On $L$-double fuzzy rough sets

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L$-double fuzzy upper (resp. lower) approximation of $L$-double fuzzy rough sets. Finally, from $L$-double fuzzy  approximation operators, we generated Alexandrov $L$-double fuzzy topology.