A new validation criteria for type-2 fuzzy c-means and possibilistic c-means

Cluster validation is a major issue in cluster analysis. Different cluster validity indexes for type-1 fuzzy clustering have been proposed in the literature so far. However, the cluster validity index for type-2 fuzzy clustering needs more investigation. This paper proposes a cluster validity index for fuzzy partitions obtained from interval type-2 fuzzy c-means clustering algorithm. The key notion of the proposed index is that each cluster is represented and regarded as an IT2 fuzzy set. Then, the similarity of each pair of IT2 fuzzy clusters is computed and the validity index is defined as the average of the degrees of similarity of all possible pairs of fuzzy sets. A small value of the index indicates a partition in which the clusters are similar to a lesser degree. Therefore, the optimum number of clusters is obtained by minimizing the proposed index over different cluster numbers. The limit analysis is applied to study the behavior of the cluster validity index as the fuzzifiers go to their extremes. This analysis shows that in general in order to get credible results, the design parameters should not take extreme values. The performance of the proposed validity index is also compared to some type-1 cluster validity indexes. We also show that the proposed CVI is efficient for PCM. The experimental results indicate that the new cluster validity is useful when it is used as a reliable tool to evaluate the partitions produced by the IT2 FCM.