DEA-based Fuzzy Comprehensive Evaluation And Its Applications

The fuzzy comprehensive evaluation (FCE) method is one of the mathematical methods in the comprehensive evaluation system. It is used to evaluate a fuzzy system which is prevalent in real life. FCE has been widely used in the environmental, weather forecasting, economic management, as well as areas such as evaluation of the teaching process. In the practical application, the evaluation of the quantitative indicators needs to be considered, thus, the traditional FCE can no longer have good credibility. A method of DEA-based fuzzy comprehensive evaluation is proposed in this paper, where three research aspects are included as follow:(1) A method of fuzzy comprehensive assessment based on data envelopment analysis is proposed in this paper, where the expert's scores of FCE are replaced with the fuzzy DEA results. This method optimizes the raw quantifiable data and non-quantifiable data with DEA and FCE respectively, and then assesses the performance of the system synthesizing the fuzzy DEA relative-efficiencies together with the FCE results. The novel method, combining the advantages of both FCE and DEA, is more objective than the FCE method as it introduces the fuzzy DEA results instead of the subjective scores of FCE.(2) The effect of PCA dccorrelation and dimension reduction function on the results of DEA is addressed. Example shows that, by using the PCA decorrelation, the results of DEA do not change. But, the PCA dimension reduction acted on the DEA will result in uncertainty of sorting.(3) Instead of fuzzy membership function, by the theory of backward cloud generator and the algorithm of cloud, the fuzzy comprehensive system with the cloud model is presented, which has the characteristic of fuzzy, random and statistic. Comparing with the normal method of fuzzy membership, the proposed method of cloud model has more advantages in the aspect of researching the intrinsic fuzzy and random of the object.(4) The evaluation of the public test resource laboratories with the DEA-based FCE method is given at the end of the paper. The problem of the improvement for the ineffective decision making units is solved with the projection model, with which the resources can be rational allocated and help the government to make decisions.