The richness of soft clustering algorithms in the scientific literature reflects from one side the complexity of the underlying problem and from the other the many attempts that have been made to preserve interpretability while modeling vagueness through different theories. In this paper a hybrid rough-fuzzy unsupervised learning algorithm called Variable Width Rough-Fuzzy c-Means (VWRFCM) is derived from a unifying view of the most popular crisp, fuzzy, rough and fuzzy-rough partitive clustering algorithms. VWRFCM provides a user-defined parameter that sets the width of the core regions of all clusters in a probabilistic sense, allowing the domain experts to have both an intuitive interpretation and a powerful control possibility on the maximum allowed degree of vagueness in the clustering solution. Tests on several real datasets show a good effectiveness together with a speed-up in efficiency of VWRFCM compared to its baseline competitors.