Qualitative factors in data envelopment analysis: A fuzzy number approach

Chiang Kao, Pei Huang Lin

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


Qualitative factors are difficult to mathematically manipulate when calculating the efficiency in data envelopment analysis (DEA). The existing methods of representing the qualitative data by ordinal variables and assigning values to obtain efficiency measures only superficially reflect the precedence relationship of the ordinal data. This paper treats the qualitative data as fuzzy numbers, and uses the DEA multipliers associated with the decision making units (DMUs) being evaluated to construct the membership functions. Based on Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the α-cuts of the fuzzy efficiencies. Fuzzy efficiencies contain more information for making better decisions. A performance evaluation of the chemistry departments of 52 UK universities is used for illustration. Since the membership functions are constructed from the opinion of the DMUs being evaluated, the results are more representative and persuasive.

Original languageEnglish
Pages (from-to)586-593
Number of pages8
JournalEuropean Journal of Operational Research
Issue number3
Publication statusPublished - 2011 Jun 16

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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