Fuzzy Slack Based Measure of Data Envelopment Analysis: A Possibility Approach

  • Shivi Agarwal
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 258)


Slack based measure (SBM) model of Data Envelopment Analysis (DEA) is very effective to evaluate the relative efficiency of decision making units (DMUs). It deals with the directly input excess and output shortfall to assess the effect of slacks on efficiency with common crisp inputs and outputs. In some cases, input and output data of DMUs can’t be precisely measured, so, the uncertain theory has played an important role in DEA. In these cases, the data can be represented as linguistic variable characterized by fuzzy numbers. This paper attempts to extend the traditional DEA model to a fuzzy framework, thus proposing a fuzzy SBM DEA model based on possibility approach to deal with the efficiency measuring problem with the given fuzzy input and output data. Finally, numerical examples are presented to illustrate the proposed fuzzy SBM model. By extending to fuzzy environment, the DEA approach is made more powerful for application.


Data envelopment analysis SBM Efficiency Fuzzy LPP Possibility theory 


  1. 1.
    Agarwal, S.: Efficiency measure by fuzzy data envelopment analysis model. In: IXX International Conference: (IMST 2010–FIM XIX) on Interdisciplinary Mathematical and Statistical Techniques held at Patna University, Patna, 18–20 Dec 2010Google Scholar
  2. 2.
    Agarwal, S., Yadav, S.P., Singh, S.P.: A new slack DEA model to estimate the impact of slacks on the efficiencies. Int. J. Oper. Res. 12(3), 241–256 (2011)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Ammar, S., Wright, R.: Applying fuzzy set theory to performance evaluation. Socio-Econ. Plann. Sci. 34, 285–302 (2000)CrossRefGoogle Scholar
  4. 4.
    Banker, R.D., Charnes, A., Cooper, W.W.: Some models for the estimation of technical and scale inefficiencies in data envelopment analysis. Manage. Sci. 30, 1078–1092 (1984)CrossRefMATHGoogle Scholar
  5. 5.
    Charnes, A., Cooper, W.W.: Chance-constrained programming. Manage. Sci. 6, 73–79 (1959)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Charnes, A., Cooper, W.W., Rhodes, E.: Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2, 429–441 (1978)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Dubois, D., Prade, H.: Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New York (1988)CrossRefMATHGoogle Scholar
  8. 8.
    Guo, P., Tanaka, H.: Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst. 119, 149–160 (2001)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Hougaard, J.L.: Fuzzy scores of technical efficiency. Eur. J. Oper. Res. 115, 529–541 (1999)CrossRefMATHGoogle Scholar
  10. 10.
    Kao, C., Liu, S.T.: Fuzzy efficiency measure in data envelopment analysis. Fuzzy Sets Syst. 113, 427–437 (2000)CrossRefMATHGoogle Scholar
  11. 11.
    Lertworasirikul, S., Fang, S., Joines, J.A., Nuttle, H.L.W.: Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst. 139, 379–394 (2003)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Lertworasirikul, S., Fang, S., Nuttle, H.L.W., Joines, J.A.: Fuzzy BCC model for data envelopment analysis. Fuzzy Optim. Decis. Making 2, 337–358 (2003)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Liu, B.: Uncertain programming. Wiley-Interscience Publication, New York (1999)Google Scholar
  14. 14.
    Liu, S.T., Chuang, M.: Fuzzy efficiency measure in fuzzy DEA/AR with application to university libraries. Fuzzy Sets Syst. 36(2), 1105–1113 (2009)Google Scholar
  15. 15.
    Saati, S., Memariani, A.: SBM model with fuzzy input-output levels in DEA. Aust. J. Basic Appl. Sci. 3(2), 352–357 (2009)Google Scholar
  16. 16.
    Sengupta, J.K.: A fuzzy system approach in data envelopment analysis. Comput. Math. Appl. 24, 259–266 (1992)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Tone, K.: A slack based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res. 130, 498–509 (2001)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Wen, M., Li, H.: Fuzzy data envelopment analysis (DEA): model and ranking method. J. Comput. Appl. Math. 223(2), 872–878 (2009)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of MathematicsBITSPilaniIndia

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