Theory And Application Of Interval DEA

System efficiency evaluation under uncertainty conditions, which shows significantly important theoretic and practical values, has always been a frontier topic of study in data envelopment analysis (DEA). In practical research, due to various limitations, e.g., measurement errors, data noise, incomplete information, technical limitations and stochastic impacts of economic phenomena and laws, input and output values of decision-making units (DMUs) cannot be accurately determined. To overcome these limitations, researchers tend to rely on their own experiences in interval estimation of the values with some kinds of approaches, such as forecasting technologies and simulation analysis. This thesis focuses on interval DEA modeling, efficiency evaluation, ranking, etc.It is divided into eight chapters, and the main contents are as follows:The first chapter addresses the importance of efficiency evaluation with interval constraints, and then reviews the basic theory of interval DEA, and its current research status. Furthermore, some problems existed in research are also defined. Lastly, the main research methods and conclusions are in discussion.Chapter two summarizes the existing theories of interval DEA, and especially emphasizes to introduce the principles of variable alternation and interval efficiency. The internal relationship and weakness of these two methods are discussed in details.In chapter three, to overcome the weakness of the existing methods, a new interval DEA method with common weights under the viewpoints of average efficiency evaluation is presented. A numerical example is employed to demonstrate the rationality and superiority of the developed DEA method.The fourth chapter develops an additive interval DEA approach based on the proposed average efficiency evaluation methods, to study the problem of efficiency evaluation and improvement. An example with complicated linear interval outputs is applied to elaborate the rationality of the presented approach. Considering how to effectively measure the discriminating capacity of DEA models based on Shannon entropy, Chapter five elaborates an interval DEA method with average efficiency evaluation through a numerical example, and demonstrates the feasibility and advantages of applying the average efficiency evaluation to interval DEA methods.In order to fully rank all DMUs, the sixth chapter presents a viewpoint of virtual efficiency frontier, and proposes two DEA models based on the optimal virtual frontier or the worst virtual Fortier. Then, based on TOPSIS, an integrated ranking method is presented. The rationality of the proposed ranking approach is illustrated by a numerical example.Chapter seven discusses the problem of efficiency evaluation for DMUs with parallel sub-DMUs under constraints of interval data. In view of the perspective of average efficiency evaluation, an average efficiency evaluation interval network DEA model is developed, which can evaluate the DMUs'efficiencies and their sub-DMUs'efficiencies simultaneously, and determine all precise data on interval inputs/outputs. An example is applied to illustrate the feasibility and rationality of the proposed approach.The last chapter is a summary of the thesis, and to present some plans for future research.The thesis presents some new approaches for interval DEA theories. Contributions of this thesis are briefly summarized as follows: firstly, under the viewpoint of average efficiency evaluation, two interval DEA methods are developed; secondly, an integrated ranking method is defined to completely rank DMUs, based on the virtual frontier and the TOPSIS.