Chance-constrained random fuzzy CCR model in presence of skew-normal distribution

Abstract

Data envelopment analysis (DEA) is a mathematical method to evaluate the performance of decision-making units. In the classic DEA theory, assume deterministic and precise values for the input and output observations; however, in the real world, the observed values of the inputs and outputs data are mainly fuzzy and random. In the present paper, the fuzzy data were assumed random with a skew-normal distribution, whereas previous works have been based on the assumption of data normality, which might not be true in practice. Therefore, the use of a normal distribution would result in an incorrect conclusion. In the present work, the random fuzzy DEA models were investigated in two states of possibility–probability and necessity–probability in the presence of a skew-normal distribution with a fuzzy mean and a fuzzy threshold level. Finally, a set of numerical example is presented to demonstrate the efficacy of procedures and algorithms.