Abstract In this paper, the relation between two definitions of locally convex I -topological vector spaces is studied. These two definitions are introduced by Katsaras [Fuzzy topological vector spaces II, Fuzzy Sets and Systems 12 (1984) 143–154] and Wu and Li [Convexity and fuzzy topological vector spaces, Science Exploration (China) 4(1) (1984) 1–4], respectively. We prove that the locally convex I -topological vector space in the sense of Wu and Li is a special case of that in the sense of Katsaras. We introduce the notion of generalized fuzzy semi-norm and prove that every locally convex I -vector topology in the sense of Katsaras on X can be determined by a family of generalized fuzzy semi-norms on X .