AFS Clustering Analysis Method And Its Applications On Fuzzy Datasets

The theory of fuzzy sets and systems has been studied widely and applied in many engineering fields as a new mathematics method since it was proposed by professor L.A.Zadeh, an American cyberneticist, in 1965. AFS theory is a new method to study fuzzy set which was proposed by professor Liu Xiaodong in 1995. It makes some of the mechanisms of decompose and composition of human conceptions to be understood with mathematical terms. It is more suitalbe to describe the logic of human and more comfortable to the disposal of computer. For ages, there exist the arguments for the basic issues exist in fuzzy set theroy about how to establish the membership function of the fuzzy concept with a rigor and uniform method and the accurate representions of the fuzzy logic operations. In order to deal with the above issues, AFS theory analyze and study these issues further. Many experimental studies show that AFS theroy is more close to the thought of humanity. Recently, AFS theory has been developed further and applied to fuzzy clustering analysis, fuzzy decision trees, credit rating analysis , pattern recognition and hitch diagnoses, etc.In this paper, in order to be more practical to the fuzzy data set, the AFS Fuzzy logic clustering algorithm (X. D. Liu, W. Wang and T. Y. Chai, IEEE Transaction on Systems, Man, Cybernetics, 2005) have been studied further by the improvement of the algorithm in the method to describe the objects and the fuzzy clustering validity index. Then it applies the new AFS fuzzy clustering method to the fuzzy data set (The evaluate results of 30 companies). The clustering algorithm proposed in this paper imitates the clustering procedure of human, and just depends on the ordered relation on the attributes. Thus AFS theory can be used to deal with the fuzzy data sets which can not be described by the numbers, even the fuzzy data described by the linguistic values of human as it shown in this paper. The study shows that the results can be almost consistent with the experts' intuition descriptions by using the proposed new AFS clustering method. More further, the results present the proposed fuzzy clustering meth- od is practical and useful.