Covering based rough sets have been introduced as an extension of the basic rough sets introduced by Pawlak [5, 6]. There is only one way to define the lower approximation of a set using covering. However, as many as four definitions have been proposed for covering based upper approximation. Accordingly, we find four types of covering based rough sets in the literature. In , the concept of rough equivalences of sets, which extended the corresponding notions of approximate equalities of Novotny and Pawlak [2, 3, 4] were introduced and their properties were studied. In this article we further generalize these concepts to the setting of covering based rough sets and establish some of their properties. © 2009 IEEE.