TY - JOUR
ID - 138
TI - ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Huang, Chun-E
AU - Shi, Fu-Gui
AD - Biochemical engineering college, Beijing Union University, Beijing
100023, P. R. China
AD - Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing 100081, P. R. China
Y1 - 2012
PY - 2012
VL - 9
IS - 4
SP - 141
EP - 150
KW - Fuzzy vector space
KW - Fuzzy basis
KW - Fuzzy dimension
KW - Direct sum
DO - 10.22111/ijfs.2012.138
N2 - 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.
UR - https://ijfs.usb.ac.ir/article_138.html
L1 - https://ijfs.usb.ac.ir/article_138_f039ecb754d89261c9c1e68ef58032fc.pdf
ER -