This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1038,
author = {Seok-Zun Song and Soo-Roh Park},
title = {Maximal column rank preservers of fuzzy matrices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {21},
year = {2001},
pages = {207-218},
zbl = {1006.15018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1038}
}
Seok-Zun Song; Soo-Roh Park. Maximal column rank preservers of fuzzy matrices. Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001) pp. 207-218. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1038/
[000] [1] L.B. Beasley and N.J. Pullman, Semiring rank versus column rank, Linear Algebra Appl. 101 (1988), 33-48. | Zbl 0642.15002
[001] [2] L.B. Beasley and N.J. Pullman, Fuzzy rank-preserving operators, Linear Algebra Appl. 73 (1986), 197-211. | Zbl 0578.15002
[002] [3] L.B. Beasley and N.J. Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77. | Zbl 0536.20044
[003] [4] S.G. Hwang, S.J. Kim and S.Z. Song, Linear operators that preserve maximal column rank of Boolean matrices, Linear and Multilinear Algebra 36 (1994), 305-313. | Zbl 0804.15002
[004] [5] S.Z. Song, Linear operators that preserve column rank of fuzzy matrices, Fuzzy Sets and Systems, 62 (1994), 311-317. | Zbl 0827.15002
[005] [6] S.Z. Song, S.D. Yang, S.M. Hong, Y.B. Jun and S.J. Kim, Linear operators preserving maximal column ranks of nonbinary Boolean matrices, Discussiones Math. - Gen. Algebra Appl., 20 (2000), 255-265. | Zbl 0983.20061