This paper suggests new approximations that are inspired by topological structures. The primary goal of this work is to define four neighborhoods resulting from a binary relation. Thus, we have four distinct techniques for approximating rough sets. The suggested approaches represent topological generalizations of the previous works. The characteristics and connections of these approaches are investigated. For the sake of the application, we provide some useful examples to compare our techniques to those in the published literature. The merit of the current technique is to obtain a more accurate decision for the problems in which these cases are the appropriate frame to describe them; for instance, machine learning (ML, for short) applications of finance, etc. To demonstrate this fact, an economic application is proposed. We employ the proposed technique in defining accurate decisions to identify the growth of countries. An algorithm for decision-making problems is proposed and tested on fictitious data to compare our methods with the previous approaches.