Summary: Since the core violates related properties of (weak) converse consistency proposed by Y. H. Liao [“Consistency and the core for fuzzy non-transferable-utility games”, Economics Bulletin 3, 1–6 (2008)] on fuzzy non-transferable-utility (NTU) games, two converse consistent enlargements of the core are proposed. These two converse consistent enlargements are the smallest (weak) converse consistent solutions that contain the core. Further, we introduce a revised complement-reduction to characterize the core.