An Adaptive Cluster Validity Index for the Fuzzy C-means

Based on the basic theory of fuzzy set, this paper suggests the notion of FCM fuzzy set, which is subject to the constraint condition of fuzzy c-means clustering algorithm. The cluster fuzzy degree and the lattice degree of approaching for the FCM fuzzy set are presented, and their functions in the validation process of fuzzy clustering are deeply analyzed. A new cluster validity index is proposed, in which the two factors such as the cluster fuzzy degree and the lattice degree of approaching are taken into comprehensive account. The notable advantage of the index is that it can adaptively adjust the relative significance levels of the two factors. Also, this paper gives the algorithm to apply the cluster validity index to the cluster validation for the fuzzy c-means algorithm. The experimental results indicate the effectiveness and adaptability of the proposed cluster validity index.