In this paper, a two-phase methodology is proposed for robot selection. In phase 1, data envelopment analysis is used as a means to determine the technically efficient robot alternatives, considering cost and technical performance parameters. Using data envelopment analysis permits us to consider the face that the performance parameters specified by the vendors are generally unattainable in practice. In the second phase, a fuzzy robot selection algorithm is utilized to rank the technically efficient robots according to both predetermined objective criteria and additional vendor-related subjective criteria. The algorithm is based on calculating fuzzy suitability indices for the technically efficient robot alternatives, and then, ranking the fuzzy indices to select the best robot alternative. A comprehensive example is provided to illustrate the decision procedure. The algorithm proposed in here is also applicable to a broader area of decision problems, e.g. facility site selection, determination of the best CNC machine or flexible manufacturing system among a set of mutually exclusive alternatives.