Author/Authors :
Chun-E Huang، Chun-E Huang نويسنده Chun-E Huang, Chun-E Huang , Fu-Gui Shi، Fu-Gui Shi نويسنده Fu-Gui Shi, Fu-Gui Shi
Abstract :
In this paper, firstly, it is proved that, for a fuzzy vector space,
the set of its fuzzy bases defined by Shi and Huang, is equivalent to the family
of its bases defined 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 finite 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.
