Technology selection is an important part of management of technology. Traditionally, technology selection models are based on cardinal data with less emphasis on ordinal data. However, with respect to technology selection complexity, emphasis has shifted to the simultaneous consideration of cardinal and ordinal data in technology selection process. The application of data envelopment analysis (DEA) for technology selection problems is based on total flexibility of the weights. However, the problem of allowing total flexibility of the weights is that the values of the weights obtained by solving the unrestricted DEA program are often in contradiction to prior views or additional available information. On the other hand, current models of technology selection problems assume complete discretion of decision-making criteria and do not assume technology selection in the conditions that some factors are nondiscretionary. To select the best technologies in the presence of cardinal data, ordinal data, nondiscretionary factors, and weight restrictions, the objective of this paper is to propose a new pair of assurance region-nondiscretionary factors-imprecise data envelopment analysis (AR-NF-IDEA) models. A numerical example demonstrates the application of the proposed method.