Using one axiom to characterize L-fuzzy rough approximation operators based on residuated lattices

Axiomatic characterization of approximation operators plays an important role in the study of rough set theory. Different axiom sets of abstract operators can illustrate different classes of rough set systems. In this paper, we are devoted to searching for a single axiom to characterize L-fuzzy rough approximation operators based on residuated lattices. Axioms of L-fuzzy set theoretic operators make sure of the existence of certain types of L-fuzzy relations which produce the same operators. We demonstrate that the lower (upper) L-fuzzy rough approximation operators generated by a generalized L-fuzzy relation can be characterized by only one axiom. Furthermore, we also use one axiom to characterize L-fuzzy rough approximation operators produced by the L-fuzzy serial, reflexive, symmetric and T-transitive relations as well as any of their compositions.