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Uncertain Data Envelopment Analysis for Cross Efficiency Evaluation with Imprecise Data

Author

Listed:
  • Bao Jiang

    (Department of International Trade and Economy, Ocean University of China, Qingdao 266100, China
    These authors contributed equally to this work.)

  • Enxin Chi

    (Department of International Trade and Economy, Ocean University of China, Qingdao 266100, China
    These authors contributed equally to this work.)

  • Jian Li

    (Department of International Trade and Economy, Ocean University of China, Qingdao 266100, China)

Abstract

Self evaluation and peer evaluation in data envelopment analysis (DEA) are effective means to comprehensively reflect the efficiencies of decision-making units (DMUs). However, when some of the inputs and outputs of DMUs cannot be accurately observed, the traditional evaluation methods will lose their applicability. This paper attempts to treat the imprecise inputs and outputs as uncertain variables based on uncertainty theory and hence to propose a new uncertain DEA model for cross-efficiency evaluation via the evaluation of both self efficiency and peer efficiency. Moreover, the equivalent form and the proof of the new model are also presented for accurate calculation. Finally, a numerical example is given to illustrate the evaluation results.

Suggested Citation

  • Bao Jiang & Enxin Chi & Jian Li, 2022. "Uncertain Data Envelopment Analysis for Cross Efficiency Evaluation with Imprecise Data," Mathematics, MDPI, vol. 10(13), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2161-:d:844017
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    References listed on IDEAS

    as
    1. Waichon Lio & Baoding Liu, 2018. "Uncertain data envelopment analysis with imprecisely observed inputs and outputs," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 357-373, September.
    2. Liang, Liang & Wu, Jie & Cook, Wade D. & Zhu, Joe, 2008. "Alternative secondary goals in DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 113(2), pages 1025-1030, June.
    3. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    4. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    5. Charnes, A. & Cooper, W. W. & Rhodes, E., 1979. "Measuring the efficiency of decision-making units," European Journal of Operational Research, Elsevier, vol. 3(4), pages 339-338, July.
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