Improvement of cross-efficiency based on prospect theory

Abstract

Cross-efficiency assessment method is a useful tool for assessing the relative performance of decision-making units (DMUs). It is generally assumed that decision makers (DMs) are completely rational in the cross-efficiency model, and DMs’ risk attitude has not been considered important in the evaluation process. When the self-evaluation score of the DMU is optimal, the input and output weights are non-unique, resulting in non-unique cross-efficiency score, which affects the ranking result. The relative importance of DMUs is ignored when aggregating cross-efficiency scores. in view of the above problems, a cross-efficiency method based on prospect theory is proposed to capture the bounded rational psychological behavior of risk DMs. This method considers all multiple optimal solutions and constructs interval cross-efficiency. The credibility of each cross-efficiency score is obtained based on the D-S evidence theory, and the weight of each DMU is obtained by using the Dempster rule. DMUs are ranked by calculating the prospect value. The validity and feasibility of the proposed method and how does the risk preference of DMs characterized by parameters α, β, λ affect the evaluation results are verified by an illustrative example.