IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v211y2011i3p586-593.html
   My bibliography  Save this article

Qualitative factors in data envelopment analysis: A fuzzy number approach

Author

Listed:
  • Kao, Chiang
  • Lin, Pei-Huang

Abstract

Qualitative factors are difficult to mathematically manipulate when calculating the efficiency in data envelopment analysis (DEA). The existing methods of representing the qualitative data by ordinal variables and assigning values to obtain efficiency measures only superficially reflect the precedence relationship of the ordinal data. This paper treats the qualitative data as fuzzy numbers, and uses the DEA multipliers associated with the decision making units (DMUs) being evaluated to construct the membership functions. Based on Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the [alpha]-cuts of the fuzzy efficiencies. Fuzzy efficiencies contain more information for making better decisions. A performance evaluation of the chemistry departments of 52 UK universities is used for illustration. Since the membership functions are constructed from the opinion of the DMUs being evaluated, the results are more representative and persuasive.

Suggested Citation

  • Kao, Chiang & Lin, Pei-Huang, 2011. "Qualitative factors in data envelopment analysis: A fuzzy number approach," European Journal of Operational Research, Elsevier, vol. 211(3), pages 586-593, June.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:586-593
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00840-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. K S Park, 2007. "Efficiency bounds and efficiency classifications in DEA with imprecise data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 533-540, April.
    3. Kao, Chiang, 1994. "Evaluation of junior colleges of technology: The Taiwan case," European Journal of Operational Research, Elsevier, vol. 72(1), pages 43-51, January.
    4. Cook, Wade D. & Zhu, Joe, 2006. "Rank order data in DEA: A general framework," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1021-1038, October.
    5. 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.
    6. Medaglia, Andres L. & Fang, Shu-Cherng & Nuttle, Henry L. W. & Wilson, James R., 2002. "An efficient and flexible mechanism for constructing membership functions," European Journal of Operational Research, Elsevier, vol. 139(1), pages 84-95, May.
    7. Joe Zhu, 2004. "Imprecise DEA via Standard Linear DEA Models with a Revisit to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 52(2), pages 323-329, April.
    8. Charnes, A. & Cooper, W. W., 1984. "The non-archimedean CCR ratio for efficiency analysis: A rejoinder to Boyd and Fare," European Journal of Operational Research, Elsevier, vol. 15(3), pages 333-334, March.
    9. Beasley, J. E., 1990. "Comparing university departments," Omega, Elsevier, vol. 18(2), pages 171-183.
    10. R G Dyson & E A Shale, 2010. "Data envelopment analysis, operational research and uncertainty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 25-34, January.
    11. William W. Cooper & Kyung Sam Park & Gang Yu, 2001. "An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 49(6), pages 807-820, December.
    12. Park, K. Sam, 2010. "Duality, efficiency computations and interpretations in imprecise DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 289-296, January.
    13. William W. Cooper & Kyung Sam Park & Gang Yu, 1999. "IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA," Management Science, INFORMS, vol. 45(4), pages 597-607, April.
    14. Kao, Chiang, 2006. "Interval efficiency measures in data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1087-1099, October.
    15. 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.
    16. Despotis, Dimitris K. & Smirlis, Yiannis G., 2002. "Data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 140(1), pages 24-36, July.
    17. 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.
    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. Entezam, Hasan Farmani & Sobhani, Farzad Movahedi & Najafi, Seyed Esmaeil & Roshdi, Israfil, 2020. "A multi-component enhanced Russell measure of efficiency: With application to water supply plans," Socio-Economic Planning Sciences, Elsevier, vol. 70(C).
    2. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    3. Yu-Jie Zheng & Yu Yang & Na Zhang & Yao Jiao, 2016. "A Supernetwork-Based Model for Design Processes of Complex Mechanical Products," Sustainability, MDPI, vol. 8(10), pages 1-25, October.
    4. Xiyang Lei & Yongjun Li & Alec Morton, 2022. "Dominance and ranking interval in DEA parallel production systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 649-675, June.
    5. Vladimir Pajković & Mirjana Grdinić-Rakonjac, 2021. "Evaluation of Road Safety Performance Based on Self-Reported Behaviour Data Set," Sustainability, MDPI, vol. 13(24), pages 1-18, December.
    6. Ding, Tao & Zhang, Yun & Zhang, Danlu & Li, Feng, 2023. "Performance evaluation of Chinese research universities: A parallel interactive network DEA approach with shared and fixed sum inputs," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    7. Ya Chen & Wade D. Cook & Juan Du & Hanhui Hu & Joe Zhu, 2017. "Bounded and discrete data and Likert scales in data envelopment analysis: application to regional energy efficiency in China," Annals of Operations Research, Springer, vol. 255(1), pages 347-366, August.
    8. Sarah J.-Sharahi & Kaveh Khalili-Damghani & Amir-Reza Abtahi & Alireza Rashidi Komijan, 2021. "A new network data envelopment analysis models to measure the efficiency of natural gas supply chain," Operational Research, Springer, vol. 21(3), pages 1461-1486, September.
    9. Xiao Shi & Ali Emrouznejad & Minyue Jin & Feng Yang, 2020. "A new parallel fuzzy data envelopment analysis model for parallel systems with two components based on Stackelberg game theory," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 311-332, September.

    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. H-T Lin, 2011. "Efficiency analysis of chain stores: a case study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1268-1281, July.
    2. Shaher Z. Zahran & Jobair Bin Alam & Abdulrahem H. Al-Zahrani & Yiannis Smirlis & Stratos Papadimitriou & Vangelis Tsioumas, 2020. "Analysis of port efficiency using imprecise and incomplete data," Operational Research, Springer, vol. 20(1), pages 219-246, March.
    3. Kao, Chiang & Liu, Shiang-Tai, 2009. "Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks," European Journal of Operational Research, Elsevier, vol. 196(1), pages 312-322, July.
    4. Park, K. Sam, 2010. "Duality, efficiency computations and interpretations in imprecise DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 289-296, January.
    5. HATAMI-MARBINI, Adel & AGRELL, Per & AGHAYI, Nazila, 2013. "Imprecise data envelopment analysis for the two-stage process," LIDAM Discussion Papers CORE 2013004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Kao, Chiang, 2006. "Interval efficiency measures in data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1087-1099, October.
    7. Shabani, Amir & Visani, Franco & Barbieri, Paolo & Dullaert, Wout & Vigo, Daniele, 2019. "Reliable estimation of suppliers’ total cost of ownership: An imprecise data envelopment analysis model with common weights," Omega, Elsevier, vol. 87(C), pages 57-70.
    8. Kao, Chiang & Liu, Shiang-Tai, 2004. "Predicting bank performance with financial forecasts: A case of Taiwan commercial banks," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2353-2368, October.
    9. Toloo, Mehdi & Mensah, Emmanuel Kwasi & Salahi, Maziar, 2022. "Robust optimization and its duality in data envelopment analysis," Omega, Elsevier, vol. 108(C).
    10. Adel Hatami-Marbini & Zahra Ghelej Beigi & Hirofumi Fukuyama & Kobra Gholami, 2015. "Modeling Centralized Resources Allocation and Target Setting in Imprecise Data Envelopment Analysis," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1189-1213, November.
    11. Lampe, Hannes W. & Hilgers, Dennis, 2015. "Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA," European Journal of Operational Research, Elsevier, vol. 240(1), pages 1-21.
    12. Bohlool Ebrahimi & Madjid Tavana & Andreas Kleine & Andreas Dellnitz, 2021. "An epsilon-based data envelopment analysis approach for solving performance measurement problems with interval and ordinal dual-role factors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1103-1124, December.
    13. Cui, Qiang & Lin, Jing-ling & Jin, Zi-yin, 2020. "Evaluating airline efficiency under “Carbon Neutral Growth from 2020” strategy through a Network Interval Slack-Based Measure," Energy, Elsevier, vol. 193(C).
    14. Jolly Puri & Shiv Prasad Yadav, 2017. "Improved DEA models in the presence of undesirable outputs and imprecise data: an application to banking industry in India," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1608-1629, November.
    15. 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.
    16. Anna Labijak-Kowalska & Miłosz Kadziński, 2023. "Exact and stochastic methods for robustness analysis in the context of Imprecise Data Envelopment Analysis," Operational Research, Springer, vol. 23(1), pages 1-34, March.
    17. Adel Hatami-Marbini & Zahra Ghelej Beigi & Jens Leth Hougaard & Kobra Gholami, 2014. "Estimating Returns to Scale in Imprecise Data Envelopment Analysis," MSAP Working Paper Series 07_2014, University of Copenhagen, Department of Food and Resource Economics.
    18. Adel Hatami-Marbini & Per J. Agrell & Hirofumi Fukuyama & Kobra Gholami & Pegah Khoshnevis, 2017. "The role of multiplier bounds in fuzzy data envelopment analysis," Annals of Operations Research, Springer, vol. 250(1), pages 249-276, March.
    19. Toloo, Mehdi & Keshavarz, Esmaeil & Hatami-Marbini, Adel, 2018. "Dual-role factors for imprecise data envelopment analysis," Omega, Elsevier, vol. 77(C), pages 15-31.
    20. Mehdi Toloo & Esmaeil Keshavarz & Adel Hatami-Marbini, 2021. "An interval efficiency analysis with dual-role factors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 255-287, March.

    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:eee:ejores:v:211:y:2011:i:3:p:586-593. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.