A Fully Fuzzy DEA Approach for Cost and Revenue Efficiency Measurements in the Presence of Undesirable Outputs and Its Application to the Banking Sector in India

This paper extends the conventional cost efficiency (CE) and revenue efficiency (RE) models to fully fuzzy environments to account for real situations where input-output data and their corresponding prices are not known precisely. Owing to the importance of the presence of undesirable outputs in the production process, these are also incorporated into the production technologies of the proposed models. This paper endeavours to propose fully fuzzy CE (FFCE) and fully fuzzy RE (FFRE) models where input-output data and prices include uncertainty of fuzzy forms, in particular, of triangular membership forms. Further, the concepts of fully fuzzy linear programming problems (FFLPPs) and linear ranking functions are used to transform FFCE and FFRE models into the crisp linear programming problems (LPPs), and to evaluate fuzzy CE (FCE) and fuzzy RE (FRE) measures of the decision-making units as triangular fuzzy numbers. Moreover, the proposed models are compared with some existing approaches and are also illustrated with an application to the banking sector in India for proving their acceptability and effectiveness in real-world systems.