Local convexity and local boundedness of induced I(L)-topological vector spaces

In this paper, we prove that an L-topological vector space is locally convex (locally bounded) iff its induced I(L)-topological vector space is locally convex (locally bounded), where I(L) is the L-fuzzy unit interval. Also, we give a necessary and sufficient condition for the induced I(L)-topological vector space to be I(L)-fuzzy normable.