A Novel Fully Fuzzy DEA Approach for Measuring Cost and Revenue Efficiency with Target Setting

In this paper, we present cost and revenue efficiency evaluation models and target setting in data envelopment analysis (DEA) in the presence of fuzzy inputs and outputs that the corresponding prices of inputs and outputs are also fuzzy numbers. We proposed a fuzzy value-based technology based on fuzzy input and output data at corresponding prices. We provide an approach for calculating fuzzy cost (revenue) efficiency based on value fuzzy based technology. The proposed fully fuzzy model is transformed into a four-objective model of non-fuzzy linear programming and solved by the weighted sum method. We show that the proposed approach is suitable than the previous approaches based on traditional models from a computational point of view. The innovation of this research is to present and solve a fully fuzzy model to obtain fuzzy cost (revenue) efficiency score as a fuzzy number and we do not need additional comparisons to detect the efficient unit in previous approaches. We also obtain benchmark corresponding to the all DMUs. In the following, with two numerical examples, we obtain the results of the presented approach and compare it with the results of the previous approaches, and at the end, we present the results of the research.