Probability-possibility DEA model with Fuzzy random data in presence of skew-Normal distribution

Data envelopment analysis (DEA) is a mathematical method to evaluate the performance of decision-making units (DMU). In the performance evaluation of an organization based on the classical theory of DEA, input and output data are assumed to be deterministic, while in the real world, the observed values of the inputs and outputs data are mainly fuzzy and random. A normal distribution is a continuous distribution which is extremely important in statistics because of its behavior.It is assumed in most cases that fuzzy random data are normally distributed, while such an assumption may not hold in practice. Therefore, using the normal distribution leads to erroneous conclusions. In the present study, we investigated DEA fuzzy random model under condition of probability -possibility, in the presence of a skew-normal distribution.In other words, this method embraced the previous methods in a specific state. Finally, a set of numerical example is presented to demonstrate the efficacy of procedure and algorithm.