*Article L***-Fuzzy Sub-Effect Algebras**

**Yan-Yan Dong \* and Fu-Gui Shi**

> Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China; fuguishi@bit.edu.cn

**\*** Correspondence: 3120195725@bit.edu.cn

**Abstract:** In this paper, the notions of *L*-fuzzy subalgebra degree and *L*-subalgebras on an effect algebra are introduced and some characterizations are given. We use four kinds of cut sets of *L*-subsets to characterize the *L*-fuzzy subalgebra degree. We induce an *L*-fuzzy convexity by the *L*-fuzzy subalgebra degree, and we prove that a morphism between two effect algebras is an *L*-fuzzy convexity preserving mapping and a monomorphism is an *L*-fuzzy convex-to-convex mapping. Finally, it is proved that the set of all *L*-subalgebras on an effect algebra can form an *L*-convexity, and its *L*-convex hull formula is given.

**Keywords:** effect algebra; *L*-fuzzy subalgebra degree; *L*-subalgebra; *L*-fuzzy convexity; *L*-convex hull formula
