IDEAS home Printed from https://ideas.repec.org/a/spr/fuzodm/v16y2017i1d10.1007_s10700-016-9240-1.html
   My bibliography  Save this article

Fuzzy cross-efficiency evaluation: a possibility approach

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10700-016-9240-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10700-016-9240-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. José L. Ruiz & Diego Pastor & Jesús T. Pastor, 2013. "Assessing Professional Tennis Players Using Data Envelopment Analysis (DEA)," Journal of Sports Economics, , vol. 14(3), pages 276-302, June.
    6. 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.
    7. Chen, Tser-yieth, 2002. "An assessment of technical efficiency and cross-efficiency in Taiwan's electricity distribution sector," European Journal of Operational Research, Elsevier, vol. 137(2), pages 421-433, March.
    8. Sinuany-Stern, Zilla & Friedman, Lea, 1998. "DEA and the discriminant analysis of ratios for ranking units," European Journal of Operational Research, Elsevier, vol. 111(3), pages 470-478, December.
    9. Kristof Witte & Lenka Hudrlikova, 2013. "What about excellence in teaching? A benevolent ranking of universities," Scientometrics, Springer;Akadémiai Kiadó, vol. 96(1), pages 337-364, July.
    10. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    11. Cooper, W. W. & Tone, K., 1997. "Measures of inefficiency in data envelopment analysis and stochastic frontier estimation," European Journal of Operational Research, Elsevier, vol. 99(1), pages 72-88, May.
    12. 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.
    13. Timothy Anderson & Keith Hollingsworth & Lane Inman, 2002. "The Fixed Weighting Nature of A Cross-Evaluation Model," Journal of Productivity Analysis, Springer, vol. 17(3), pages 249-255, May.
    14. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min, 2016. "Research fronts in data envelopment analysis," Omega, Elsevier, vol. 58(C), pages 33-45.
    15. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Preference voting and project ranking using DEA and cross-evaluation," European Journal of Operational Research, Elsevier, vol. 90(3), pages 461-472, May.
    16. Muhittin Oral & Ossama Kettani & Pascal Lang, 1991. "A Methodology for Collective Evaluation and Selection of Industrial R&D Projects," Management Science, INFORMS, vol. 37(7), pages 871-885, July.
    17. 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.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Pejman Peykani & Farhad Hosseinzadeh Lotfi & Seyed Jafar Sadjadi & Ali Ebrahimnejad & Emran Mohammadi, 2022. "Fuzzy chance-constrained data envelopment analysis: a structured literature review, current trends, and future directions," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 197-261, June.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wenli Liu & Ying-Ming Wang & Shulong Lv, 2017. "An aggressive game cross-efficiency evaluation in data envelopment analysis," Annals of Operations Research, Springer, vol. 259(1), pages 241-258, December.
    2. Wang, Ying-Ming & Chin, Kwai-Sang, 2011. "The use of OWA operator weights for cross-efficiency aggregation," Omega, Elsevier, vol. 39(5), pages 493-503, October.
    3. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2011. "Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation," Omega, Elsevier, vol. 39(6), pages 634-641, December.
    4. Jie Wu & Junfei Chu & Qingyuan Zhu & Pengzhen Yin & Liang Liang, 2016. "DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 5990-6007, October.
    5. Davtalab-Olyaie, Mostafa & Asgharian, Masoud, 2021. "On Pareto-optimality in the cross-efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 288(1), pages 247-257.
    6. Oukil, Amar, 2020. "Exploiting value system multiplicity and preference voting for robust ranking," Omega, Elsevier, vol. 94(C).
    7. Wu, Jie & Chu, Junfei & Sun, Jiasen & Zhu, Qingyuan, 2016. "DEA cross-efficiency evaluation based on Pareto improvement," European Journal of Operational Research, Elsevier, vol. 248(2), pages 571-579.
    8. Liu, Hui-hui & Song, Yao-yao & Yang, Guo-liang, 2019. "Cross-efficiency evaluation in data envelopment analysis based on prospect theory," European Journal of Operational Research, Elsevier, vol. 273(1), pages 364-375.
    9. 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.
    10. 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.
    11. 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.
    12. Jie Wu & Junfei Chu & Qingyuan Zhu & Yongjun Li & Liang Liang, 2016. "Determining common weights in data envelopment analysis based on the satisfaction degree," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1446-1458, December.
    13. 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.
    14. 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.
    15. Ruiz, José L., 2013. "Cross-efficiency evaluation with directional distance functions," European Journal of Operational Research, Elsevier, vol. 228(1), pages 181-189.
    16. Liu, Hui-hui & Song, Yao-yao & Liu, Xiao-xiao & Yang, Guo-liang, 2020. "Aggregating the DEA prospect cross-efficiency with an application to state key laboratories in China," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    17. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.
    18. Kairui Zuo & Jiancheng Guan, 2017. "Measuring the R&D efficiency of regions by a parallel DEA game model," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 175-194, July.
    19. Soltanifar, Mehdi & Shahghobadi, Saeid, 2013. "Selecting a benevolent secondary goal model in data envelopment analysis cross-efficiency evaluation by a voting model," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 65-74.
    20. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:fuzodm:v:16:y:2017:i:1:d:10.1007_s10700-016-9240-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.