article · Journal of the Egyptian Mathematical Society
Rough set theory provides a mathematical foundation for handling uncertainty, fuzziness, and incomplete information in data analysis. A novel formulation expands generalised rough sets by constructing neighbourhood systems from arbitrary binary relations. Within this framework, four distinct pairs of dual approximation operators are derived directly from the core of these neighbourhood systems. The mathematical interrelationships connecting these different approximation operators are formally analysed. Furthermore, the core structures of these neighbourhood systems are employed to construct various topological spaces, allowing for an in-depth examination of the relationships between the resulting topologies. Together, these theoretical developments extend the formal mechanics of rough set approximations and link algebraic binary relation models with abstract topological structures.
Managing ambiguous or incomplete information is a fundamental challenge across computational mathematics and data processing. By establishing connections between neighbourhood systems, rough sets, and topological spaces, this theoretical work deepens the formal mathematical tools available for reasoning about imprecise data and abstract spatial relationships.
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Rough sets theory is an important method for dealing with uncertainty, fuzziness and undefined objects. In this paper, we introduce a new approach for generalized rough sets based on the neighborhood systems induced by an arbitrary binary relation. Four pairs of the dual approximation operators are generated from the core of neighborhood systems. Relationship among different approximation operators are presented. We generate different topological spaces by using the core of these neighborhood systems. Relationship among different generated topologies are discussed.
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DOI: 10.1016/j.joems.2016.02.002
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