Fuzzy DEA model based on cloud theory

Traditional data envelopment analysis (DEA) models require the values for all inputs and outputs should be known exactly. However, it is essential to take into account the presence of qualitative factors of inputs and outputs in a real evaluation problem. By referring to the cloud theory and conventional interval DEA model, this paper develops a new fuzzy DEA model called Cloud DEA (C-DEA) model to deal with qualitative factors. Through three digital parameters (Ex, En, He), the fuzziness and randomness of qualitative factors are integrated in a unified way. Based on cloud generator and alpha-level sets, qualitative information and fuzzy data are converted into interval data, respectively, and are incorporated into the interval DEA models. It shows in a numerical example that the C-DEA model has many advantages over the conventional DEA methodology and can be used to evaluate the relative efficiency of decision making units (DMUs) under uncertainty.