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In this paper, two kinds of remote neighborhood operators in $(L,M)$-fuzzy convex spaces are proposed, which are called convex $(L,M)$-fuzzy remote neighborhood operators. It is proved that these two kinds of convex $(L,M)$-fuzzy remote neighborhood operators can be used to characterize $(L,M)$-fuzzy convex structures. In addition, the lattice structures of two kinds of convex $(L,M)$-fuzzy remote neighborhood operators are also given.