Base axioms and Subbase axioms in M-fuzzifying convex spaces

Based on a completely distributive lattice M, base axioms and subbase axioms are introduced in M-fuzzifying convex spaces. It is shown that a mapping B (resp. φ) with the base axioms (resp. subbase axioms) can induce a unique M -fuzzifying convex structure with B (resp. φ) as its base (resp. subbase). As applications, it is proved that bases and subbases can be used to characterize CP mappings and CC mappings between M-fuzzifying convex spaces.