Abstract: Mathematical morphology is a general theory in the shapes of images and its transformations. Rough set theory deals with vagueness and uncertainty in the approximation space. The existence of these theories based on operators which are dual in nature. Aim of this paper is to develop an approximation space using set theoretical and topological concepts. For that purpose a new result is developed using binary relations and topological concepts and there by introducing a pre-topological approximation space. This result is applicable in wide range of data mining and image segmentation process.

Keywords: Approximation Space; Mathematical Morphology; Rough Set; Topology; Pre-Topological Approximation Spaces; Pre-Closure and Pre-Interior Operator, Dilation; Erosion.