**5. Conclusions**

In this paper, we proposed the notion of *L*-fuzzy subalgebra degree on an effect algebra based on a completely distributive lattice *L*. We gave their characterizations in terms of four kinds of cut sets of *L*-subsets. We say an *L*-subset is an *L*-subalgebra if its *L*-fuzzy subalgebra degree is equal to *L*. In fact, the *L*-fuzzy subalgebra degree can describe the degree to which an *L*-subset is an *L*-fuzzy subalgebra. An *L*-fuzzy convex structure on an effect algebra was naturally constructed and some of its properties were studied. For instance, an *L*-convex structure was induced by the set of all *L*-subalgebras and its *L*-convex hull formula was given.

It should be noted that the same thought can be applied to different algebraic structure such as *MV*-algebras, *BL*-algebras, residuated lattices and so on. Thus, there exist *L*-fuzzy convexities in many logical algebras, which enrich the convexity theory in logical algebras.

**Author Contributions:** Conceptualization, Y.-Y.D.; formal analysis, Y.-Y.D. and F.-G.S.; funding acquisition, F.-G.S.; investigation, Y.-Y.D. and F.-G.S.; methodology, Y.-Y.D. and F.-G.S.; project administration, Y.-Y.D. and F.-G.S.; supervision, F.-G.S.; validation, Y.-Y.D. and F.-G.S.; visualization, F.-G.S.; writing—original draft, Y.-Y.D.; writing—review and editing, Y.-Y.D. and F.-G.S. Both authors have read and agreed to the published version of the manuscript.

**Funding:** The project is funded by the National Natural Science Foundation of China (11871097, 12071033), Beijing Institute of Technology Science and Technology Innovation Plan Cultivation Project (No. 2021CX01030) and Chinese Postdoctoral Science Foundation (No. 2020M670142).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors express thanks to the handling Editor and the reviewers for their careful reading and useful suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest. # **References**


