Abstract

In this paper, we focus on the extension of the theory of rough set in lattice-theoretic setting. First we introduce the definition for generalized lower and upper approximation operators determined by mappings between two complete atomic Boolean algebras. Then we find the conditions which permit a given lattice-theoretic operator to represent a upper (or lower) approximation derived from a special mapping. Different sets of axioms of lattice-theoretic operator guarantee the existence of different types of mappings which produce the same operator

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