Fuzzy variable precision rough sets based on residuated lattices

There are many ways to generalize rough sets. Researching fuzzy rough sets under the framework of residuated lattices is one of the generalizations that broadens the truth values to lattices. This paper studies fuzzy variable precision approximation operators based on residuated lattices and presents the concept of -fuzzy variable precision rough sets. After the presentation of this concept, we investigate the corresponding properties and some special classes of -fuzzy variable precision rough sets based on different -relations. Finally, we study the topological structures of -fuzzy variable precision rough sets based on -lower sets and -upper sets, and conclude that the family of all -lower exact -sets and the family of all -upper exact -sets are -topologies, for each .