Efficiency evaluation with regret-rejoice cross-efficiency DEA models under the distributed linguistic environment

Abstract

Data envelopment analysis (DEA) is an effective mathematical method for evaluating the efficiencies of decision-making units (DMUs). However, in the process of cross-efficiency evaluation, DEA models commonly neglect the regret aversion psychological characteristics of decision makers (DMs). Therefore, this paper focuses on the construction of regret-rejoice cross-efficiency linguistic distribution DEA (RCE-LDDEA) method with regret theory, in which the input and output data by means of linguistic distributions and the regret aversion psychological characteristics of DMs are considered. First, a linguistic distribution DEA model is proposed to derive the self-evaluation efficiencies of DMUs with linguistic distribution evaluation information. Then, based on regret theory, a regret-rejoice cross-efficiency evaluation (RCEE) model is developed to evaluate the cross-efficiencies of DMUs. Subsequently, based on the regret-rejoice super-efficiency evaluation (RSEE) model, a RCE-LDDEA method is designed to generate the complete ranking of DMUs. Finally, an example for evaluating performance of 10 public hospitals in China is provided to illustrate the implementation of the proposed RCE-LDDEA method. The stability and advantages of the proposed RCE-LDDEA method is performed by sensitivity analysis and comparative analysis.