Rough topology on covering-based rough sets

摘要

A classical rough set theory was given by Pawlak (1982). Since then rough set theory has been investigated by many researchers. Rough set theory can be viewed as an approach to vagueness. Many scientific fields find vagueness concepts interesting; therefore, the rough set theory has important applications in fields such as data analysis and information systems. There are many works on topological and algebraic approaches to rough sets. For example, the union and intersection operations of classical rough sets were introduced by Pomykala and Pomykala (1988). Classical rough sets have been defined on partitions which is a special case of the formalism of coverings. This allows us to study covering-based rough sets. In this paper, we consider covering-based rough sets as an extension of classical rough sets studied by Bryniarski (1989). We also construct a rough topology on a given covering-based rough set. In order to do that, union and intersection operations will be extended to covering-based rough sets. In the future, our aim is to examine applications of rough topology on covering-based rough sets. This work leads us to study some properties of covering-based rough topology.