On Topological Structures and Granular Computing

Recently, the general topology has become the appropriated frame for every collection connected by relations. It should be noted that the generation of topology by relations and the representation of topological concepts via relations will narrow the gap between topologists and those who are interested in applications of topology in their ¿elds. This book consists of five chapters and conclusion, the ¿rst chapter is an introduction of some basic concepts of general topology, rough set theory, and granular computing. The second and third chapters are devoted to studying the building block of rough set theory "Pawlak approximation space". We establish a new generalization which represents a complete framework analogy with Pawlak rough set theory, based on new generalized neighborhoods systems, but from topological view with a binary relation. The fourth chapter presents some basic topological concepts via relations. Finally, the fifth chapter is devoted to introducing the generalized covering approximation space as a generalization to rough set theory and covering approximation space.