Efficiency decomposition and measurement in two-stage fuzzy DEA models using a bargaining game approach

Abstract

Abstract In this paper, a fuzzy two-stage Game-DEA (FTSGDEA) approach is proposed using a bargaining game model. Each decision-making unit (DMU) consists of two serially connected sub-DMUs. The first sub-DMU uses several inputs to produce several outputs. The outputs of the first sub-DMU, called intermediated measures, are the inputs of the second sub-DMU. Intermediate measures are used by the second sub-DMU to produce the final output of the main DMU. In standard TSGDEA settings, the product of the distance of the efficiency scores of each sub-DMU, which defines its breakdown payoff, is maximized. This approach leads to the overall enhancement of the efficiency scores through a cooperative game environment. We extend this setting to a fuzzy environment where the uncertainty of inputs, intermediate measures, and outputs is accounted for using linguistic terms parameterized via fuzzy sets. The proposed FTSGDEA associates an interval efficiency score to each DMU and sub-DMU, which allows the model to handle real-life problems involving uncertainties. We apply FTSGDEA to a case study involving the assessment of sixty branches from the Saman bank in Iran.