The Research Of Interval DEA Model Based On Super Efficiency And Cross Efficiency

In the practice of social production, people often need to evaluate the similardepartments or units. And the Data Envelopment Analysis is a kind of nonparameterevaluation method, to evaluate the relative effection of decision making units withmultiple input and multiple output. But the traditional DEA approach requires accurateinput/output data,while in practice work, observation error and incomplete informationwill lead to input or output data are uncertain. At this time, it is necessary to breakthrough the traditional research conditions of DEA method to study the problem aboutevaluateing decision making units with uncertain data.From the decision making units data are interval number, this article researchesinterval efficiency values of interval DEA and the sorting. Interva data is often used todescribe the uncertainty data, Therefore, the paper discusses the Interval DEA.Thispaper starts from obtaining the full sorting and a more comprehensive evaluationmethod, combining with the super efficiency model and cross efficiency mechanism,and studies the interval DEA efficiency value and the sorting. The key problems in thestudy are to determine the model about solving the interval efficiency value and toprocess interval matrix, this paper’s main work and results obtained as follows:1. The evaluationed unit has benn moved from the reference set in the Superefficiency model, making the efficiency value of the effective decision units are greaterthan1, can be distinguished between each other. This paper presents new input typesuper efficiency interval DEA models, and proves the relationship between the optimalvalue of the four models, and determines the models of solving the interval efficiencyvalue based on this theorem.2. In order to more comprehensive analysis the relative effectivenes of decisionmaking units, after getting self-assessment value of each decision-making unit, thispaper introduce the cross efficiency thought. In the best case and the worst case, werespectively combined with Aggessive formulation and Benevolen iformulation,obtained the models of solving the superiority cross efficiency interval matrix and theinferiority cross efficiency interval matrix, and this interval matrices ensure therationality of interval data in interval matrix(that is, the upper limit must be greater thanor equal to the lower).3. On the basis of the Interval number processing method-probably matrix method, we reduce the amount of calculation of the probably matrix method, and through thetheorem prove that the simplified method does not change the results of the originalmethod. According to the different optimism of decision makers, Mr Hurwiczcompromise criterion has been introduced to determine the eventual full sorting.4. The whole solving process of the interval DEA method with interval matrices isgiven. The Excel and Matlab software has been used in the calculation process. Theexample analysis proves the models and evaluation methods in this paper arecomprehensive and practical. The sorting result is compared with other articles, thisevaluation method is more reasonable and more comprehensive.