Adjustable Fuzzy Chance Constrained DEA Model With Undesirable Outputs And Its Applications

As a method of measuring relative efficiency and ranking homogeneous decision-making units,Data Envelopment Analysis(DEA)is widely used in many fields,such as financial and medical.Traditional DEA models require accurate numbers for input and output.However,in practical applications,we sometimes cannot obtain accurate input and output data.For example,some qualitative indicators are difficult to accurately quantify into the DEA model.Fuzzy numbers can represent uncertain information very well.Therefore,researches on fuzzy DEA based on fuzzy numbers have attracted much attention.In addition,the traditional data envelopment analysis model is carried out under the assumption that “the more output the better,the less input the better”,but in the practical production process,there may be some undesired outputs,such as waste and pollution.For this type of outputs,decision makers hope them as few as possible,which is contrary to the assumptions of traditional DEA models.Therefore,this paper studies the fuzzy DEA model with undesired output.The main contents of this paper are summarized as follows:(1)A single-stage adjustable fuzzy chance constraints DEA model with undesired outputs is proposed.In this part,the multi-input multi-output single-stage system with fuzzy data and undesired output is investigated.First,for the DEA model of undesired output represented by precise numbers,its equivalent model is given and proved.Secondly,the equivalent model is extended to the fuzzy DEA situation,and an adjustable fuzzy DEA model with undesired output is constructed.Finally,the proposed adjustable fuzzy DEA model is applied to evaluate the barley production farms.(2)A two-stage adjustable fuzzy chance constraints DEA model with undesired outputs is constructed.Aimed at two-stage production and management problems in real life,where there are undesired outputs in the intermediate and final processes,a fuzzy two-stage DEA model with adjustable fuzzy opportunity constraints is constructed.First,in the crisp number environment,Chen's additive efficiency decomposition model is extended to undesired output situation.Secondly,using generalized fuzzy measures and chance-constrained programming,the model is further extended to an undesired output fuzzy DEA model,and a two-stage DEA model with adjustable fuzzy chance constraints is constructed.Finally,the proposed model is applied to the efficiency evaluation of a bank.(3)An adjustable fuzzy chance constrained SBM model with undesired output is constructed.Based on the Slack-Based Measure(SBM)based model,an adjustable fuzzy chance constrained SBM model with undesired output is constructed.First,with the assumption of variable returns to scale,a fuzzy production possible set with undesired output is constructed.Secondly,an adjustable fuzzy chance constrained SBM model with undesired output is built based on the fuzzy production possible set.Finally,the model is applied to the efficiency evaluation problem of the pallet rental industry.The research results have shown that the proposed adjustable fuzzy chance constrained DEA model can effectively evaluate the efficiency of actual production and operation activities.The research results of this paper not only enrich the existing theoretical system of DEA model,but also have broad application prospects.