Rough filters based on residuated lattices

摘要

The paper is devoted to introduce the notion of rough sets within the context of residuated lattices. By considering the notion of a residuated lattice, we concern a relationship between rough sets theory and residuated lattices theory. We shall introduce the notion of rough subalgebra (resp. filter) with respect to a filter of a residuated lattice, which is an extended notion of subalgebra (resp. filter) in a residuated lattice and investigate some of their properties.