IF rough approximations based on lattices.

An IF rough set, which is the result of approximation of an IF set with respect to an IF approximation space, is an extension of fuzzy rough sets. This paper studies rough set theory within the context of lattices. First, we introduce the concepts of IF rough sets and IF rough approximation operators based on lattices. Then, we give some properties on IF rough approximations of IF sublattices such as IF ideals and IF filters. [ABSTRACT FROM AUTHOR]