Data clustering has been playing important roles in many areas like pattern recognition, image segmentation, social networks and database anonymisation. Since most of the data available in real life situation are imprecise by nature, many imprecision based data clustering algorithms are found in literature using individual imprecise models as well as their hybrids. It was observed by Krishnapuram and Keller that the possibilistic approach to the basic clustering algorithms is more efficient as the drawbacks of the basic algorithms are removed. This approach was used to develop the possibilistic versions of fuzzy, rough and rough fuzzy C-Means algorithms to develop their corresponding possibilistic versions. In this paper, we extend these algorithms further by proposing a possibilistic rough intuitionistic fuzzy C-Means algorithm (PRIFCM) and compare its efficiency with other possibilistic algorithms and the RIFCM. Experimental analysis is carried out by taking both numeric as well as the image data. Also, DB and the D indices are used for the comparison which establishes the superiority of PRIFCM. © 2015 IEEE.