L-fuzzy ordered subsemigroup degrees in ordered semigroups

Based on a completely distributive lattice L, we propose a degree approach to L-fuzzy ordered subsemigroups of an ordered semigroup. Firstly, we introduce the concept of L-fuzzy ordered subsemigroup degree function 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 ordered subsemigroup. Secondly, we use four kinds of cut sets depending on L to characterize the L-fuzzy ordered subsemigroup degree function. Finally, we provide a natural way to construct an L-fuzzy convex structure on an ordered semigroup via the L-fuzzy ordered subsemigroup degree function, 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 between the resulting L-fuzzy convex spaces.