Clustering Analysis For Experimental Data Based On Uncertain Set

Uncertain set is a set-valued function defined on uncertainty space, and attempts to model “unsharp concepts” that are essentially sets but their boundaries are not sharply described. Membership function is used to model uncertain set. It is a key step to obtain membership function of uncertain set for applications in the real world. Data sample is classified into a number of groups by cluster analysis, so that objects in the same groups are more similar to each other than to those in other groups. Based on uncertainty theory and uncertain statistics, in order to obtain membership function and classify experts’ opinions, some content as follows is studied in the dissertation:Firstly, an uncertain method of moments is presented for estimating the unknown parameters of membership function. As l empirical moment of empirical membership function, l moment is designed and proved. The equations about the unknown parameters are built by the empirical moment and the corresponding theoretical moment and the solution of the equations is the estimated value.Secondly, in order to obtain the membership function via multiple experts’ experimental data, a method by combination of uncertain statistics and Delphi method is introduced in this dissertation. The questionnaire is designed based on uncertain statistics. Multiple experts’ experimental data is obtained by combination of uncertain statistics and Delphi method. Based on the decision criterion, the membership function is obtained by the multiple experts’ experimental data. At the same time, a real example is given to illustrated the efficiency of the proposed approach.Finally, in order to classify the experts’ opinion, uncertainty cluster method is proposed in this dissertation. The experts’ experimental data obtained by combination of uncertain statistics and Delphi method is classified with SPSS. The experts which are classified into the same group are considered to have the similar opinion. Otherwise they don’t have the similar opinion. The efficiency of this method is illustrated in this dissertation.