The main objective of this paper is to provide some characterizations of M-fuzzifying convex structures in terms of derived operators. We first introduce the notion of M-fuzzifying convexly derived operators, and then establish the one-to-one correspondence between M-fuzzifying convexly derived operators and M-fuzzifying convex structures. Additionally, it is proved that M-fuzzifying CP mappings can be expressed as formulas of derived sets. Finally, we introduce the notion of M-fuzzifying restricted convexly derived operators and prove that it is isomorphic to M-fuzzifying convex structures.
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