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 by the similarity of the
shape and density of their respective clusters. These advantages are supported by simulations for real and synthetic
datasets.