ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES

Document Type: Research Paper

Authors

1 Biochemical engineering college, Beijing Union University, Beijing 100023, P. R. China

2 Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, P. R. China

Abstract

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.

Keywords


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