Cross-efficiency Evaluation Of DEA Based On Social Network Analysis And Prospect Theory

In order to solve the problem that traditional DEA methods cannot rank efficient DMUs and the weight selection may be unreasonable,the cross-efficiency evaluation method further distinguishes efficiency performance through peer-evaluation among DMUs,and reduces the effect of unrealistic weights on efficiency values.However,the traditional cross-evaluation model chooses weights with the goal of maximizing the efficiency scores of evaluating DMU,which may be unfair or inappropriate for evaluated DMU.In addition,the ranking result based on CCR is usually inconsistent with that obtained by cross-evaluation method,which increases the difficulty for decision makers to judge whether the DMU performs well.On the other hand,the consistent ranking results meet the actual management needs.In order to eliminate the influence of weight selection on cross-efficiency evaluation and obtain objective efficiency scores,one of the main research of this paper is to propose a cross-efficiency evaluation model based on social network analysis.Different from previous traditional cross-efficiency evaluation methods,this paper proposes three concepts of acceptable level,self-evaluation objective coefficient and peer-evaluation objective coefficient by analyzing the relationship between CCR evaluation and cross-efficiency evaluation.And a social network formed by DMUs is constructed through transforming the evaluation relationship to the social network relationship.Then we introduce the HITS algorithm to obtain the convergent solutions of objective coefficients,which are used to eliminate the non-objective parts caused by weight selection in traditional CCR and cross-efficiency values.Finally,the DMUs can be ranked based on the two objective efficiency scores.We prove that the ranking results based on objective CCR and cross-efficiency values are the same,which is more in line with actual cognitive and management needs.The cross-efficiency evaluation method of two-stage DEA is the second focus of this paper.In existing studies,only a few papers have studied cross-efficiency evaluation methods of two-stage systems,and these studies are based on the assumption of complete rationality of decision makers.However,the irrational factors will affect the evaluation process and results.This paper describes the limited cognition and psychological behavior of decision makers through prospect theory,and integrates the risk attitudes of decision makers about income perception and loss avoidance into the cross-efficiency evaluation framework.Then two-stage DEA cross-efficiency evaluation models based on the prospect theory are constructed under the situations of centralized and decentralized decisions environment.The cross-efficiency evaluation model based on HITS algorithm proposed in this paper describes the evaluation relationship among DMUs from a new perspective,and introduce social network analysis methods to cross-efficiency evaluation to obtain objective efficiency values.Another proposed two-stage DEA cross-efficiency evaluation method based on the prospect theory also expands the generality of cross-efficiency evaluation methods and can provides more scientific and reasonable support for decision makers in actual operation.The contributions of this study are as follows:1)Cognize the evaluation relationship of cross-efficiency deeply,and understand the evaluation relations among DMUs from the perspective of social network analysis.2)Make the ranking results of DMUs based on self-evaluation consistent with peer-evaluation.3)The influence of decision-makers' irrational factors on the evaluation process and results is considered,which makes the two-stage DEA cross-efficiency evaluation model more in line with practical applications.