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.
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References
Azzalini A (1985) A class of distribution which includes the normal ones. Scand J Stat 12:171–178
Azzalini A, Capitano A (1999) Statistical application of the multivariate skew normal distribution. J R Stat Soc B 61:579–602
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444
Dubois D, Prade H (1978) operations on fuzzy numbers. Int J Syst Sci 9(6):291–297
Khanjani SR, Jalalzadeh L, Paryab K, Fukuyama H (2014a) Imprecise data envelopment analysis model with bifuzzy variables. J Intell Fuzzy Syst 27(1):37–48
Khanjani SR, Charles V, Jalalzadeh L (2014b) Fuzzy rough DEA model: a possibility and expected value approaches. Expert Syst Appl 41(2):434–444
Khanjani SR, Tavana M, Di Caprio D (2017) Chance-constrained data envelopment analysis modeling with random-rough data. RAIRO-Oper Res. doi:10.1051/ro/2016076
Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: theory and application. Prentice-Hall, New York
Kwakernaak H (1978) Fuzzy random variables. Part I: definitions and theorems. Inf Sci 15(1):1–29
Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10(4):445–450
Liu YK, Liu B (2003) Fuzzy random variables: a scalar expected value operator. Fuzzy Optim Decis Mak 2(2):143–160
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 39:12247–12259
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 52:32–52
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):271–281
Zadeh LA (1978) Fuzzy sets as a basis for theory of possibility. Fuzzy Sets Syst 1(1):3–28
Zimmermann HJ (2001) Fuzzy sets theory and its applications, 4th edn. Kluwer Academic Publishers, Dordrecht
Zhu J (2003) Imprecise data envelopment analysis (IDEA): a review and improvement with an application. Eur J Oper Res 144:513–529
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Communicated by V. Loia.
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Mehrasa, B., Behzadi, M.H. Chance-constrained random fuzzy CCR model in presence of skew-normal distribution. Soft Comput 23, 1297–1308 (2019). https://doi.org/10.1007/s00500-017-2848-4
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DOI: https://doi.org/10.1007/s00500-017-2848-4