ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES

Abstract

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