A novel DEA model based on uncertainty theory
- 132 Downloads
In deterministic DEA models, precise values are assigned to input and output data while they are intrinsically subjected to some degree of uncertainty. Most studies in this area are based on the assumption that inputs and outputs are equipped with some pre-known knowledge that enables one to use probability theory or fuzzy theory. In the lack of such data, one has to trust on the experts’ opinions, which can be considered as a sort of uncertainty. In this situation, the axiomatic approach of uncertainty theory initiated by Liu (Uncertainty theory. Berlin: Springer, 2007) could be an adequate powerful tool. Applying this theory, Wen et al. (J Appl Math, 2014; Soft Comput 1987–1996, 2015) suggested an uncertain DEA model while it has the disadvantage of pessimism. In this paper, we introduce another uncertain DEA model with the objective of acquiring the highest belief degree that the evaluated DMU is efficient. We also apply this model in ranking of the evaluated DMUs. Implementation of the model on different illustrative examples reveals that the ranks of DMUs are almost-stable in our model. This observation states that the rank of a DMU may roughly alternate with respect to the variation of minimum belief degrees. Our proposed model also compensates the rather optimistic point of view in the Wen et al. model that identifies all DMUs as efficient for higher belief degrees.
KeywordsDEA Uncertainty theory Uncertain distribution Efficiency
The authors would like to appreciate the anonymous referees, whom their comment are invaluable in enriching the manuscript. We also thank the Azarbaijan Shahid Madani University for its support.
- Baykasoğlu, A., Gölcük, İ., & Akyol, D. E. (2017). A fuzzy multiple-attribute decision making model to evaluate new product pricing strategies, Annals of Operations Research, 251(1–2), 205–242.Google Scholar
- Emrouznejad, A., & Tavana M., Eds. (2014). Performance measurement with fuzzy data envelopment analysis, Springer.Google Scholar
- Helmer, O. (1966). The Delphi method for systematizing judgments about the future. University of California: Institute of Government and Public Affairs.Google Scholar
- Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3, 3–10.Google Scholar
- Liu, B. (2011). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.Google Scholar
- Wang, X., Gao, Z., & Guo, H. (2012). Delphi method for estimating uncertainty distributions. Information: An International Interdisciplinary Journal, 15, 449–460.Google Scholar
- Wen, M., Guo, L., Kang, R., & Yang, Y. (2014). Data envelopment analysis with uncertain inputs and outputs, Journal of Applied Mathematics, 2014, 307108.Google Scholar
- Wen, M., Qin, Z., Kang, R., Yang, Y. (2015). Sensitivity and stability analysis of the additive model in uncertain data envelopment analysis. Soft Computing, 19(7), 1987–1996.Google Scholar
- Xu, J., & Zhou, X. (2011). Fuzzy-like multiple objective decision making. Berlin: Springer.Google Scholar
- Zhou, X., Tu, Y., Hu, R., & Lev, B. (2015). A Class of Chance Constrained Linear Bi-Level Programming with Random Fuzzy Coefficients. In Proceedings of the 9th International Conference on Management Science and Engineering Management (pp. 423–433, Springer).Google Scholar
- Zhou, X., Luo, R., Tu, Y., Lev, B., & Pedrycz, W. (2017). Data envelopment analysis for bi-level systems with multiple followers. New Lebanon: Omega.Google Scholar