The L-fuzzy bi-ideal degrees and its induced convex structure

In this paper, considering L being a completely distributive lattice, we propose a degree approach to L-fuzzy bi-ideals in an ordered semigroup. Firstly, we introduce the concept of L-fuzzy bi-ideal degree with respect to an ordered semigroup, which can be used to describe the degree to which an L-fuzzy subset of the ordered semigroup becomes an L-fuzzy bi-ideal. Secondly, we characterize L-fuzzy bi-ideal degree by cut sets. Finally, we provide a natural way to construct an L-fuzzy convex structure on an ordered semigroup via the L-fuzzy bi-ideal degree, and show that the homomorphism between two ordered semigroups is an L-fuzzy convexity-preserving mapping and the monohomomorphism is an L-fuzzy convex-to-convex mapping.