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Fuzzy measures for fuzzy cross efficiency in data envelopment analysis

Author

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  • Shiang-Tai Liu

    (Vanung University)

  • Yueh-Chiang Lee

    (Vanung University)

Abstract

The cross-efficiency evaluation measures the efficiencies of decision-making units (DMUs) through both self- and peer-evaluation methods. Since the cross-efficiency is effective in discriminating among DMUs, this evaluation technique has been widely used in many applications. In the real world, there are cases in which the observations are difficult to measure precisely. The existing approaches of fuzzy cross-efficiency evaluation employ the secondary goal approach to determine the weights for measuring fuzzy cross-efficiencies. However, the different approaches for determining the weights may produce different fuzzy cross-efficiencies. In this paper, we propose a novel method that considers all possible weights of all the DMUs simultaneously to calculate the fuzzy cross-efficiency directly, and the choice of weights is not required. Since the α-level-based approach is one of the most popular approaches for developing fuzzy data envelopment analysis models, this approach is employed to formulate the proposed fuzzy cross-efficiency evaluation. A pair of linear programs is developed to calculate the fuzzy cross-efficiency. At a specific α-level, solving the pair of linear programs generates the lower bound and upper bound of the fuzzy efficiency score. The illustrated examples show that the fuzzy cross-efficiency evaluation method proposed in this paper has discriminative power in ranking the DMUs when the data are fuzzy numbers.

Suggested Citation

  • Shiang-Tai Liu & Yueh-Chiang Lee, 2021. "Fuzzy measures for fuzzy cross efficiency in data envelopment analysis," Annals of Operations Research, Springer, vol. 300(2), pages 369-398, May.
    • Handle: RePEc:spr:annopr:v:300:y:2021:i:2:d:10.1007_s10479-019-03281-4
    DOI: 10.1007/s10479-019-03281-4
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    1. Nuria Ramón & José L Ruiz & Inmaculada Sirvent, 2014. "Dominance relations and ranking of units by using interval number ordering with cross-efficiency intervals," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(9), pages 1336-1343, September.
    2. Yang, Feng & Ang, Sheng & Xia, Qiong & Yang, Chenchen, 2012. "Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis," European Journal of Operational Research, Elsevier, vol. 223(2), pages 483-488.
    3. Du, Juan & Cook, Wade D. & Liang, Liang & Zhu, Joe, 2014. "Fixed cost and resource allocation based on DEA cross-efficiency," European Journal of Operational Research, Elsevier, vol. 235(1), pages 206-214.
    4. Lu, Wen-Min & Lo, Shih-Fang, 2007. "A closer look at the economic-environmental disparities for regional development in China," European Journal of Operational Research, Elsevier, vol. 183(2), pages 882-894, December.
    5. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2010. "On the choice of weights profiles in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1564-1572, December.
    6. Hai-Liu Shi & Ying-Ming Wang & Sheng-Qun Chen & Yi-Xin Lan, 2017. "An approach to two-sided M&A fits based on a cross-efficiency evaluation with contrasting attitudes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 41-52, January.
    7. Lim, Sungmook & Oh, Kwang Wuk & Zhu, Joe, 2014. "Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market," European Journal of Operational Research, Elsevier, vol. 236(1), pages 361-368.
    8. Oral, Muhittin & Oukil, Amar & Malouin, Jean-Louis & Kettani, Ossama, 2014. "The appreciative democratic voice of DEA: A case of faculty academic performance evaluation," Socio-Economic Planning Sciences, Elsevier, vol. 48(1), pages 20-28.
    9. K F Lam, 2010. "In the determination of weight sets to compute cross-efficiency ratios in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 134-143, January.
    10. Boussofiane, A. & Dyson, R. G. & Thanassoulis, E., 1991. "Applied data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 52(1), pages 1-15, May.
    11. H. Örkcü & Mehmet Ünsal & Hasan Bal, 2015. "A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity," Annals of Operations Research, Springer, vol. 235(1), pages 599-623, December.
    12. Hatami-Marbini, Adel & Emrouznejad, Ali & Tavana, Madjid, 2011. "A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making," European Journal of Operational Research, Elsevier, vol. 214(3), pages 457-472, November.
    13. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    14. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    15. Y-M Wang & K-S Chin & S Wang, 2012. "DEA models for minimizing weight disparity in cross-efficiency evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(8), pages 1079-1088, August.
    16. Joe Zhu, 2014. "DEA Cross Efficiency," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 4, pages 61-92, Springer.
    17. Azedine Boulmakoul & Mohamed Haitam Laarabi & Roberto Sacile & Emmanuel Garbolino, 2017. "An original approach to ranking fuzzy numbers by inclusion index and Bitset Encoding," Fuzzy Optimization and Decision Making, Springer, vol. 16(1), pages 23-49, March.
    18. Shang, Jen & Sueyoshi, Toshiyuki, 1995. "A unified framework for the selection of a Flexible Manufacturing System," European Journal of Operational Research, Elsevier, vol. 85(2), pages 297-315, September.
    19. Alcaraz, Javier & Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2013. "Ranking ranges in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 226(3), pages 516-521.
    20. Shiang-Tai Liu, 2018. "A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio," Annals of Operations Research, Springer, vol. 261(1), pages 207-232, February.
    21. José L. Ruiz & Inmaculada Sirvent, 2017. "Fuzzy cross-efficiency evaluation: a possibility approach," Fuzzy Optimization and Decision Making, Springer, vol. 16(1), pages 111-126, March.
    22. Adler, Nicole & Friedman, Lea & Sinuany-Stern, Zilla, 2002. "Review of ranking methods in the data envelopment analysis context," European Journal of Operational Research, Elsevier, vol. 140(2), pages 249-265, July.
    23. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "Data envelopment analysis 1978–2010: A citation-based literature survey," Omega, Elsevier, vol. 41(1), pages 3-15.
    24. C Kao & H-T Hung, 2005. "Data envelopment analysis with common weights: the compromise solution approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1196-1203, October.
    25. Talluri, Srinivas & Paul Yoon, K., 2000. "A cone-ratio DEA approach for AMT justification," International Journal of Production Economics, Elsevier, vol. 66(2), pages 119-129, June.
    26. Liang Liang & Jie Wu & Wade D. Cook & Joe Zhu, 2008. "The DEA Game Cross-Efficiency Model and Its Nash Equilibrium," Operations Research, INFORMS, vol. 56(5), pages 1278-1288, October.
    27. SHOKOUHI, Amir H. & HATAMI-MARBINI, Adel & TAVANA, Madjid & SAATI, Saber, 2010. "A robust optimization approach for imprecise data envelopment analysis," LIDAM Reprints CORE 2215, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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