ROUGH SETS AND NELSON ALGEBRAS

Article type: Research Article

Authors: Pagliani, Piero

Affiliations: Research Group on Knowledge and Communication Models. Via Imperia. 6. 00161 Roma, Italy

Abstract: 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.

DOI: 10.3233/FI-1996-272308

Journal: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 205-219, 1996