Research On Interval Cross Efficiency Based On Prospect Theory

Data envelopment analysis is a non-parametric performance evaluation method extended from mathematics,operations research,management science and other disciplines.However,the data envelopment analysis method cannot distinguish all decision-making units and obtain the rankings of all decision-making units.In addition,it allows each decision-making unit to choose its own most preferred weight,which will lead to irrational input-output weights,which results in cross-efficiency evaluation method.The cross-efficiency method performs mutual evaluation between decision-making units,not just a pure self-evaluation form.Using the cross-efficiency evaluation method has the following advantages:(1)It can rank all peer decision-making units;(2)It can eliminate unrealistic weighting schemes without the need to limit the weight of application domain experts;(3)It can effectively distinguish Outstanding and poor performers in all peer DMUs.However,with the widespread application of cross-efficiency evaluation methods,it still has some problems.First,Optimal weights of input and output obtained from the CCR model may not be unique,resulting in non-unique cross-efficiency values and unable to perform effective ranking of decision-making units;Second,the final aggregation of cross efficiency scores gives each decision-making unit the same weight,ignoring the different importance of decision-making units;Third,cross-efficiency evaluation is a decision-making method that does not take into account the limited psychological behavior of decision-makers in the decision-making process.Therefore,based on the problems of the above cross efficiency,this paper improves the cross-efficiency method and applies it to sustainable supplier selection.The main work and research results are as follows:(1)A cross-efficiency model based on evidence theory and prospect theory is constructed.Considering the existence of multiple optimal solutions to the cross-efficiency value,a uniformly distributed interval cross-efficiency is constructed based on the improved aggressive and benevolent models;weights of decision-making units are obtained based on the idea of evidence credibility;Combining prospect theory,the ordering of decision-making units is obtained by calculating the prospect value of each decision-making unit,and the different ranking results of decision-makers under different risk preferences are obtained by combining parameters ?,?,and ? changes.(2)A cross-efficiency model of normal distribution interval cross-efficiency scores based on relative entropy and prospect theory is constructed.Considering the multiple optimal solution problem of the cross-efficiency score comprehensively,based on the interval cross-efficiency,it is further considered that it obeys the normal distribution,and the interval cross-efficiency of the normal distribution is constructed by introducing the normal distribution number.The relative entropy formula of normal distribution interval cross efficiency scores was improved,and the gain and loss of efficiency scores relative to the reference point were calculated.Finally,the weight of each decision-making unit is obtained based on the principle of the maximum comprehensive prospect value,and the prospect value of each decision-making unit is sorted.Combined with the change of parameter ?,different ranking results of different decision-makers' psychological preferences are obtained.(3)Applying the two models proposed in the sustainable supplier selection example.Provides a new model for decision makers of different risk and psychological preferences to select sustainable suppliers.And provide new ideas for research on sustainable supplier selection.