Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

Abstract

In this paper, we show that every quasiorder $R$ induces a Nelson algebra $\mathbb{RS}$ such that the underlying rough set lattice $RS$ is algebraic. We note that $\mathbb{RS}$ is a three-valued Łukasiewicz algebra if and only if $R$ is an equivalence. Our main result says that if $\mathbb{A}$ is a Nelson algebra defined on an algebraic lattice, then there exists a set $U$ and a quasiorder $R$ on $U$ such that $\mathbb{A}\cong \mathbb{RS}$.

arXiv comment16 pages

References in corpus (1)

• Rough Sets Determined by Quasiorders

Cited by in corpus (7)

• Rough sets determined by tolerances
• Information completeness in Nelson algebras of rough sets induced by quasiorders
• Representing regular pseudocomplemented Kleene algebras by tolerance-based rough sets
• Pseudo-Kleene algebras determined by rough sets
• Nelson algebras, residuated lattices and rough sets: A survey
• Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets
• The structure of rough sets defined by reflexive relations