Efficiency Measurement in Data Envelopment Analysis with Fuzzy Data

  • Chiang KaoEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 221)


Conventional data envelopment analysis (DEA) requires the data to have crisp values, which can be measured precisely. However, there are cases where data is missing and has to be estimated, or the situation has not occurred yet and the data has to be predicted. There are also cases where the factors are qualitative, and thus the data cannot be measured precisely. In these cases, fuzzy numbers can be used to represent the imprecise values, and this paper discusses the corresponding measurement of efficiency. Based on the extension principle, two approaches are proposed; one views the membership function of the fuzzy data vertically, and the results are represented by membership grades. The other views it horizontally, and the results are represented by α-cuts. The former approach is easier to understand, yet is applicable only to very simple problems. The latter, in contrast, can be applied to all problems, and is easier to implement. An example explains the development and implementation of these two approaches.


Data envelopment analysis Fuzzy data Two-level programming Extension principle 


  1. Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag Sci 30:1078–1092CrossRefGoogle Scholar
  2. Bellman R, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17B:141–164CrossRefGoogle Scholar
  3. Castelli L, Pesenti R, Ukovich W (2010) A classification of DEA models when the internal structure of the decision making units is considered. Ann Oper Res 173:207–235CrossRefGoogle Scholar
  4. Charnes A, Cooper WW (1984) The non-Archimedean CCR ratio for efficiency analysis: a rejoinder to Boyd and Färe, Eur J Oper Res 15:333–334CrossRefGoogle Scholar
  5. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444CrossRefGoogle Scholar
  6. Chen CB, Klein CM (1997) A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Trans Syst Man Cybern Part B: Cybern 27:26–35CrossRefGoogle Scholar
  7. Cook WD, Seiford LM (2009) Data envelopment analysis (DEA)—thirty years on. Eur J Oper Res 192:1–17CrossRefGoogle Scholar
  8. Dia M (2004) A model of fuzzy data envelopment analysis. INFOR 42:267–279Google Scholar
  9. Guo PJ (2009) Fuzzy data envelopment analysis and its application to location problems. Inf Sci 179:820–829CrossRefGoogle Scholar
  10. Jahanshahloo GR, Soleimani-damaneh M, Nasrabadi E (2004) Measure of efficiency in DEA with fuzzy input-output levels: a methodology for assessing, ranking and imposing of weights restrictions. Appl Maths Comput 156:175–187CrossRefGoogle Scholar
  11. Kao C, Lin PH (2011) Qualitative factors in data envelopment analysis: a fuzzy number approach. Eur J Oper Res 211:586–593CrossRefGoogle Scholar
  12. Kao C, Lin PL (2012) Efficiency of parallel production systems with fuzzy data. Fuzzy Sets Syst 198:83–98CrossRefGoogle Scholar
  13. Kao C, Liu ST (2000a) Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst 113:427–437CrossRefGoogle Scholar
  14. Kao C, Liu ST (2000b) Data envelopment analysis with missing data: an application to university libraries in Taiwan. J Oper Res Soc 51:897–905CrossRefGoogle Scholar
  15. Kao C, Liu ST (2004) Predicting bank performance with financial forecasts: a case of Taiwan commercial banks. J Bank Financ 28:2353–2368CrossRefGoogle Scholar
  16. Kao C, Liu ST (2011) Efficiencies of two-stage systems with fuzzy data. Fuzzy Sets Syst 176:20–35CrossRefGoogle Scholar
  17. Leon T, Liern V, Ruiz JL, Sirvent I (2003) A fuzzy mathematical programming approach to the assessment of efficiency with DEA models. Fuzzy Sets Syst 139:407–419CrossRefGoogle Scholar
  18. Lertworasirkul S, Fang SC, Joines JA, Nuttle HLW (2003) Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst 139:379–394CrossRefGoogle Scholar
  19. Wen ML, Li HS (2009) Fuzzy data envelopment analysis (DEA): model and ranking method. J Comput Appl Maths 223:872–878CrossRefGoogle Scholar
  20. Yager RR (1986) A characterization of the extension principle. Fuzzy Sets Syst 18:205–217CrossRefGoogle Scholar
  21. Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28CrossRefGoogle Scholar
  22. Zimmermann HZ (1996) Fuzzy set theory and its applications (3rd ed). Boston: Kluwer-NijhoffCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Industrial and Information ManagementNational Cheng Kung UniversityTainanTaiwan

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