Formulations of L -convex hulls on some algebraic structures

With a complete Heyting algebra L as the truth value table, we introduce L -ordered convex spaces, L -semilattice convex spaces, L -lattice convex spaces and L -standard convex spaces. These kinds of structures can be extracted from posets, semilattices, lattices and vector spaces. Above all, we obtain their corresponding L -convex hull formulae and analyze their corresponding L -convexity-preserving (resp., L -convex-to-convex) mappings.