Generalized Data Envelopment Analysis Based On Sample Evaluation And Its Application In Economic System

Data envelopment analysis(DEA)proposed by Charnes et al in 1978 is a nonparametric approach for measuring the relative efficiencies of decision-making units(DMUs).Great progress has been made in the improvement of the model and the application of case analysis.Environmental efficiency,network DEA(including twostage DEA,efficiency decomposition),benchmarking,bootstrap or bootstrapping,as well as returns to scale(including scale efficiency)are the main fields of current studies.Moreover,it is easy to detect that agriculture,banking,supply chain,transportation,as well as public policy are the top 5 application fields of DEA.The improvement of DEA model provides an away to describe the complex relationship among DMUs and evaluate DMUs in accordance with the actual situation,but there is still some work to be further improved.To solve some problems encountered in the evaluation process of DEA methods,this paper improved the index synthesis technology of DMUs,excavated the complex game relationship among DMUs,and gave the generalized fuzzy BC2 model base on simple by extending the precise data to the fuzzy data.Those work proposed above is based on sample evaluation theory,the partial ordering set theory and the game theory.The main work is summarized as follows.(a)A new model for evaluating multi-level complex systems is proposed in the view of input-oriented.The validity definition and related properties of the model are also given.It is worth emphasizing that this model can not only obtain the new results of the ranking of effective DMUs,but also give the improved information of the original indexes before the index synthesis.The case study under the assumption of constant returns of scale proves that the method has good innovation value and application value.(b)A new model for evaluating multi-level complex systems is proposed in the view of output-oriented.The validity definition and related properties of the model are also given.The case study under the assumption of variable returns to scale has achieved good results.At the same time,the model is extended to the generalized DEA method based on sample evaluation,which provides a new idea for searching the improvement information of the original index after index synthesis in generalized DEA method.(c)A series of new optimization models for group game strategy of DMUs is proposed based on generalized DEA method and game theory.Under the strike of unique DMU or union DMUs,a scheme is proposed for how the DMUs select partners according to the series of new models.This series of models also effectively describe the game efficiency changes of DMUs under the strike of other DMUs,and analyze the effects of various game relationships on single DMU and group DMUs.(d)A method of merging and splitting DMUs is proposed,and the definition of intersection and union operation among DMUs in different distances is provided for the designated DMUs based on partial ordered set theory.The partial order diagram of DMUs in an application case is drawn,which proves that this method provides a new way to improve DMUs,and also provides a scientific suggestion for dealing with cooperation and competition among DMUs.(e)A generalized fuzzy BC2 model based on sample evaluation and its dual model are given when the input-output data is fuzzy data and reference sets are not all DMUs.The strong efficiency,general efficiency,fuzzy efficiency and weak efficiency of this model are defined,and the generalized fuzzy BC2 model with Archimedes infinitesimal is presented.A series of concepts and related properties of production possibilities set,production frontier and projection are put forward,and the fuzzy DEA theory and generalized DEA theory are further improved.(f)The generalized DEA method is used to evaluate the interaction efficiency between the eco-environment and economic,the performance of economic achievements and the status of economic benefits in China.In these applied studies,the methods and models proposed in this paper are fully used,and better conclusions and suggestions are obtained,which provide a feasible scheme for China's economic development and environmental governance.