New definition of locally convex L-topological vector spaces

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization of the new locally convex L-topological vector spaces is presented. Finally, as applications of this characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L-fuzzy sets in locally convex L-topological vector spaces are studied.