Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | [b] Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China
Note: [1] The work is supported by the National Natural Science Foundation of China (11371002) and Specialized Research Fund for the Doctoral Program of Higher Education (20131101110048).
Abstract: The existing fuzzy data envelopment analysis (DEA) models for evaluating the relative efficiencies of a set of entities called decision making units (DMUs) converting multiple fuzzy inputs into multiple fuzzy outputs are limited to convex and normal fuzzy data, moreover, the constraint condition consists of the evaluated DMUs, and efficiency is evaluated through transforming the fuzzy DEA model into the crisp DEA model by applying an alternative α-cut technique. However, in many practical evaluation problems, the fuzzy data of inputs and outputs may be non-convex or abnormal, and the evaluated DMU may not be contrasted with the DMUs under evaluation, but with sample standards determined by production strategy. In such a case, the notion of restricted fuzzy set is proposed. The constraint condition is extended to a more general form, i.e., the constraint condition, in which the sample DMUs have similar behaviors, consists of one of sample standards determined by production strategy. The basic idea is to transform the fuzzy DEA model to the conventional DEA model by applying the formula of center of mass, and the relationship between the production frontier and fuzzy DEA efficiency is given. To reduce the computational load, an algorithm based on the golden section method is employed to locate the standard that the evaluated DMU best fits. Finally, a numerical example is provided to illustrate the proposed model.
Keywords: Data envelopment analysis (DEA), the restricted fuzzy set, the center of mass, determined constraint condition, sample standards
