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.
Data envelopment analysis Random fuzzy variable Skew-normal distribution Possibility–probability Necessity–probability
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The authors declare that they have no competing interest.
Tavana M, Shiraz RK, Hatami-Marbini A, Agrell PJ, Paryab K (2012) Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC). Expert Syst Appl 39:12247–12259CrossRefGoogle Scholar
Tavana M, Shiraz RK, Hatami-Marbini A, Agrell PJ, Paryab K (2013a) Chance-constrained DEA models with random fuzzy inputs and outputs. J Knowl Based Syst 52:32–52CrossRefGoogle Scholar
Tavana M, Shiraz RK, Hatami-Marbini A (2013b) A new chance-constrained DEA model with birandom input and output data. J Oper Res Soc. doi:10.1057/jors.2013.157
Wu D, Yang Z, Liang L (2006) Efficiency analysis of cross-region bank branches using fuzzy data envelopment analysis. Appl Math Comput 181(1):271–281MathSciNetzbMATHGoogle Scholar