Support Vector Clustering (SVC) is an important density-based clustering algorithm which can be applied in many real world applications given its ability to handle arbitrary cluster silhouettes and detect the number of classes without any prior knowledge. However, if outliers are present in the data, the algorithm leaves them unclassified, assigning a zero membership degree which leads to all these objects being treated in the same way, thus losing important information about the data set. In order to overcome these limitations, we present a novel extension of this clustering algorithm, called Rough-Fuzzy Support Vector Clustering (RFSVC), that obtains rough-fuzzy clusters using the support vectors as cluster representatives. The cluster structure is characterized by two main components: a lower approximation, and a fuzzy boundary. The membership degrees of the elements in the fuzzy boundary are calculated based on their closeness to the support vectors that represent a specific cluster, while the lower approximation is built by the data points which lie inside the hyper-sphere obtained in the training phase of the SVC algorithm. Our computational experiments verify the strength of the proposed approach compared to alternative soft clustering techniques, showing its potential for detecting outliers and computing membership degrees for clusters with any silhouette. (C) 2016 Elsevier Inc. All rights reserved.