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Since a clustering algorithm can produce as many partitions as desired, one needs to assess their quality in order to select the partition that most represents the structure in the data, if there is any. This is the rationale for the cluster-validity (CV) problem and indices. This paper presents a CV index that helps to find the optimal number of clusters of data from partitions generated by a fuzzy-clustering algorithm, such as the fuzzy c-means (FCM) or its derivatives. Given a fuzzy partition, this new index uses a measure of multiple cluster overlap and a separation measure for each data point, both based on an aggregation operation of membership degrees. Experimental results on artificial and benchmark datasets are given to demonstrate the performance of the proposed index, as compared with traditional and recent indices.