Linear systems

$Ax=b$ with fuzzy right-hand side (

$b$ and

$x$ are vectors of fuzzy numbers) were introduced by

*M. Friedman, M. Ma* and

*A. Kandel* [Fuzzy Sets Syst. 96, No. 2, 201–209 (1998); comment and reply ibid. 140, 559–561 (2003;

Zbl 0929.15004)], where the method of solutions based on associated

$2n\times 2n$ nonnegative matrix

$S$ for an

$n\times n$ square matrix

$A$ and the notions of weak and strong fuzzy solutions was presented. These results are now generalized to the case of an

$m\times n$ matrix

$A$ by using the generalized inverses of the associated matrix

$S$ (in particular the Moore-Penrose inverse). Moreover, in the case of an inconsistent system, the solution of the associated

$2m\times 2n$ linear system is replaced by the approximate solution from the least squares method.