Document Type : Review Paper


Department of Industrial Engineering, Ayandegan Insttitute of Higher Education, Tonekabon, Iran.


One of the appropriate and efficient tools in the field of productivity measurement and evaluation is data envelopment analysis, which is used as a non-parametric method to calculate the efficiency of decision-making units. Today, the use of data envelopment analysis technique is expanding rapidly and is used in the evaluation of various organizations and industries such as banks, postal service, hospitals, training centers, power plants, refineries, etc.In real-world problems, the values observed from input and output data are often ambiguous and random. To solve this problem, data envelopment analysis in stochastic fuzzy environment was proposed. Although the DEA has many advantages, one of the disadvantages of this method is that the classic DEA does not actually give us a definitive conclusion and does not allow random changes in input and output. In this paper, we review some of the proposed models in data envelopment analysis with fuzzy and random inputs and outputs.


Main Subjects

[1]     Hatami-Marbini, A., Emrouznejad, A., & Tavana, M. (2011). A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. European journal of operational research, 214(3), 457-472.
[2]     Sengupta, J. K. (1992). A fuzzy systems approach in data envelopment analysis. Computers & mathematics with applications, 24(8-9), 259-266.
[3]     Triantis, K., & Girod, O. (1998). A mathematical programming approach for measuring technical efficiency in a fuzzy environment. Journal of productivity analysis, 10(1), 85-102.
[4]     Guo, P., & Tanaka, H. (2001). Fuzzy DEA: a perceptual evaluation method. Fuzzy sets and systems, 119(1), 149-160.‏
[5]     Hatami-Marbini, A., Tavana, M., & Ebrahimi, A. (2011). A fully fuzzified data envelopment analysis model. International journal of information and decision sciences, 3(3), 252-264.‏
[6]     Lertworasirikul, S., Fang, S. C., Joines, J. A., & Nuttle, H. L. (2003). Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy sets and systems, 139(2), 379-394.‏
[7]     Wang, Y. M., Luo, Y., & Liang, L. (2009). Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert systems with applications, 36(3), 5205-5211.
[8]     Chen, C. B., & Klein, C. M. (1997). A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Transactions on systems, man, and cybernetics, part B (Cybernetics), 27(1), 26-35.
[9]     Kao, C., & Liu, S. T. (2000). Fuzzy efficiency measures in data envelopment analysis. Fuzzy sets and systems, 113(3), 427-437.
[10] Saati, S. M., Memariani, A., & Jahanshahloo, G. R. (2002). Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy optimization and decision making, 1(3), 255-267‏.
[11] Parameshwaran, R., Srinivasan, P. S. S., Punniyamoorthy, M., Charunyanath, S. T., & Ashwin, C. (2009). Integrating fuzzy analytical hierarchy process and data envelopment analysis for performance management in automobile repair shops. European journal of industrial engineering, 3(4), 450-467.‏
[12] Puri, J., & Yadav, S. P. (2014). A fuzzy DEA model with undesirable fuzzy outputs and its application to the banking sector in India. Expert systems with applications, 41(14), 6419-6432.‏
[13] Shiraz, R. K., Tavana, M., & Paryab, K. (2014). Fuzzy free disposal hull models under possibility and credibility measures. International journal of data dnalysis techniques and strategies, 6(3), 286-306.‏
[14] Momeni, E., Tavana, M., Mirzagoltabar, H., & Mirhedayatian, S. M. (2014). A new fuzzy network slacks-based DEA model for evaluating performance of supply chains with reverse logistics. Journal of intelligent & fuzzy systems, 27(2), 793-804.‏
[15] Payan, A. (2015). Common set of weights approach in fuzzy DEA with an application. Journal of intelligent & fuzzy systems, 29(1), 187-194.‏
[16] Aghayi, N., Tavana, M., & Raayatpanah, M. A. (2016). Robust efficiency measurement with common set of weights under varying degrees of conservatism and data uncertainty. European journal of industrial engineering, 10(3), 385-405.
[17] Edalatpanah, S.A., & Smarandache, F. (2020). Traingular single valued neutrosophic analysis: application to hospital performance measurement. Symmetry, 12(4), 588.
[18] Edalatpanah, S. A. (2020). Data envelopment analysis based on triangular neutrosophic numbers. CAAI transactions on intelligence technology. Retrieved from
[19] Edalatpanah, S. A., & Smarandache, F. (2019). Data envelopment analysis for simplified neutrosophic sets. Infinite Study.
[20] Edalatpanah, S. A. (2019). A data envelopment analysis model with triangular intuitionistic fuzzy numbers. International journal of data envelopment analysis7(4), 47-58.
[21] Edalatpanah, S. A. (2018). Neutrosophic perspective on DEA. Journal of applied research on industrial engineering5(4), 339-345.
[22] Soltani, M. R., Edalatpanah, S. A., Sobhani, F. M., & Najafi, S. E. (2020). A novel two-stage DEA model in fuzzy environment: application to industrial workshops performance measurement. International journal of computational intelligence systems13(1), 1134-1152.
[23] Tavana, M., Shiraz, R. K., Hatami-Marbini, A., Agrell, P. J., & Paryab, K. (2013). Chance-constrained DEA models with random fuzzy inputs and outputs. Knowledge-based systems52, 32-52.
[24] Nasseri, S. H., Ebrahimnejad, A., & Gholami, O. (2016). Fuzzy stochastic input-oriented primal data envelopment analysis models with application to insurance industry. International journal of applied decision sciences9(3), 259-282.
[25] Nasseri, S. H., Ebrahimnejad, A., & Gholami, O. (2018). Fuzzy stochastic data envelopment analysis with undesirable outputs and its application to banking industry. International journal of fuzzy systems20(2), 534-548.