A degree approach to L-fuzzy filters in effect algebras

Considering a completely distributive lattice L as the truth value table, we propose a degree approach to L-fuzzy filters in an effect algebra. Firstly, we introduce the concept of L-fuzzy filter degree with respect to an effect algebra, which can be used to describe the degree to which an L-fuzzy subset of the effect algebra becomes an L-fuzzy filter. Secondly, we make full use of the logical operations on L to characterize L-fuzzy filter degree with respect to an effect algebra via four kinds of cut sets. Finally, we provide a natural way to construct an L-fuzzy convex structure on an effect algebra via the L-fuzzy filter degree, and show that the morphism between two effect algebras is an L-fuzzy convexity-preserving mapping and the monomorphism is an L-fuzzy convex-to-convex mapping.