Carbon efficiency evaluation: an analytical framework using fuzzy DEA

Joshua Ignatius*, Mohammadreza Ghasemi, Feng Zhang, Ali Emrouznejad, Adel Hatami-Marbini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Data Envelopment Analysis (DEA) is a powerful analytical technique for measuring the relative efficiency of alternatives based on their inputs and outputs. The alternatives can be in the form of countries who attempt to enhance their productivity and environmental efficiencies concurrently. However, when desirable outputs such as productivity increases, undesirable outputs increase as well (e.g. carbon emissions), thus making the performance evaluation questionable. In addition, traditional environmental efficiency has been typically measured by crisp input and output (desirable and undesirable). However, the input and output data, such as CO2 emissions, in real-world evaluation problems are often imprecise or ambiguous. This paper proposes a DEA-based framework where the input and output data are characterized by symmetrical and asymmetrical fuzzy numbers. The proposed method allows the environmental evaluation to be assessed at different levels of certainty. The validity of the proposed model has been tested and its usefulness is illustrated using two numerical examples. An application of energy efficiency among 23 European Union (EU) member countries is further presented to show the applicability and efficacy of the proposed approach under asymmetric fuzzy numbers.
Original languageEnglish
Pages (from-to)428-440
JournalEuropean Journal of Operational Research
Issue number2
Early online date18 Feb 2016
Publication statusPublished - 1 Sept 2016

Bibliographical note

© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International


  • data envelopment analysis
  • energy efficiency
  • fuzzy expected interval
  • fuzzy expected value
  • fuzzy ranking approach


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