Central European Journal of Operations Research

, Volume 25, Issue 4, pp 889–905 | Cite as

Solving generalized fuzzy data envelopment analysis model: a parametric approach

  • Ali Asghar Foroughi
  • Roohollah Abbasi Shureshjani
Original Paper


Data envelopment analysis (DEA) is a non-parametric technique to assess the performance of a set of homogeneous decision making units (DMUs) with common crisp inputs and outputs. Regarding the problems that are modelled out of the real world, the data cannot constantly be precise and sometimes they are vague or fluctuating. So in the modelling of such data, one of the best approaches is using the fuzzy numbers. Substituting the fuzzy numbers for the crisp numbers in DEA, the traditional DEA problem transforms into a fuzzy data envelopment analysis (FDEA) problem. Different methods have been suggested to compute the efficiency of DMUs in FDEA models so far but the most of them have limitations such as complexity in calculation, non-contribution of decision maker in decision making process, utilizable for a specific model of FDEA and using specific group of fuzzy numbers. In the present paper, to overcome the mentioned limitations, a new approach is proposed. In this approach, the generalized FDEA problem is transformed into a parametric programming, in which, parameter selection depends on the decision maker’s ideas. Two numerical examples are used to illustrate the approach and to compare it with some other approaches.


Data envelopment analysis Fuzzy numbers GFDEA model Parametric programming 



The authors are grateful for the comments and suggestions made by two anonymous reviewers, which helped to improve this paper. By the agreement between EURO and IFORS, second author could be sponsored by IFORS from a non-EURO member society to participate in ESI XXXII and this paper was first presented there. Also, his travel report is published in IFORS newsletter, September 2015. Thanks to IFORS and ESI organizing committee.


  1. Abbasbandy S, Hajjari T (2009) A new approach for ranking of trapezoidal fuzzy numbers. Comput Math Appl 57:413–419CrossRefGoogle Scholar
  2. Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in DEA. Manag Sci 30(9):1078–1092CrossRefGoogle Scholar
  3. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 6:429–444CrossRefGoogle Scholar
  4. Cheng CH (1998) A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst 95:307–317CrossRefGoogle Scholar
  5. Chen S-M, Sanguansat K (2011) Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Syst Appl 38(3):2163–2171CrossRefGoogle Scholar
  6. Chu TC, Tsao CT (2002) Ranking fuzzy numbers with an area between the centroid point and the original point. Comput Math Appl 43:111–117CrossRefGoogle Scholar
  7. Cooper WW, Seiford LM, Tone K (2007) Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software, 2nd edn. Springer, New YorkGoogle Scholar
  8. Detyniecki M, Yager RR (2001) Ranking fuzzy numbers using \(\alpha \)-weighted valuations. Int J Uncertain Fuzziness Knowl-Based Syst 8(5):573–592CrossRefGoogle Scholar
  9. Emrouznejad A, Tavana M, Hatami-Marbini A (2014) The state of the art in fuzzy data envelopment analysis. In: Emrouznejad A, Tavana M (eds) Performance measurement with fuzzy data envelopment analysis (Studies in Fuzziness and Soft Computing), vol. 309. Springer, Berlin, pp 1–45Google Scholar
  10. Färe R, Grosskopf S (1985) A nonparametric cost approach to scale efficiency. Scand J Econ 87(4):594–604CrossRefGoogle Scholar
  11. Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc A 120(3):253–281CrossRefGoogle Scholar
  12. Guo P, Tanaka H (2001) Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst 119(1):149–160CrossRefGoogle Scholar
  13. Hadi-Vencheh A, Foroughi AA, Soleimani-Damaneh M (2008) A DEA model for resource allocation. Econ Model 25:983–993CrossRefGoogle Scholar
  14. Hatami-Marbini A, Saati S, Makui A (2009) An application of fuzzy numbers ranking in performance analysis. J Appl Sci 9(9):1770–1775CrossRefGoogle Scholar
  15. Hatami-Marbini A, Tavana M, Saati S, Agrell PJ (2013) Positive and normative use of fuzzy DEA-BCC models: a critical view on NATO enlargement. Int Trans Oper Res 20:411–433CrossRefGoogle Scholar
  16. Kao C, Liu ST (2000) Data envelopment analysis with missing data: an application to University libraries in Taiwan. J Oper Res Soc 51(8):897–905Google Scholar
  17. Kao C, Liu ST (2005) Data envelopment analysis with imprecise data: an application of Taiwan machinery firms. Int J Uncertain Fuzziness Knowl-Based Syst 13(2):225–240CrossRefGoogle Scholar
  18. Kuo HC, Wang LH (2007) Operating performance by the development of efficiency measurement based on fuzzy DEA. In: Second international conference on innovative computing, information and control, p 196Google Scholar
  19. Lertworasirikul S, Shu-Cherng F, Joines JA, Nuttle HLW (2003a) Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst 139(2):379–394CrossRefGoogle Scholar
  20. Lertworasirikul S, Fang SC, Nuttle HLW, Joines JA (2003b) Fuzzy BCC model for data envelopment analysis. Fuzzy Optim Decis Mak 2(4):337–358CrossRefGoogle Scholar
  21. Puri J, Yadav SP (2013) A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector. Expert Syst Appl 40:1437–1450CrossRefGoogle Scholar
  22. Saati S, Memariani A, Jahanshahloo GR (2002) Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optim Decis Mak 1:255–267CrossRefGoogle Scholar
  23. Seiford LM, Thrall RM (1990) The mathematical programming approach to frontier analysis. J Econom 46:7–38CrossRefGoogle Scholar
  24. Sengupta JK (1992) A fuzzy systems approach in data envelopment analysis. Comput Math Appl 24(9):259–266CrossRefGoogle Scholar
  25. Shureshjani RA, Darehmiraki M (2013) A new parametric method for ranking fuzzy numbers. Indag Math 24:518–529CrossRefGoogle Scholar
  26. Triantis KP, Girod O (1998) A mathematical programming approach for measuring technical efficiency in a fuzzy environment. J Product Anal 10(1):85–102CrossRefGoogle Scholar
  27. Wang YM, Yang JB, Xu DL, Chin KS (2006) On the centroids of fuzzy numbers. Fuzzy Sets Syst 157:919–926CrossRefGoogle Scholar
  28. Wang YJ, Lee HS (2008) The revised method of ranking fuzzy numbers with an area between the centroid and original points. Comput Math Appl 55:2033–2042CrossRefGoogle Scholar
  29. Wen M, Li H (2009) Fuzzy data envelopment analysis (DEA): model and ranking method. J Comput Appl Math 223:872–878CrossRefGoogle Scholar
  30. Yao J, Wu K (2000) Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets Syst 116:275–288CrossRefGoogle Scholar
  31. Yu G, Wei QL, Brockett P (1996a) A generalized data envelopment analysis model: a unification and extension of existing methods for efficiency analysis of decision making units. Ann Oper Res 66:47–89CrossRefGoogle Scholar
  32. Yu G, Wei QL, Brockett P, Zhou L (1996b) Construction of all DEA efficient surfaces of the production possibility set under the generalized data envelopment analysis model. Eur J Oper Res 95:491–510CrossRefGoogle Scholar
  33. Zhou SJ, Zhang ZD, Li YC (2008) Research of real estate investment risk evaluation based on fuzzy data envelopment analysis method. In: Proceedings of the international conference on risk management and engineering management, pp 444–448Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Ali Asghar Foroughi
    • 1
  • Roohollah Abbasi Shureshjani
    • 1
  1. 1.Department of MathematicsUniversity of QomQomIran

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