Investigating the ability of fuzzy and robust DEA models to apply uncertainty conditions: an application for date palm producers

The problem of uncertainty in data, especially in agriculture, is inevitable due to measurement errors and providing inaccurate information by farmers. This inaccurate and vague information can affect the result of the investigations and lead to incorrect decisions. In most efficiency estimation methods, including data envelopment analysis (DEA), the certainty and accuracy of the data is assumed. While in the real world, we are faced with uncertainty. Therefore, in this study, an attempt has been made to evaluate the ability of two Uncertain Data Envelopment Analysis models in applying uncertainty. This goal was carried out in the form of evaluating the efficiency of 137 in Behbahan region, Iran, with RDEA and FDEA methods. According to the results, as the protection of RDEA and FDEA models against uncertainty increases, the average of all three types of technical, pure technical, and scale efficiency decreases so that in the most pessimistic conditions there was a decrease of about 22%. Based on the calculations, all the inputs have been used more than the average optimal values and the most important inputs that caused the inefficiency of the farms are machinery, arable land, pesticides, and fertilizers which on average with a 26% reduction of these inputs in the farms it is created inefficiently to reach the efficiency frontier. Monte Carlo simulation was used to verify the results of RDEA and FDEA models and to check the compliance of unit ratings with real world conditions. The results of this simulation showed that the average rating conformity percentage in the RDEA model is higher than in the FDEA model, so that in the most optimistic case, there is a 21% difference in conformity. In other words, the RDEA model is more flexible against uncertain data. In this context, it seems appropriate to use the findings of this model to improve the efficiency of inefficient farms.