Clustering is a familiar concept in the realm of Data mining and has wide applications in areas like image processing, pattern recognition and rule generation. Uncertainty in present day databases is a common feature. In order to handle these datasets, several clustering algorithms have been formulated in the literature. The first one being the Fuzzy C-Means (FCM) algorithm and it was followed by the Rough C-Means (RCM) by Lingras. In the paper Lingras has refined his previous algorithm. We combine this algorithm with the fuzzy C-means algorithm to generate a rough fuzzy C-Means (RFCM) algorithm in this paper. Also, we provide a comparative analysis with earlier RFCM algorithm introduced by Mitra et al and establish that our algorithm performs better. We use both numeric as well as image datasets as input and use the performance indices DB and D for this purpose. © 2014 IEEE.