Abstract
Covering rough sets, a generalization of the classical rough sets, are main research topics of rough set theory. Various covering rough set models have been proposed. In this paper, ten important types of covering rough set models are first reviewed. The algebraic structures of definable sets, inner definable sets and outer definable sets in these covering rough sets are then investigated. Based on the concept of definable sets, we further explore relations among the ten covering rough sets. Finally, the conditions for neighborhood \(\{N(x):x\in U\}\) to form a partition of the universe U are discussed, and an open problem proposed by Yun et al. is answered.
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