Document Type : Research Paper


1 School of Mathematical Science, Nanjing Normal University, Nan- jing, Jiangsu 210023, P. R. China

2 Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000, P. R. China


The notion of generalized locally bounded $I$-topological vector
spaces is introduced. Some of their important properties are
studied. The relationship between this kind of spaces and the
locally bounded $I$-topological vector spaces introduced by Wu and
Fang [Boundedness and locally bounded fuzzy topological vector
spaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, we
also use the family of generalized fuzzy quasi-norms to characterize
the generalized locally bounded $I$-topological vector spaces, and
give some applications of this characterization.


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