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This study aims to present the cost and revenue efficiency evaluation models in data envelopment analysis in the presence of fuzzy inputs, outputs and their prices that the prices are also fuzzy. This study applies the proposed approach in the energy sector of the oil industry.

This study proposes a value-based technology according to fuzzy input-cost and revenue-output data, and based on this technology, the authors propose an approach to calculate fuzzy cost and revenue efficiency based on a directional distance function approach. These papers incorporated a decision-maker’s (DM) a priori knowledge into the fuzzy cost (revenue) efficiency analysis.

This study shows that the proposed approach obtains the components of fuzzy numbers corresponding to fuzzy cost efficiency scores in the interval [0, 1] corresponding to each of the decision-making units (DMUs). The models presented in this paper satisfies the most important properties: translation invariance, translation invariance, handle with negative data. The proposed approach obtains the fuzzy efficient targets corresponding to each DMU.

In the proposed approach, by selecting the appropriate direction vector in the model, we can incorporate preference information of the DM in the process of evaluating fuzzy cost or revenue efficiency and this shows the efficiency of the method and the advantages of the proposed model in a fully fuzzy environment.