In this article article, topological methodologies to extend the scope of multi-granular rough sets through the utilization of families of binary relations are proposed. The construction of a multi-topological spaces derived from multi-relations are formulated, with an aim to improve interiors and minimize closures. Also, this article discusses the properties of these new methodologies. Comparisons among the proposed definitions and previous study in published issues are thoughtfully examined. Specifically, the concept of topological membership function with respect to the j-neighborhoods of m-topologies, which integrates the principles of rough and fuzzy sets, are introduced. Our findings suggests that the generated topology from multi-granulation provides measurement of accuracy that is more precise than convential topologlical methods. Finally, the current article presented an optimization for the rough set theory to be valid to be applicable in different areas of life such as medical, industrial, engineering and facilitate sharing huge data as well as hybridization with the computer science.