In many real-life situations, decision-making units (DMUs)— such as production processes or manufacturing or service systems— involve data related to inputs and outputs that are volatile, imprecise, or even missing. This makes it difficult to measure these DMUs’ efficiency. In this context, a data envelopment analysis (DEA) is a powerful methodology to facilitate this measurement, but this is also sensitive to data: any noise or error in the data measurement can easily cause non-applicable or insignificant results. The neutrosophic theory has demonstrated its superiority over other approaches and theories in handling this type of data, and especially in its capability to consider indeterminate data. However, in the DEA context, the use of this theory remains limited to a few theoretical works. In order to filling this gap, the present paper aims to highlight the neutrosophic DEA in a real-life application. Two different neutrosophic approaches, or namely, the ranking and parametric approaches, are adjusted then applied to measure and evaluate the efficiency of 32 regional hospitals in Tunisia. These results allow a comparison of these two approaches, but more importantly, they reveal the desired efficiency measurement that permits inefficient hospitals’ necessary actions. Consequently, indeterminate inputs and outputs are no longer a handicap in using the DEA.