Document Type : Research Paper


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


Several attempts have been made to deal with uncertain input and output data in Data Envelopment Analysis (DEA). However, due to the limitation of these methods, they cannot be applied for solving DEA with indeterminacy, impreciseness, vagueness, inconsistent and incompleteness information. So this paper for the first time deals with the Neutrosophic Data Envelopment Analysis and present a new model to solve it.


Main Subjects

[1]   Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.
[2]   Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078-1092.
[3]   Cooper, W. W., Park, K. S., & Yu, G. (1999). IDEA and AR-IDEA: models for dealing with imprecise data in DEA. Management science, 45(4), 597-607.
[4]   Despotis, D. K., & Smirlis, Y. G. (2002). Data envelopment analysis with imprecise data. European Journal of operational research, 140(1), 24-36.
[5]   Kao, C. (2006). Interval efficiency measures in data envelopment analysis with imprecise data. European journal of operational research, 174(2), 1087-1099.
[6]   Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. Socio-economic planning sciences42(3), 151-157.
[7]   Jahanshahloo, G. R., & Abbasian-Naghneh, S. (2011). Data envelopment analysis with imprecise data. Applied mathematical sciences, 5(61-64), 3089-3106.
[8]   Liu, J. S., Lu, L. Y., & Lu, W. M. (2016). Research fronts in data envelopment analysis. Omega, 58, 33-45.
[9]   Wei, G., & Wang, J. (2017). A comparative study of robust efficiency analysis and data envelopment analysis with imprecise data. Expert systems with applications, 81, 28-38.
[10]Chen, Y., Cook, W. D., Du, J., Hu, H., & Zhu, J. (2017). Bounded and discrete data and Likert scales in data envelopment analysis: Application to regional energy efficiency in China. Annals of operations research, 255(1-2), 347-366.
[11]Toloo, M., Keshavarz, E., & Hatami-Marbini, A. (2018). Dual-role factors for imprecise data envelopment analysis. Omega77, 15-31.
[12]Zhou, X., Xu, Z., Yao, L., Tu, Y., Lev, B., & Pedrycz, W. (2018). A novel data envelopment analysis model for evaluating industrial production and environmental management system. Journal of cleaner production, 170, 773-788.
[13]Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
[14]Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), 141–164.
[15]Tanaka, H., & Asai, K. (1984). A formulation of fuzzy linear programming based on comparison of fuzzy number. Control and cybernet, 13, 185-194.
[16]Campos, L., & Verdegay, J. L. (1989). Linear programming problems and ranking of fuzzy numbers. Fuzzy sets and systems, 32(1), 1-11.
[17]Bezdek, J. C. (2013). Pattern recognition with fuzzy objective function algorithms. Springer Science & Business Media.
[18]Zimmermann, H. J. (2011). Fuzzy set theory—and its applications. Springer Science & Business Media.
[19]Edalatpanah, S. A., & Shahabi, S. (2012). A new two-phase method for the fuzzy primal simplex algorithm. International review of pure and applied mathematics, 8(2), 157-164.
[20]Saberi Najafi, H. , Edalatpanah, S. A., & Dutta, H. (2016). A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters. Alexandria engineering journal, 55(3), 2589-2595.
[21]Najafi, H. S., & Edalatpanah, S. A. (2013). A note on “A new method for solving fully fuzzy linear programming problems”. Applied mathematical modelling37(14-15), 7865-7867.
[22]Rodríguez R.M., Martínez L., Herrera F., Torra V. (2016) A review of hesitant fuzzy sets: quantitative and qualitative extensions. In C. Kahraman., U. Kaymak., & A. Yazici. (Eds.), Fuzzy logic in Its 50th year. Studies in Fuzziness and Soft Computing: Springer, Cham.
[23]Sengupta, J. K. (1992). A fuzzy systems approach in data envelopment analysis. Computers & mathematics with applications24(8-9), 259-266.
[24]Triantis, K., & Girod, O. (1998). A mathematical programming approach for measuring technical efficiency in a fuzzy environment. Journal of productivity analysis10(1), 85-102.
[25]Entani, T., Maeda, Y., & Tanaka, H. (2002). Dual models of interval DEA and its extension to interval data. European journal of operational research136(1), 32-45.
[26]Kao, C., & Liu, S. T. (2003). A mathematical programming approach to fuzzy efficiency ranking. International journal of production economics86(2), 145-154.
[27]Dia, M. (2004). A model of fuzzy data envelopment analysis. INFOR: information systems and operational research42(4), 267-279.
[28]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.
[29]Wang, Y. M., & Chin, K. S. (2011). Fuzzy data envelopment analysis: a fuzzy expected value approach. Expert systems with applications, 38(9), 11678-11685.
[30]Emrouznejad A., Tavana M., Hatami-Marbini A. (2014). The state of the art in fuzzy data envelopment analysis. In A. Emrouznejad., & M. Tavana. (Eds.), Performance measurement with fuzzy data envelopment analysis. Studies in Fuzziness and Soft Computing: Springer, Berlin, Heidelberg.
[31]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 applications41(14), 6419-6432.
[32]Wanke, P., Barros, C. P., & Emrouznejad, A. (2016). Assessing productive efficiency of banks using integrated Fuzzy-DEA and bootstrapping: A case of Mozambican banks. European journal of operational research, 249(1), 378-389.
[33]Hatami-Marbini, A., Agrell, P. J., Tavana, M., & Khoshnevis, P. (2017). A flexible cross-efficiency fuzzy data envelopment analysis model for sustainable sourcing. Journal of cleaner production, 142, 2761-2779.
[34]Smarandache, F. (2002). Neutrosophy and neutrosophic logic. First international conference on neutrosophy, neutrosophic logic, set, probability, and statistics university of New Mexico, Gallup, NM (pp. 338-353).
[35]Smarandache, F. (1999). A unifying field in Logics: Neutrosophic Logic. In Philosophy (pp. 1-141). American Research Press.
[36]Smarandache, F. (2005). Neutrosophic set-a generalization of the intuitionistic fuzzy set. International journal of pure and applied mathematics24(3), 287.
[37]Smarandache, F. (2017). Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. Infinite Study.
[38]Smarandache, F. (2015). Neutrosophic social structures specificities. Social sciences and education research review2(1), 3-10.
[39]Haibin, W. A. N. G., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Infinite Study.
[40]Ye, J. (2015). Trapezoidal neutrosophic set and its application to multiple attribute decision-making. Neural computing and applications, 26(5), 1157-1166.
[41]Mohamed, M., Abdel-Basset, M., Zaied, A. N. H., & Smarandache, F. (2017). Neutrosophic integer programming problem. Infinite Study.
[42]Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016). Single valued neutrosophic graphs. Journal of new theory, (10), 86-101.
[43]Deli, I., & Şubaş, Y. (2017). A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. International journal of machine learning and cybernetics, 8(4), 1309-1322.
[44]Liang, R., Wang, J., & Zhang, H. (2017). Evaluation of e-commerce websites: An integrated approach under a single-valued trapezoidal neutrosophic environment. Knowledge-based systems, 135, 44-59.
[45]Thanh, N. D., & Ali, M. (2017). A novel clustering algorithm in a neutrosophic recommender system for medical diagnosis. Cognitive computation, 9(4), 526-544.
[46]Zavadskas, E. K., Bausys, R., Kaklauskas, A., Ubarte, I., Kuzminske, A., & Gudiene, N. (2017). Sustainable market valuation of buildings by the single-valued neutrosophic MAMVA method. Applied soft computing, 57, 74-87.