Several data clustering techniques have been developed in literature. It has been observed that the algorithms developed by using imprecise models like rough sets, fuzzy sets and intuitionistic fuzzy sets have been better than the crisp algorithms. Also, the hybrid models provide far better clustering algorithms than the individual models. Several such models have been developed by using a combination of fuzzy set introduced by Zadeh, the rough set introduced by Pawlak and the intuitionistic fuzzy introduced by Atanassov. Notable among them being the Rough Fuzzy C-Means (RFCM) introduced by Mitra et al and the rough intuitionistic fuzzy c-means algorithm (RIFCM) introduced and studied by Tripathy et al Krishnapuram and Keller observed that the basic clustering algorithms have the probabilistic flavour; for example due to the presence of the constraint on the memberships used in the fuzzy C-Means (FCM) algorithm. So, they introduced the concept of possibilistic approach and developed a possibilistic fuzzy C-means (PFCM) algorithm. Another approach to PFCM is due to Pal et al. In this paper, we improve a possibilistic rough C-Means (PRCM) algorithm introduced by Anuradha et, al. and introduce a new algorithm, which we call as possibilistic rough fuzzy C-Means (PRFCM) and compare its efficiency with the improved PRCM and the basic PRFCM algorithm to establish experimentally that this algorithm is comparatively better than PRCM and the corresponding RCM algorithm. We perform the experimental analysis by taking different types of numerical datasets and images as inputs and using standard accuracy measures like the DB and the D-index. © 2014 IEEE.