Chun-E Huang - Biochemical engineering college, Beijing Union University, Beijing ۱۰۰۰۲۳, P. R. China
Fu-Gui Shi - Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing ۱۰۰۰۸۱, P. R. China

In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however, the converse is not true. Finally, fuzzy dimension of direct sum is considered, for a nite number of fuzzy vector spaces and it is proved that fuzzy dimension of their direct sum is equal to the sum of fuzzy dimensions of fuzzy vector spaces.

Fuzzy vector space, Fuzzy basis, Fuzzy dimension, Direct sum