Inconsistent fuzzy linear systems (Q856074)

Linear systems \(Ax =b\) with fuzzy right-hand side (\(b\) and \(x\) are vectors of fuzzy numbers) were introduced by \textit{M. Friedman, M. Ma} and \textit{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 an 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).