Fuzzy rough sets based on residuated lattices

Rough sets were developed by Pawlak as a formal tool for representing and processing information in data tables. Fuzzy generalizations of rough sets were introduced by Dubois and Prade. In this paper, we consider L-fuzzy rough sets as a further generalization of the notion of rough sets. Specifically, we take a residuated lattice L as a basic structure. L-fuzzy rough sets are defined using the product operator and its residuum provided by the residuated lattice L. Depending on classes of binary fuzzy relations, we define several classes of L-fuzzy rough sets and investigate properties of these classes.