Generalized locally bounded \(L\)-topological vector spaces (Q622084)

The notion of generalized locally bounded \(L\)-topological vector spaces is introduced. The relationship between this kind of space and locally bounded \(L\)-topological vector space as defined by \textit{C.-C. Yan} and \textit{J.-X. Fang} [Inf. Sci. 159, No.~3--4, 273--281 (2004; Zbl 1047.46054)] is investigated. Finally, the Hausdorff separation property, convergence of molecule nets and boundedness of \(L\)-fuzzy sets in generalized locally bounded \(L\)-topological vector spaces are studied. Especially, the concept of generalized locally bounded \(L\)-topological vector spaces can be characterized by a family of generalized \(L\)-fuzzy quasi norms, which are also defined in the paper.