Qualitative factors in data envelopment analysis: A fuzzy number approach

• Published in: European journal of operational research Vol. 211; no. 3; pp. 586 - 593
• Main Authors: Kao, Chiang, Lin, Pei-Huang
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.06.2011; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Assurance region; Computational efficiency; Computing time; Data envelopment analysis; Data envelopment analysis Two-level mathematical programming Fuzzy sets Assurance region Qualitative data Ordinal data; Decision making units; Decision theory. Utility theory; Exact sciences and technology; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Fuzzy systems; Mathematical analysis; Mathematical functions; Mathematical models; Mathematics; Nonparametric inference; Operational research and scientific management; Operational research. Management science; Operations research; Ordinal data; Probability and statistics; Qualitative data; Sciences and techniques of general use; Statistics; Two-level mathematical programming; United Kingdom > UK; Two-level mathematical programming; Fuzzy sets; Assurance region; Qualitative data; Data envelopment analysis; Ordinal data; Performance evaluation; Membership function; Factor analysis; Ordinal analysis; Decision support system; Decision making; Non parametric estimation; Bilevel programming; Fuzzy set; Fuzzy logic; Multiplier; Ordering; Qualitative analysis; Factorial design; Mathematical programming
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.12.004

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.