Three methods to generalize Pawlak approximations via simply open concepts with economic applications

The generalizations of rough sets based on topological structures have become the hot topic of rough set theory. In the present article, based on the notion of j -neighborhood space and the related concept of j -simply open sets, three new methods for generalizing Pawlak rough sets are proposed and their properties are studied. These methods are compared with some of the previous methods. Moreover, we prove that the suggested approaches are more accurate than the other methods and then these approaches may be useful in real-life applications. Finally, an economic application in decision-making is introduced as a simple practical example to demonstrate the ideas proposed. It is providing a comparison between the proposed methods with already existing in the literature.