ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES

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.