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Qualitative factors in data envelopment analysis: A fuzzy number approach

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  • Kao, Chiang
  • Lin, Pei-Huang
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 211 (2011)
    Issue (Month): 3 (June)
    Pages: 586-593

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    Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:586-593

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Data envelopment analysis Two-level mathematical programming Fuzzy sets Assurance region Qualitative data Ordinal data;

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    1. 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.
    2. 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.
    3. 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.
    4. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages B141-B164, December.
    5. 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.
    6. 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.
    7. Beasley, J. E., 1990. "Comparing university departments," Omega, Elsevier, vol. 18(2), pages 171-183.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
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