Topological approaches for generalized multi-granulation rough sets with applications

Methods of data classifications are considered as a major preprocessing step for pattern recognition, machine learning, and data mining. In this paper, we give two topological approaches to generalize multi-granular rough sets using families of binary relations. In the first approach, we define a family of topological spaces using families of relations to maximize the interiors and minimize the closures. In the second approach we define minimal neighborhoods to classify multi-data of information systems and generate a multi-granular knowledge base. Moreover, we present some important algorithms to reduce all topological reductions of the information system using topological bases. We round off by studying real life applications of this work using medical data.