Rough sets and Nelson algebras
Fundamenta Informaticae - Special issue: rough sets
Rough sets through algebraic logic
Fundamenta Informaticae - Special issue: to the memory of Prof. Helena Rasiowa
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Rough Sets: Mathematical Foundations
Rough Sets: Mathematical Foundations
A Generalized Definition of Rough Approximations Based on Similarity
IEEE Transactions on Knowledge and Data Engineering
On Generalizing Pawlak Approximation Operators
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
On the structure of rough approximations
Fundamenta Informaticae
Modal-Like Operators in Boolean Lattices, Galois Connections and Fixed Points
Fundamenta Informaticae
A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic)
New Approach in Defining Rough Approximations
RSFDGrC '09 Proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
Constructive and algebraic methods of the theory of rough sets
Information Sciences: an International Journal
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
New approach for basic rough set concepts
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
Information Sciences: an International Journal
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In this paper, we discuss some algebraic structures of the set of all lower(B∇) and upper(BΔ) approximations defined through the basic map ϕ in the general setting of complete atomic Boolean lattice B. In fact, we prove that if ϕ is extensive and closed, then B∇ and BΔ are algebraic completely distributive lattices. A representation theorem for algebraic completely distributive lattices in terms of B∇ under the existence of an extensive and closed map ϕ is given. We also prove that if ϕ is extensive and symmetric, then B∇ and BΔ are complete ortholattices. A representation theorem for complete ortholattices in terms of BΔ under the existence of an extensive and symmetric map ϕ is shown. Further, we define a map ϕ induced from the basic map ϕ and study the properties of the rough approximations defined with respect to ϕ under various conditions on the basic map ↦.