Fuzzy Clustering Based on Quotient Space and Its Application in CRM

By using method of fuzzy mathematics to quantitatively determine fuzzy relationship between samples, the fuzzy clustering analysis is able to reflect the world objectively and accurately. In this paper, combing the ideas of quotient space theory, hierarchical structure and fuzzy synthetic evaluation, a new model of fuzzy clustering analysis is proposed based on quotient space, which uses theory of granularities for attributes naturalization. The method not only reduces dimensions of attributes but also takes into account all effects of the important attributes by mapping them from low levels to high levels. Additionally, a new formula is proposed for similar matrix construction. In order to reduce the blindness for determination of the categories number, the threshold process is introduced, and we can gain the cluster outcome as soon as possible by regulating the grain-size. Finally, we did customer relationship management (CRM) in application and it is proved that the model is effective and reasonable for classification of Multi-dimensional data.