Properties of the Fifth Type of Covering-Based Rough Sets

Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets is an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, a covering can also generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the covering-based lower and upper approximation operations.