Rough Sets: A Topological View

Arun Kumar () and Shilpi Kumari
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Arun Kumar: Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
Shilpi Kumari: Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 02, 661-675

Abstract: This paper explores the topological aspects of algebras determined by rough sets. It is well known that the lattice structure of rough sets is characterized by the lattices of the form 2I ×3J. We show that algebras determined by the rough sets are characterized by the condition “any chain of completely prime filters has at most two elements†. We introduce the notion of rough topological space in which the basic open set has at most two elements. We further provide representations of rough topological spaces in terms of topologies determined by algebras of rough sets.

Keywords: Rough sets; Heyting algebra; Kleene algebra; rough topological space (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500309

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