A dual sbm model with fuzzy weights in fuzzy DEA

Abstract

The dual part of a SBM model in data envelopment analysis (DEA) aims to calculate the optimal virtual costs and prices (also known as weights) of inputs and outputs for the concerned decision-making units (DMUs). In conventional dual SBM model, the weights are found as crisp quantities. However, in real-world problems, the weights of inputs and outputs in DEA may have fuzzy essence. In this paper, we propose a dual SBM model with fuzzy weights for input and output data. The proposed model is then reduced to a crisp linear programming problem by using ranking function of a fuzzy number (FN). This model gives the fuzzy efficiencies and the fuzzy weights of inputs and outputs of the concerned DMUs as triangular fuzzy numbers (TFNs). The proposed model is illustrated with a numerical example.