Article ID Journal Published Year Pages File Type
390761 Fuzzy Sets and Systems 2009 11 Pages PDF
Abstract

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.

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