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 project 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 conventional data envelopment analysis (DEA) models for evaluating the relative efficiencies of a set of entities called decision making units (DMUs) converting multiple inputs into multiple outputs are limited to crisp data. In more general cases, the data of inputs and outputs, which are collected from observation or investigation, are often fluctuated and imprecise. There are many fuzzy DEA models with convex and normal fuzzy data, and those fuzzy data were transformed into crisp data by α-cuts or the lower and upper bounds to evaluate the efficiencies of DMUs. However, in many practical evaluation problems, the fuzzy data of inputs and outputs may be non-convex/convex, abnormal/normal. In such a case, the notion of fuzzy set, whose membership function is continuous and support is an interval, is presented. Based on the fundamental CCR model, a new fuzzy DEA model with the fuzzy set is proposed. The centroid formula of fuzzy set is established and introduced to evaluate DMUs. In order to illustrate the model more fully, the relationship between production frontier and fuzzy DEA efficiency is given. Finally, three numerical examples are provided to illustrate the proposed model.
Keywords: Data envelopment analysis (DEA), fuzzy set, the centroid formula
