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Fuzzy efficiency ranking in fuzzy two-stage data envelopment analysis

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Abstract

Data envelopment analysis (DEA) is a useful tool for efficiency measurement of firms and organizations. Many production systems in the real world are composed of two processes connected in series. Measuring the system efficiency without taking the operation of each process into consideration will obtain misleading results. Two-stage DEA models show the performance of individual processes, thus is more informative than the conventional one-stage models for making decisions. When input and output data are fuzzy numbers, the derived efficiencies become fuzzy as well. This paper proposes a method to rank the fuzzy efficiencies when the exact membership functions of the overall efficiencies derived from fuzzy two-stage model are unknown. By incorporating the fuzzy two-stage model with the fuzzy number ranking method, a pair of nonlinear program is formulated to rank the fuzzy overall efficiency scores of DMUs. Solving the pair of nonlinear programs determines the efficiency rankings. An example of the ranking of the 24 non-life assurance companies in Taiwan is illustrated to explain how the proposed method is applied.

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Acknowledgments

This research was supported by National Science Council of the Republic of China under Contract No. NSC100-2410-H-238-006. The author is indebted to the reviewers for their constructive comments that improve the quality of this paper.

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  1. Graduate School of Business and Management, Vanung University, Chung-Li, Tao-Yuan 320, Taiwan, Taiwan, ROC

    Shiang-Tai Liu

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Correspondence to Shiang-Tai Liu.

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Liu, ST. Fuzzy efficiency ranking in fuzzy two-stage data envelopment analysis. Optim Lett 8, 633–652 (2014). https://doi.org/10.1007/s11590-012-0602-5

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