Research On Fuzzy Data Envelopment Analysis

Conventional data envelopment analysis(DEA) model(CCR model or BCC model ) is data sensitive,requiring all input and output data are precise.In real situation,some data information are fuzzy,because of property restricting of criteria evaluated or the need of prior forecast or incompleteness of information.It is more reasonable and reliable that representing these uncertain information by flexible data structure like fuzzy number and then application of DEA model based on fuzzy analysis and research on the solution,than representing these uncertain information by approximation or estimation and then using conventional DEA model.The present paper will make research on DEA model in which the inputs and outputs of objective evaluated all or part are not precise but can be represented by fuzzy number,i.e.the fuzzy extension of DEA.In charper 1,the present paper first introduces the efficiency evaluation idea of DEA and two basic DEA model---CCR model or BCC model;then,reviews on fuzzy DEA,and introduces two existed representive fuzzy DEA models;in the end,narrates the content and significance of the present paper.Subsequently,innovative fruits of research in present paper are presented,mainly they are:(1) A fuzzy DEA model that subjective elements of decision maker can be incorporated is constructed based on weighted average value of fuzzy number.Its advantage over other existed fuzzy DEA models is that risk preference of decision maker is incorporated into model,interactive results can be achieved by virtue of psychological elements of decision maker;it is important that we have this advantage. Corresponding content is included in charpter 2.(2) The ranking problem of fuzzy decision making units(DMUs ) is solved.The ranking for fuzzy DMUs is an interesting problem just as for DMUs whose inputs and outputs are precise;it is convenient for application that all fuzzy DMUs are ranked, because the purpose of evaluation for fuzzy DMUs is to know which fuzzy DMU is excellent and which fuzzy DMU is bad.Further,the information included in fuzzy DMUs are deeply mined and fuzzy DMUs are evluated comprehensively would be infavor of judgement of decision maker.These problems are settled by fuzzy extension of super efficiency DEA model and context-dependent DEA model. Corresponding content is included in charpter 3.(3) A model which can measure efficiency of fuzzy DMUs reasonablely and comprehensively----fuzzy non-radial DEA model is constructed.All fuzzy DEA models in literature is the extnsion of CCR model or BCC model,but measures of these two models are incomplete,they are only input-oriented or output-oriented,so only input efficiency or output efficiency of DMUs can be given,the measure of input efficiency and output efficiency simultaneously can not be given;moreover,their efficiency index omits non-zero input and output slacks,so all inefficiency of DMUs can not be measured.Enhanced russell graph efficiency measure(ERM ) can measure input and output efficiency simultaneously,and can unify ratio efficiency and slacks into a scalar.The ERM model is introduced and extends to fuzzy environment, then the fuzzy ERM model is solved by using three different methods.The advantage of this fuzzy non-radial model over anciently fuzzy DEA models is that it is based on ERM model,not based on CCR model or BCC model,so its efficiency evlauation for fuzzy DMUs is more comprehensive and more reasonable than the others. Corresponding content is included in charpter 4.(4) Malmquist index based on fuzzy DEA is introduced,it can measure the efficiency change of fuzzy DMUs under dynamic environment.Corresponding content acting as application of fuzzy DEA is included in final part of charpter 4.(5) The concept of interval efficiency value of DMU in CCR model is introduced and interval efficiency value of DMU in CCR model is constructed.In CCR model,the maximum of relative ratio of weighted sum of outputs to that of inputs is regarded as the efficiency,but we think that all the possible ratio of weighted sum of outputs to that of inputs are assumed as the possible efficiencies,then the efficiency can be an interval.We formulate a CCR model with an interval efficiency which consists of efficiencies obtained from the cross efficiency.Interval efficiencies obtained from our approach measures the performances of DMUs not only more comprehensively than traditional CCR efficiency,but also more reasonable and credible than the existed interval efficiencies constructed by the other approaches,for the essential self-evaluation and peer-evaluation concept of cross efficiency approach. Corresponding content is included in first part of charpter 5.(6) Nash bargaining efficiency of DMU is achieved based on interval DEA model by using bargaining game.In the game,each DMU will be an independent player,and the bargaining solution between upper bound of interval efficiency and lower bound of interval efficiency can be obtained by using the classical Nash bargaining game model.The advantage of the bargaining efficiency lies on that it is a pareto one and all the DMUs have motivation to accept it.Corresponding content is included in final part of charpter 5.The last chapter summarizes all the work of this thesis,and gives some useful suggestions for future research.