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Fuzzy cross-efficiency evaluation: a possibility approach

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  • José L. Ruiz

    (Universidad Miguel Hernández)

  • Inmaculada Sirvent

    (Universidad Miguel Hernández)

Abstract

Cross-efficiency evaluation is an extension of data envelopment analysis (DEA) aimed at ranking decision making units (DMUs) involved in a production process regarding their efficiency. As has been done with other enhancements and extensions of DEA, in this paper we propose a fuzzy approach to the cross-efficiency evaluation. Specifically, we develop a fuzzy cross-efficiency evaluation based on the possibility approach by Lertworasirikul et al. (Fuzzy Sets Syst 139:379–394, 2003a) to fuzzy DEA. Thus, a methodology for ranking DMUs is presented that may be used when data are imprecise, in particular for fuzzy inputs and outputs being normal and convex. We prove some results that allow us to define “consistent” cross-efficiencies. The ranking of DMUs for a given possibility level results from an ordering of cross-efficiency scores, which are real numbers. As in the crisp case, we also develop benevolent and aggressive fuzzy formulations in order to deal with the alternate optima for the weights.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:16:y:2017:i:1:d:10.1007_s10700-016-9240-1
    DOI: 10.1007/s10700-016-9240-1
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    References listed on IDEAS

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    Cited by:

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    2. Adel Hatami-Marbini & Saber Saati & Seyed Mojtaba Sajadi, 2018. "Efficiency analysis in two-stage structures using fuzzy data envelopment analysis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 909-932, December.
    3. 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.
    4. M. Bagheri & A. Ebrahimnejad & S. Razavyan & F. Hosseinzadeh Lotfi & N. Malekmohammadi, 2022. "Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem," Operational Research, Springer, vol. 22(2), pages 1479-1509, April.
    5. Yu Yu & Weiwei Zhu & Qian Zhang, 2019. "DEA cross-efficiency evaluation and ranking method based on interval data," Annals of Operations Research, Springer, vol. 278(1), pages 159-175, July.

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