## General fuzzy linear systems.(English)Zbl 1122.15005

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.

### MSC:

 15A06 Linear equations (linear algebraic aspects) 15B48 Positive matrices and their generalizations; cones of matrices 15A09 Theory of matrix inversion and generalized inverses 08A72 Fuzzy algebraic structures 15B33 Matrices over special rings (quaternions, finite fields, etc.)

Zbl 0929.15004
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