Maximal column rank preservers of fuzzy matrices

Seok-Zun Song; Soo-Roh Park

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 2, page 207-218
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Seok-Zun Song, and Soo-Roh Park. "Maximal column rank preservers of fuzzy matrices." Discussiones Mathematicae - General Algebra and Applications 21.2 (2001): 207-218. <http://eudml.org/doc/287600>.

@article{Seok2001,
abstract = {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.},
author = {Seok-Zun Song, Soo-Roh Park},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {linear operator on matrices; fuzzy matrix; maximal column rank of a matrix; congruence operator on matrices; chain semiring; maximal column rank; congruence operator; Boolean matrices; fuzzy semiring},
language = {eng},
number = {2},
pages = {207-218},
title = {Maximal column rank preservers of fuzzy matrices},
url = {http://eudml.org/doc/287600},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Seok-Zun Song
AU - Soo-Roh Park
TI - Maximal column rank preservers of fuzzy matrices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 2
SP - 207
EP - 218
AB - 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.
LA - eng
KW - linear operator on matrices; fuzzy matrix; maximal column rank of a matrix; congruence operator on matrices; chain semiring; maximal column rank; congruence operator; Boolean matrices; fuzzy semiring
UR - http://eudml.org/doc/287600
ER -

References

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  1. [1] L.B. Beasley and N.J. Pullman, Semiring rank versus column rank, Linear Algebra Appl. 101 (1988), 33-48. Zbl0642.15002
  2. [2] L.B. Beasley and N.J. Pullman, Fuzzy rank-preserving operators, Linear Algebra Appl. 73 (1986), 197-211. Zbl0578.15002
  3. [3] L.B. Beasley and N.J. Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77. Zbl0536.20044
  4. [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. Zbl0804.15002
  5. [5] S.Z. Song, Linear operators that preserve column rank of fuzzy matrices, Fuzzy Sets and Systems, 62 (1994), 311-317. Zbl0827.15002
  6. [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. Zbl0983.20061

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