A Compromise Solution Approach for Fuzzy Data Envelopment Analysis: A Case of the Efficiency Prediction
محورهای موضوعی : Fuzzy Optimization and Modeling Journal
Nam Hyok Kim
1
,
Feng He
2
,
Kwang-Chol Ri
3
,
Son-Il Kwak
4
1 - School of Economics and Management, University of Science & Technology Beijing, Beijing 100083, PR China
2 - School of Economics and Management, University of Science & Technology Beijing, Beijing 100083, PR China
3 - Faculty of Information Science, Kim Il Sung University, Pyongyang, DPR Korea
4 - Faculty of Information Science, Kim Il Sung University, Pyongyang, DPR Korea
کلید واژه: Fuzzy Data Envelopment Analysis, Common Weight, Efficiency Prediction, Energy Efficiency,
چکیده مقاله :
The data envelopment analysis (DEA) a data-oriented approach for evaluating the relative performance of decision-making units (DMUs). The traditional DEA applies only to crisp data, whereas the data collected in the real world may be ambiguous and imprecise. The fuzzy DEA is an extension of the DEA using the fuzzy variable to deal with uncertain or imprecise data. This paper proposes two new fuzzy arithmetic-based DEA models with dynamic weights and common weights, formulated as multiple objective decision-making (MODM), and proposed models are represented as the linear programs providing the compromise solutions. The numerical experiment is illustrated to examine the validity of the proposed models, and the experiment shows that the proposed models give better results than other models. The proposed fuzzy DEA models are applied to predict the energy efficiency of 40 iron and steel enterprises in China.
The data envelopment analysis (DEA) a data-oriented approach for evaluating the relative performance of decision-making units (DMUs). The traditional DEA applies only to crisp data, whereas the data collected in the real world may be ambiguous and imprecise. The fuzzy DEA is an extension of the DEA using the fuzzy variable to deal with uncertain or imprecise data. This paper proposes two new fuzzy arithmetic-based DEA models with dynamic weights and common weights, formulated as multiple objective decision-making (MODM), and proposed models are represented as the linear programs providing the compromise solutions. The numerical experiment is illustrated to examine the validity of the proposed models, and the experiment shows that the proposed models give better results than other models. The proposed fuzzy DEA models are applied to predict the energy efficiency of 40 iron and steel enterprises in China.
1. Amirteimoori, A., Azizi, H., & Kordrostami, S. (2020). Double frontier two-stage fuzzy data envelopment analysis. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 28(01), 117-152.
2. Angiz Z, L, M., Emrouznejad, A., & Mustafa, A. (2012). Fuzzy data envelopment analysis. Expert Systems with Application, 39(3), 2263-2269.
3. Azar, A., Zarei Mahmoudabadi, M., & Emrouznejad, A. (2016). A new fuzzy additive model for determining the common set of weights in Data Envelopment Analysis. Journal of Intelligent & Fuzzy Systems, 30(1), 61-69.
4. Bagheri, M., Ebrahimnejad, A., Razavyan, S., Hosseinzadeh Lotfi, F., & Malekmohammadi, N. (2020). Solving the fully fuzzy multi-objective transportation problem based on the common set of weights in DEA. Journal of Intelligent & Fuzzy Systems, 39(3), 3099-3124.
5. Bhardwaj, B., Kaur, J., & Kumar, A. (2017). A new fuzzy CCR data envelopment analysis model and its application to manufacturing enterprises. In Soft computing applications for group decision-making and consensus modeling (pp. 345-368). Cham: Springer International Publishing.
6. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.
7. Chen, L., He, F., Zhang, Q., Jiang, W., & Wang, J. (2017). Two-stage efficiency evaluation of production and pollution control in Chinese iron and steel enterprises. Journal of Cleaner Production, 165, 611-620.
8. Cinaroglu, S. (2023). Fuzzy efficiency estimates of the Turkish health system: A comparison of interval, bias-corrected, and fuzzy data envelopment analysis. International Journal of Fuzzy Systems, 25(6), 2356-2379.
9. Cook, W. D., & Kress, M. (1990). A data envelopment model for aggregating preference rankings. Management Science, 36(11), 1302-1310.
10. Darijani, M., Amiri, M., Taghavifard, M. T., & Hanafizadeh, P. (2021). Efficiency assessment using common-weight FDEA under a multi-objective approach as well as possibility and necessity theory. Economic Computation & Economic Cybernetics Studies & Research, 55(3), 119-136.
11. Emrouznejad, A., & Tavana, M. (Eds.). (2013). Performance measurement with fuzzy data envelopment analysis (Vol. 309). Springer.
12. Gerami, J., Mozaffari, M. R., Wanke, P. F., & Tan, Y. (2023). Fully fuzzy DEA: a novel additive slacks-based measure model. Soft Computing, 1-25. https://doi.org/10.1007/s00500-023-09254-x
13. Hatami-Marbini, A., Ebrahimnejad, A., & Lozano, S. (2017). Fuzzy efficiency measures in data envelopment analysis using lexicographic multiobjective approach. Computers & Industrial Engineering, 105, 362-376.
14. He, F., Zhang, Q., Lei, J., Fu, W., & Xu, X. (2013). Energy efficiency and productivity change of China’s iron and steel industry: Accounting for undesirable outputs. Energy Policy, 54, 204-213.
15. Hu, C. K., Liu, F. B., & Hu, C. F. (2017). Efficiency measures in fuzzy data envelopment analysis with common weights. Journal of Industrial & Management Optimization, 13(1).
16. Huang, Y., & Wang, M. (2024). Heterogeneous multi-attribute group decision making based on a fuzzy data envelopment analysis cross-efficiency model. Expert Systems with Applications, 238, 121914.
17. Kachouei, M., Ebrahimnejad, A., & Bagherzadeh-Valami, H. (2020). A common-weights approach for efficiency evaluation in fuzzy data envelopment analysis with undesirable outputs: application in banking industry. Journal of Intelligent & Fuzzy Systems, 39(5), 7705-7722.
18. Kahraman, C., & Tolga, E. (1998, May). Data envelopment analysis using fuzzy concept. In Proceedings. 1998 28th IEEE International Symposium on Multiple-Valued Logic (Cat. No. 98CB36138) (pp. 338-343). IEEE.
19. Kao, C. (2010). Malmquist productivity index based on common-weights DEA: The case of Taiwan forests after reorganization. Omega, 38(6), 484-491.
20. Kao, C., & Hung, H. (2005). Data envelopment analysis with common weights: the compromise solution approach. Journal of the operational research society, 56(10), 1196-1203.
21. Kao, C., & Hung, H. (2005). Data envelopment analysis with common weights: the compromise solution approach. Journal of the operational research society, 56(10), 1196-1203.
22. Kazemi, S., Mavi, R. K., Emrouznejad, A., & Kiani Mavi, N. (2021). Fuzzy clustering of homogeneous decision making units with common weights in data envelopment analysis. Journal of Intelligent & Fuzzy Systems, 40(1), 813-832.
23. Kuosmanen, T., Kortelainen, M., Sipiläinen, T., & Cherchye, L. (2010). Firm and industry level profit efficiency analysis using absolute and uniform shadow prices. European Journal of Operational Research, 202(2), 584-594.
24. 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.
25. Liu, J., Song, J., Xu, Q., Tao, Z., & Chen, H. (2019). Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations. Fuzzy Optimization and Decision Making, 18, 345-370.
26. Lotfi, F. H., Jahanshahloo, G. R., Vahidi, A. R., & Dalirian, A. (2009). Efficiency and effectiveness in multi-activity network DEA model with fuzzy data. Applied Mathematical Sciences, 3(52), 2603-2618.
27. Zarei Mahmoudabadi, M., & Emrouznejad, A. (2022). Balanced performance assessment under uncertainty: an integrated CSW-DEA and balanced scorecard (BSC). Annals of Operations Research, 1-16.
28. Majdi, M., Ebrahimnejad, A., & Azizi, A. (2023). Common-weights fuzzy DEA model in the presence of undesirable outputs with ideal and anti-ideal points: development and prospects. Complex & Intelligent Systems, 9(6), 6223-6240.
29. Nastis, S. A., Bournaris, T., & Karpouzos, D. (2019). Fuzzy data envelopment analysis of organic farms. Operational Research, 19, 571-584.
30. Omrani, H., Fahimi, P., & Emrouznejad, A. (2022). A common weight credibility data envelopment analysis model for evaluating decision making units with an application in airline performance. RAIRO-Operations Research, 56(2), 911-930.
31. Payan, A. (2015). Common set of weights approach in fuzzy DEA with an application. Journal of Intelligent & Fuzzy Systems, 29(1), 187-194.
32. Ren, J., Chen, C., & Gao, B. (2020). Additive integer-valued DEA models with fuzzy undesirable outputs: Closest benchmarking targets and super-efficiency. IEEE access, 8, 124857-124868.
33. Ruiz, J. L., & Sirvent, I. (2016). Common benchmarking and ranking of units with DEA. Omega, 65, 1-9.
34. Ruiz, J. L., & Sirvent, I. (2017). Fuzzy cross-efficiency evaluation: a possibility approach. Fuzzy Optimization and Decision Making, 16, 111-126.
35. Saati, S. A. B. E. R., and Azizollah Memariani. "Reducing weight flexibility in fuzzy DEA." Applied Mathematics and Computation 161.2 (2005): 611-622.
36. Sengupta, J. K. (1992). A fuzzy systems approach in data envelopment analysis. Computers & Mathematics with Applications, 24(8-9), 259-266.
37. Shabani, A., Visani, F., Barbieri, P., Dullaert, W., & Vigo, D. (2019). Reliable estimation of suppliers’ total cost of ownership: An imprecise data envelopment analysis model with common weights. Omega, 87, 57-70.
38. Song, M. L., Zhou, Y. X., Zhang, R. R., & Fisher, R. (2017). Environmental efficiency evaluation with left–right fuzzy numbers. Operational Research, 17, 697-714.
39. Tabatabaei, S., Mozaffari, M. R., Rostamy-Malkhalifeh, M., & Hosseinzadeh Lotfi, F. (2022). Fuzzy efficiency evaluation in relational network data envelopment analysis: application in gas refineries. Complex & Intelligent Systems, 8(5), 4021-4049.
40. Wang, X., He, F., Zhang, L., & Chen, L. (2018). Energy efficiency of China’s iron and steel industry from the perspective of technology heterogeneity. Energies, 11(5), 1247.
41. 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.
42. Zhu, J. (2003). Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European journal of operational research, 144(3), 513-529.
43. Zohrehbandian, M., Makui, A., & Alinezhad, A. (2010). A compromise solution approach for finding common weights in DEA: An improvement to Kao and Hung's approach. Journal of the Operational Research Society, 61(4), 604-610.
