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arXiv · 1007.1199

Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

Jouni Järvinen·Sándor Radeleczki
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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 $\mathbb{A} \cong \mathbb{RS}$.

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Jouni Järvinen, Sándor Radeleczki. 2011-02-19. Representation of Nelson Algebras by Rough Sets Determined by Quasiorders. https://doi.org/10.1007/s00012-011-0149-9

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