Comparison of two types of rough approximation via grill

Rough set theory and topology are now branching far into applied areas, such as economics, data processing, imaging and chemistry. As a consequence of this importance gained from topology after the advent of a rough set theory which helps to quantify things that were previously difficult to measure. It was important to work on the extension of the topological space with new concepts such as grill and ideal. In this paper, we present new approximations of rough sets via a grill concept which has helped to extend the topological spaces. In addition, the topology created by the present method is finer than other methods. Finally, grill topological spaces will be obtained in terms of relations and grills aimed at minimizing the boundary regions.