Advancements in Topological Approaches via Core Minimal Neighborhoods and Their Applications

Graph theory provides many topological systems for modelling blood circulation. The main object is determining the best topology for a successful correct diagnosis. This work illustrates the justification for using topology, rough sets, and graph analysis through neighborhoods. Generalization for an approximation space and a model of the topological graph is presented. Investigating core minimal neighborhoods is essential for categorizing subsets and computing, these techniques perform better than current techniques while maintaining Pawlak’s characteristics. This work presents a method for generalizing rough sets utilizing core minimal neighborhoods using binary relations. Moreover, we will construct four types of dual approximations concerning core minimal neighborhoods as lower and upper approximations. A comparison between different types of dual approximations is discussed. Core minimal neighborhoods induce certain types of topological structures. Finally, we compare different topologies that assist us in determining the main parts of a human heart’s graph.