Skip to main content
SpringerLink
Log in

Fuzzy Data Envelopment Analysis Models with R Codes

  • Chapter
  • First Online:
Data Envelopment Analysis with R

Part of the book series: Studies in Fuzziness and Soft Computing ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  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)

    MATH  Google Scholar 

  2. Kao, C., Liu, S.T.: Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113, 427–437 (2000)

    Article  Google Scholar 

  3. Kao, C., Liu, S.T.: A mathematical programming approach to fuzzy efficiency ranking. Int. J. Prod. Econ. 86, 145–154 (2003)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  5. Saati, S., Memariani, A.: Reducing weight flexibility in fuzzy DEA. Appl. Math. Comput. 161(2), 611–622 (2005)

    MathSciNet  MATH  Google Scholar 

  6. Hatami-Marbini, A., Saati, S., Tavana, M.: An ideal-seeking fuzzy data envelopment analysis framework. Appl. Soft Comput. 10, 1062–1070 (2010)

    Article  Google Scholar 

  7. Kao, C., Liu, S.T.: Efficiencies of two-stage systems with fuzzy data. Fuzzy Sets Syst. 176, 20–35 (2011)

    Article  MathSciNet  Google Scholar 

  8. Kao, C., Liu, S.T.: Efficiency of parallel production systems with fuzzy data. Fuzzy Sets Syst. 198, 83–98 (2012)

    Article  MathSciNet  Google Scholar 

  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. Lozano, S.: Process efficiency of two-stage systems with fuzzy data. Fuzzy Sets Syst. 243, 36–49 (2014)

    Article  MathSciNet  Google Scholar 

  11. Yager, R.R.: A characterization of the extension principle. Fuzzy Sets Syst. 18, 205–217 (1986)

    Article  MathSciNet  Google Scholar 

  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) 28-44

    Article  MathSciNet  Google Scholar 

  13. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)

    Article  MathSciNet  Google Scholar 

  14. Zimmermann, H.J.: Fuzzy Set Theory and Its Applications, 2nd edn. Kluwer-Nijhoff, Boston (1991)

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  16. Chen, S.H.: Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst. 17, 113–129 (1985)

    Article  MathSciNet  Google Scholar 

  17. Guo, P., Tanaka, H.: Fuzzy DEA: a perceptual evaluation method. Fuzzy Sets Syst. 119, 149–160 (2001)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  21. Guo, P.: Fuzzy data envelopment analysis and its application to location problems. Inf. Sci. 179, 820–829 (2009)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  25. Ramik, J., Rimanek, J.: Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets Syst. 16, 123–138 (1985)

    Article  MathSciNet  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  27. Yao, J.-S., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets Syst. 116, 275–288 (2000)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  30. Ruiz, J.L., Sirvent, I.: Fuzzy cross-efficiency evaluation: a possibility approach. Fuzzy Optim. Decis. Making 16(1), 111–126 (2017)

    Article  MathSciNet  Google Scholar 

  31. Charnes, A., Cooper, W.W.: Chance-constrained programming. Manage. Sci. 6, 73–79 (1959)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Farhad Hosseinzadeh Lotfi

  2. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

    Ali Ebrahimnejad

  3. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

    Mohsen Vaez-Ghasemi

  4. Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran

    Zohreh Moghaddas

Authors
  1. Farhad Hosseinzadeh Lotfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Ebrahimnejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohsen Vaez-Ghasemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zohreh Moghaddas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Ebrahimnejad .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hosseinzadeh Lotfi, F., Ebrahimnejad, A., Vaez-Ghasemi, M., Moghaddas, Z. (2020). Fuzzy Data Envelopment Analysis Models with R Codes. In: Data Envelopment Analysis with R. Studies in Fuzziness and Soft Computing, vol 386. Springer, Cham. https://doi.org/10.1007/978-3-030-24277-0_5

Download citation

Publish with us

Policies and ethics

Search

Navigation