summary:In this paper, considering L being a completely distributive lattice, we first introduce the concept of L-fuzzy ideal degrees in an effect algebra E, in symbol Dei. Further, we characterize L-fuzzy ideal degrees by cut sets. Then it is shown that an L-fuzzy subset A in E is an L-fuzzy ideal if and only if Dei(A)=⊤, which can be seen as a generalization of fuzzy ideals. Later, we discuss the relations between L-fuzzy ideals and cut sets (Lβ-nested sets and Lα-nested sets). Finally, we obtain that the L-fuzzy ideal degree is an (L,L)-fuzzy convexity. The morphism between two effect algebras is an (L,L)-fuzzy convexity-preserving mapping