Geodesic
Maximal column rank preservers of fuzzy matrices
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 207-218

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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.
Keywords: linear operator on matrices, fuzzy matrix, maximal column rank of a matrix, congruence operator on matrices, chain semiring 
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Song, Seok-Zun; Park, Soo-Roh. Maximal column rank preservers of fuzzy matrices. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 207-218. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a5/