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

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