Algebraic properties of L-fuzzy approximation operators on extended residuated lattices

We consider properties of L-fuzzy relations on extended residuated lattice L and show a characterization theorem of $$*$$ -confluent L-fuzzy relation, which includes many cases of L-fuzzy relations such as, reflexive, symmetric, transitive, Euclidean and so on, by using only the notion of Galois connection of operators defined by L-fuzzy relation. Since our method is based on operator-base, it enables us to provide simpler and shorter proofs to the results obtained so far and to be able to get new results about properties of L-fuzzy relations of other algebras L.