Discussiones Mathematicae General Algebra and Applications 21(2) (2001)207-218
doi: 10.7151/dmgaa.1038

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MAXIMAL COLUMN RANK PRESERVERS OF FUZZY MATRICES

Seok-Zun Song and Soo-Roh Park

Department of Mathematics, Cheju National University
Cheju 690-756, South Korea
e-mail:
szsong@cheju.cheju.ac.kr

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.

Keywords: linear operator on matrices, fuzzy matrix, maximal column rank of a matrix, congruence operator on matrices, chain semiring.

1991 Mathematics Subject Classification: 15A03, 15A04, 15A33, 08A72, 16Y60.

References

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[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.

Received 31 March 2001
Revised 27 August 2001
Revised 11 December 2001