In this paper, aiming at the shortcomings of the definition of LRG-Galois connections in [51], we give a new definition of (strong) LRG-Galois connections, and we also introduce the notions of (L, N)-fuzzy betweenness relations. By using a strong LRG-Galois connection in our sense, it is shown that the category of (L, N)-fuzzy betweenness spaces and the category of (L, M)-fuzzy convex spaces are isomorphic. Moreover, it is proved that the lattice of (L, M)-fuzzy convex structures and the lattice of (L, N)-fuzzy betweenness relations are complete lattice isomorphic.