On axiomatic characterization of approximation operators based on atomic boolean algebras

Authors:
Tongjun Li
Affiliations:
Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi, P.R. China
Venue:
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
Year:
2006

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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