Representation of Nelson algebras by rough sets determined by quasiorders |
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Authors: | Jouni J?rvinen S??ndor Radeleczki |
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Institution: | 1. University of Turku, FI-20014, Turku, Finland 2. Institute of Mathematics, University of Miskolc, 3515, Miskolc-Egyetemv??ros, Hungary
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Abstract: | In this paper, we show that every quasiorder R induces a Nelson algebra ${{\mathbb R}{\mathbb S}}$ such that the underlying rough set lattice RS is algebraic. We note that ${{\mathbb R}{\mathbb S}}$ is a three-valued ?ukasiewicz 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 ${{\mathbb A} \cong {\mathbb R}{\mathbb S}}$ . |
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