Rening membership degrees obtained from fuzzy C-means by re-fuzzication

Fuzzy C-mean (FCM) is the most well-known and widely-used fuzzy clustering algorithm. However, one of the weak- nesses of the FCM is the way it assigns membership degrees to data which is based on the distance to the cluster centers. Unfortunately, the membership degrees are determined without considering the shape and density of the clus- ters. In this paper, we propose an algorithm which takes the FCM clustering results and re-fuzzies them by taking into account the shape and density of the clusters. The algorithm rst defuzzies the FCM clustering results. Then the crisp result is fuzzied again. Re-fuzzication in our algorithm has some advantages. The main advantage is that the fuzzy membership degrees of data points are obtained based on the shape and density of clusters. Adding the ability to eliminate noise and outlier data is the other advantage of our algorithm. Finally, our proposed re-fuzzication algorithm can slightly improve the FCM clustering quality, because the data points change their clusters according to similarity to the shape and density of their respective clusters. These advantages are supported by simulations on real and synthetic datasets.