Refining membership degrees obtained from fuzzy C-means by re-fuzzification

Document Type : Research Paper


1 Department of Computer Engineering, Faculty of Information Technology, Kermanshah University of Technology, Kermanshah, Iran

2 Islamic Azad University Central Tehran Branch, Tehran, Iran

3 Department of Computer Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran

4 Department of Computer Science and Statistics, Faculty of Mathematics, K.N. Toosi University of Technology, Tehran, Iran


Fuzzy C-mean (FCM) is the most well-known and widely-used fuzzy clustering algorithm. However, one of the weaknesses 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 clusters. In this paper, we propose an algorithm which takes the FCM clustering results and re-fuzzifies them by taking into account the shape and density of the clusters. The algorithm first defuzzifies the FCM clustering results. Then the crisp result is fuzzified again. Re-fuzzification 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-fuzzification 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.