Axiomatic systems for rough sets and fuzzy rough sets

Rough set theory is an important tool for approximate reasoning about data. Axiomatic systems of rough sets are significant for using rough set theory in logical reasoning systems. In this paper, outer product method are used in rough set study for the first time. By this approach, we propose a unified lower approximation axiomatic system for Pawlak's rough sets and fuzzy rough sets. As the dual of axiomatic systems for lower approximation, a unified upper approximation axiomatic characterization of rough sets and fuzzy rough sets without any restriction on the cardinality of universe is also given. These rough set axiomatic systems will help to understand the structural feature of various approximate operators. (C) 2008 Elsevier Inc. All rights reserved.