Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
A Pure Logic-Algebraic Analysis of Rough Top and Rough Bottom Equalities
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
Fundamenta Informaticae - From Physics to Computer Science: to Gianpiero Cattaneo for his 70th birthday
Generalized Rough Logics with Rough Algebraic Semantics
International Journal of Cognitive Informatics and Natural Intelligence
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Any Rough Sets System induced by an Approximation Space can be given several logic-algebraic interpretations. In this paper a Rough Sets System is investigated as a finite semi-simple Nelson algebra whose structure is inherently described using the properties of the underlying Approximation Space. Moreover some of the most characterizing features of Rough Sets Systems are derived from this interpretation in logic-algebraic terms. Particularly the logic-algebraic structure given to the Rough Sets System, qua a Nelson algebra is equipped by a weak negation and a strong negation, and, since it is a finite distributive lattice, it can be regarded also as a Heyting algebra equipped by its own pseudocomplementation. Moreover the weak Nelson negation reveals to be a dual pseudocomplementation in the lattice of Rough Sets. In this way we are able, for instance, to recover the well-known fact that Rough Sets Systems are double Stone algebras, and to exploit both their properties and the general properties of Nelson algebras in order to analyse the notions of ”definable set” and ”rough top (bottom) equality” in Approximation Spaces.