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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 {\it M. Friedman, M. Ma} and {\it 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 algebra) 15B48 Positive matrices and their generalizations; cones of matrices 15A09 Matrix inversion, generalized inverses 08A72 Fuzzy algebraic structures 15B33 Matrices over special rings (quaternions, finite fields, etc.)
Full Text:
##### References:
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