An Exponential Cluster Validity Index for Fuzzy Clustering with Crisp and Fuzzy Data


Department of Industrial Engineering,Amirkabir University of Technology


This paper presents a new cluster validity index for finding a suitable number of fuzzy
clusters with crisp and fuzzy data. The new index, called the ECAS-index, contains exponential
compactness and separation measures. These measures indicate homogeneity within clusters and
heterogeneity between clusters, respectively. Moreover, a fuzzy c-mean algorithm is used for fuzzy
clustering with crisp data, and a fuzzy k-numbers clustering is used for clustering with fuzzy data. In
comparison to other indices, it is evident that the proposed index is more e ective and robust under
different conditions of data sets, such as noisy environments and large data sets.