A New Cluster Validity Index for Fuzzy Clustering based on Combination of Dual Triples

Cluster validity indexes aim at evaluating the degree to which a partition obtained from a clustering algorithm approximates the real structure of a data set. Most of them reduce to the search of the right number of clusters. This paper presents such a new validity index for fuzzy clustering based on the aggregation of the resulting membership degrees with no additional information, e.g. lite geometrical structure of the data. It exploits the tendency for a data point to belong to a unique cluster, i.e. both the tendency to belong to one cluster and the tendency not to belong to the others clusters.