Technological revolutions, the rapid pace of life, and the rapid development of approximate theory have led to the need for improved methodologies to deal with huge amounts of data in a short period and give results that are more accurate. This article establishes a model for Multi-Granular Rough Sets (MGRS) within neighborhood systems from a topological perspective. The approach involves approximating a target concept using the j-neighborhoods of objects within a given universe set. We propose extending the multi-granular rough sets framework by employing families of binary relations and constructing multi-topological spaces derived from these multi-relations. This method aims to enhance interior structures and minimize closures. Furthermore, the article examines the properties of these novel methodologies and compares them with previous research. It introduces the concept of a topological membership function in relation to j-neighborhoods of m-topologies, which integrates the principles of rough and fuzzy sets. Our findings indicate that the topology generated from multi- granulation offers more precise accuracy measurements compared to conventional topological methods. Finally, the article presents a real-world application involving medical records to demonstrate the effectiveness of our MGRS classification approach.