关键词: 模糊聚类, 聚类有效性, 模糊c均值, 聚类紧密度, 聚类分离度

Abstract: Cluster validity index is used to evaluate the validity of clustering.The clustering result will tend to be more logical on the condition that the initial clustering number is accurately ascertained.According to the basic theory of fuzzy indetermination and the properties of clustering，a new cluster validity function is proposed to identify the optimal cluster number based on the newly introduced index D_i（U；c） that can measure the clustering compactness.Both the geometry structure of dataset and the membership degree are taken into account in the validity function，which based on the properties of clustering compactness and separation.The experimental results indicate that the new validity function can find out the only cluster number if the dataset has the obvious cluster trend and it is also non-sensitive to the weighting coefficient m.

Key words: fuzzy clustering, clustering validity, fuzzy c-means, clustering compactness, clustering separation