Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

Mohammad Izadikhah, Razieh Roostaee, Ali Emrouznejad

Research output: Contribution to journalArticlepeer-review


In this paper, we reformulate the conventional DEA models as an imprecise DEA problem and propose a novel method for evaluating the DMUs when the inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose, we convert all data into interval data. In order to convert each fuzzy number into interval data, we use the nearest weighted interval approximation of fuzzy numbers by applying the weighting function, and we convert each ordinal data into interval one. In this manner, we could convert all data into interval data. The presented models determine the interval efficiencies for DMUs. To rank DMUs based on their associated interval efficiencies, we first apply the Ω-index that is developed for ranking of interval numbers. Then, by introducing an ideal DMU, we rank efficient DMUs to present a complete ranking. Finally, we use one example to illustrate the process and one real application in health care to show the usefulness of the proposed approach. For this evaluation, we consider interval, ordinal, and fuzzy data alongside the precise data to evaluate 38 hospitals selected by OIG. The results reveal the capabilities of the presented method to deal with the imprecise data.
Original languageEnglish
Pages (from-to)385-410
Number of pages26
JournalInternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Issue number3
Early online date27 May 2021
Publication statusPublished - 1 Jun 2021

Bibliographical note

Electronic version of an article published in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 29 (3), 2021. Article DOI: 10.1142/s0218488521500173 © copyright World Scientific Publishing Company.


  • Data Envelopment Analysis
  • efficiency
  • fuzzy data
  • interval data
  • nearest weighted interval approximation
  • ordinal data
  • ranking


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