On L-fuzzy approximation operators and L-fuzzy relations on residuated lattices

Abstract

We consider properties of L-fuzzy relations and L-normal operators for a residuated lattice L in detail and show that the class RL(U) of all L-fuzzy relations on U and the class NL(U) of all L-normal operators are residuated lattices and they are isomorphic as lattices. Moreover, we prove that for any L-normal operators F, it is reflexive (or transitive) if and only if the L-fuzzy relation RF induced by F is reflexive (or transitive) respectively.