follow. In this paper, a method of determining appropriate weights by which the opinions of the experts can be used to calculate the efficiency of alternatives is proposed. One radial model and one slacks-based measure (SBM) model are constructed based on this idea. It is shown that, for both models the results obtained from aggregating the opinions at the data level and at the efficiency level are the same. The final efficiencies are thus reliable. A case of a robot selection problem for a manufacturing company in Taiwan is used for the purpose of illustration. The results show that the radial efficiency is dependent on the non-Archimedean number and will overstate the performance of the robot. The SBM efficiency, which does not have this drawback, is more reliable than the radial efficiency to be used for ranking. A robot is suitably selected based on the SBM efficiency.
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