Fuzzy Data Envelopment Analysis Models with R Codes

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


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.


Data envelopment analysis Fuzzy numbers Fuzzy ranking Possibility measure Fuzzy arithmetic R code 


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© 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

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