Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

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