We consider efficiency measurement methods in the presence of uncertain input and output data, and without the (empirically problematic) assumption of convexity of the production technology. In particular, we perform a simulation study in order to contrast two well-established methods, IDEA and Fuzzy DEA, with a recently suggested extension of Fuzzy DEA in the literature (dubbed the HB method). We demonstrate that the HB method has important advantages over the conventional methods, resulting in more accurate efficiency estimates and narrower bounds for the efficiency scores of individual Decision Making Units (DMUs): thereby providing more informative results that may lead to more effective decisions. The price is computational complexity. Although we show how to significantly speed up computational time compared to the original suggestion, the HB method remains the most computationally heavy method among those considered. This may limit the use of the method in cases where efficiency estimates have to be computed on the fly, as in interactive decision support systems based on large data sets.