Generalized rough set models

Abstract

Rough set theory is an important tool for dealing with uncertain and vague data. In this project work, we study some different approaches of generalized rough sets, like generalized rough sets induced by an arbitrary binary relation, generalized rough sets based on neighborhood systems and the covering based rough sets. We further explore the properties and structure of rough set model induced by an arbitrary binary relation. We also investigate the relationship between Alexandrov space and generalized approximation space induced by an arbitrary binary relation. A one-to-one correspondence between the class of generalized approximation spaces based on pre-order relations and the class of Alexandrov spaces are given. In addition, several counter-examples are provided to indicate counter connections.