This paper introduces the relations between covering and dicovering in the framework of rough sets. The natural counterpart of a covering in textures is given by a family of pairs of sets which is called a dicovering. This leads us to two dual concepts which are called star and co-star of a set, respectively. Here, we define dicovering approximation space and we discuss on covering and dicovering based rough sets. In this context, star corresponds to the upper approximation operator defined by Zakowski and co-star corresponds to the lower approximation operator studied by Pomykala, Yao, and Zhu and Wang. (C) 2011 Elsevier Inc. All rights reserved.