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

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Seok-Zun Song and Soo-Roh Park

Department of Mathematics, Cheju National University
Cheju 690-756, South Korea


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.


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