Data envelopment analysis (DEA) is a method to measure relative efficiency of a set of decision-making units (DMUs) which uses multiple inputs and produces multiple outputs. In the conventional DEA, crisp inputs and outputs are fundamentally necessary. But the observed values of inputs and outputs in real-world problems are sometimes imprecise. Thus, performance measurement often needs to be done under uncertainty conditions. This paper uses the DEA with double frontiers approach for selecting the best DMU in a fuzzy environment. In this approach, in addition to the optimistic fuzzy efficiency of each DMU, pessimistic fuzzy efficiency is considered. In contrast to the models of existing fuzzy DEA approaches, the proposed approach can accurately and easily identify the best DMU. The approach will be used to evaluate the performance of eight production units to demonstrate its simplicity and usefulness in selecting the best DMU.