Summary: We give a new decomposition theorem of \(L\)-fuzzy sets. Then we use this theorem to discuss the relations between the crisp topological vector spaces and the \(L\)-fuzzy topological vector spaces [J.-X. Fang and the author, J. Fuzzy Math. 5, No. 1, 133-144 (1997; Zbl 0874.46051)], and we obtain some interesting properties.