Advertisement

Fuzzy Data Envelopment Analysis Models with R Codes

  • Farhad Hosseinzadeh Lotfi
  • Ali EbrahimnejadEmail author
  • Mohsen Vaez-Ghasemi
  • Zohreh Moghaddas
Chapter
First Online:
  • 548 Downloads
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 386)

Abstract

The conventional DEA models such as CCR and BBC models require precise input and output data, which may not always be available in real world applications. However, in real life problems, inputs and outputs are often imprecise. To deal with imprecise data, the notion of fuzziness has been introduced in DEA and so the DEA has been extended to fuzzy DEA (FDEA). In this chapter, the main approaches for solving FDEA models are classified into five groups and the mathematical approaches of each category are described briefly. Then, R codes for each FDEA model are provided. Finally, numerical examples are provided to illustrate the main advantages of R in FDEA models.

Keywords

Data envelopment analysis Fuzzy numbers Fuzzy ranking Possibility measure Fuzzy arithmetic R code 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Emrouznejad, A., Tavana, M., Hatami-Marbini, A.: The state of the art in fuzzy data envelopment analysis. In: Performance Measurement with Fuzzy Data Envelopment Analysis. Studies in Fuzziness and Soft Computing, vol. 309, pp. 1–48. Springer, Berlin (2014)zbMATHGoogle Scholar
  2. 2.
    Kao, C., Liu, S.T.: Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113, 427–437 (2000)CrossRefGoogle Scholar
  3. 3.
    Kao, C., Liu, S.T.: A mathematical programming approach to fuzzy efficiency ranking. Int. J. Prod. Econ. 86, 145–154 (2003)CrossRefGoogle Scholar
  4. 4.
    Saati, S., Memariani, A., Jahanshahloo, G.R.: Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optim. Decis. Making 1, 255–267 (2002)CrossRefGoogle Scholar
  5. 5.
    Saati, S., Memariani, A.: Reducing weight flexibility in fuzzy DEA. Appl. Math. Comput. 161(2), 611–622 (2005)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Hatami-Marbini, A., Saati, S., Tavana, M.: An ideal-seeking fuzzy data envelopment analysis framework. Appl. Soft Comput. 10, 1062–1070 (2010)CrossRefGoogle Scholar
  7. 7.
    Kao, C., Liu, S.T.: Efficiencies of two-stage systems with fuzzy data. Fuzzy Sets Syst. 176, 20–35 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kao, C., Liu, S.T.: Efficiency of parallel production systems with fuzzy data. Fuzzy Sets Syst. 198, 83–98 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hatami-Marbini, A., Tavana, M., Emrouznejad, A., Saati, S.: Efficiency measurement in fuzzy additive data envelopment analysis. Int. J. Ind. Syst. Eng. 10(1), 1–20 (2012)Google Scholar
  10. 10.
    Lozano, S.: Process efficiency of two-stage systems with fuzzy data. Fuzzy Sets Syst. 243, 36–49 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yager, R.R.: A characterization of the extension principle. Fuzzy Sets Syst. 18, 205–217 (1986)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Systems Man Cybemet. SMC-1 (1973) 28-44MathSciNetCrossRefGoogle Scholar
  13. 13.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Zimmermann, H.J.: Fuzzy Set Theory and Its Applications, 2nd edn. Kluwer-Nijhoff, Boston (1991)CrossRefGoogle Scholar
  15. 15.
    Chen, C.B., Klein, C.M.: A simple approach to ranking a group of aggregated fuzzy utilities, IEEE Trans. Syst. Man Cybernet. Part B: Cybemet. 27, 26–35 (1997)CrossRefGoogle Scholar
  16. 16.
    Chen, S.H.: Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst. 17, 113–129 (1985)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Guo, P., Tanaka, H.: Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst. 119, 149–160 (2001)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Leon, T., Liern, V., Ruiz, J.L., Sirvent, I.: A fuzzy mathematical programming approach to the assessment of efficiency with DEA models. Fuzzy Sets Syst. 139, 407–419 (2003)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Soleimani-damaneh, M., Jahanshahloo, G.R., Abbasbandy, S.: Computational and theoretical pitfalls in some current performance measurement techniques and a new approach. Appl. Math. Comput. 181, 1199–1207 (2006)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Guo, P., Tanaka, H.: Decision making based on fuzzy data envelopment analysis. In: Ruan, D., Meer, K. (eds.) Intelligent Decision and Policy Making Support Systems, pp. 39–54. Springer, Berlin (2008)CrossRefGoogle Scholar
  21. 21.
    Guo, P.: Fuzzy data envelopment analysis and its application to location problems. Inf. Sci. 179, 820–829 (2009)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Shahverdi, R., Adabitabar, M., Rostami-Malkhalifeh, M., Sohraiee, S.: Ranking DMUs by l1-norm with fuzzy data in DEA. Chaos, Solitons Fractals 39(5), 2294–2302 (2009)CrossRefGoogle Scholar
  23. 23.
    Ebrahimnejad, A.: Cost efficiency measures with trapezoidal fuzzy numbers in data envelopment analysis based on ranking functions: application in insurance organization and hospital. Int. J. Fuzzy Syst. Appl. 2(3), 51–68 (2012)CrossRefGoogle Scholar
  24. 24.
    Ebrahimnejad, A.: A new link between output-oriented BCC model with fuzzy data in the present of undesirable outputs and MOLP. Fuzzy Inf. Eng. 2, 113–125 (2011)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Ramik, J., Rimanek, J.: Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets Syst. 16, 123–138 (1985)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Tanaka, H., Ichihasi, H., Asai, K.: A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers. Control Cybern. 13, 185–194 (1984)MathSciNetzbMATHGoogle Scholar
  27. 27.
    Yao, J.-S., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets Syst. 116, 275–288 (2000)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Lertworasirikul, S., Fang, S.C., Joines, J.A., Nuttle, H.L.W.: Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst. 139, 379–394 (2003)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Lertworasirikul, S., Fang, S.C., Nuttle, H.L.W., Joines, J.A.: Fuzzy BCC model for data envelopment analysis. Fuzzy Optim. Decis. Making 2(4), 337–358 (2003)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Ruiz, J.L., Sirvent, I.: Fuzzy cross-efficiency evaluation: a possibility approach. Fuzzy Optim. Decis. Making 16(1), 111–126 (2017)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Charnes, A., Cooper, W.W.: Chance-constrained programming. Manage. Sci. 6, 73–79 (1959)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Wang, Y.M., Luo, Y., Liang, L.: Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert Syst. Appl. 36, 5205–5211 (2009)CrossRefGoogle Scholar
  33. 33.
    Bhardwaj, B., Kaur, J., Kumar, A.: A new fuzzy CCR data envelopment analysis model and its application to manufacturing enterprises. In: Collan, M., Kacprzyk, J. (eds.) Soft Computing Applications for Group Decision-making and Consensus Modeling. Studies in Fuzziness and Soft Computing, vol. 357. Springer, Cham (2018)Google Scholar
  34. 34.
    Azar, A., Zarei Mahmoudabadi, M., Emrouznejad, A.: A new fuzzy additive model for determining the common set of weights in Data Envelopment Analysis. J. Intell. Fuzzy Syst. 30(1), 61–69 (2016)CrossRefGoogle Scholar
  35. 35.
    Hatami-Marbini, A., Ebrahimnejad, A., Lozano, S.: Fuzzy efficiency measures in data envelopment analysis using lexicographic multiobjective approach. Comput. Ind. Eng. 105, 362–376 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Farhad Hosseinzadeh Lotfi
    • 1
  • Ali Ebrahimnejad
    • 2
    Email author
  • Mohsen Vaez-Ghasemi
    • 3
  • Zohreh Moghaddas
    • 4
  1. 1.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of Mathematics, Qaemshahr BranchIslamic Azad UniversityQaemshahrIran
  3. 3.Department of Mathematics, Rasht BranchIslamic Azad UniversityRashtIran
  4. 4.Department of Mathematics, Qazvin BranchIslamic Azad UniversityQazvinIran

Personalised recommendations

Cite chapter

Buy options