L-fuzzy relations on residuated lattices

We consider properties of L-fuzzy relations and L- normal operators for a residuated lattice
$L$
by means of operator-based method and show that there is a one-to-one correspondence between them. By considering L-fuzzy approximation spaces as a fuzzy-version of Kripke semantics in modal logic, we also prove that some properties of L-fuzzy relations such as reflexivity and symmetry can be characterized by similar formulas of sequence of L-fuzzy relations
$\overline{\mathrm{R}}$
and
$\underline{\mathrm{R}}$
.