6 research outputs found
Representation of Nelson Algebras by Rough Sets Determined by Quasiorders
In this paper, we show that every quasiorder induces a Nelson algebra
such that the underlying rough set lattice is algebraic. We
note that is a three-valued {\L}ukasiewicz algebra if and only if
is an equivalence. Our main result says that if is a Nelson
algebra defined on an algebraic lattice, then there exists a set and a
quasiorder on such that .Comment: 16 page
Pseudo-Kleene algebras determined by rough sets
We study the pseudo-Kleene algebras of the Dedekind-MacNeille completion of
the ordered set of rough set determined by a reflexive relation. We
characterize the cases when PBZ and PBZ*-lattices can be defined on these
pseudo-Kleene algebras.Comment: 24 pages, minor update to the initial versio