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Zbl 1122.15004
Wang, Ke; Zheng, Bing
Inconsistent fuzzy linear systems.
(English)
[J] Appl. Math. Comput. 181, No. 2, 973-981 (2006). ISSN 0096-3003

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 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).
[Józef Drewniak (Rzeszów)]
MSC 2000:
*15A06 Linear equations (linear algebra)
15A48 Positive matrices and their generalizations
15A09 Matrix inversion
08A72 Fuzzy algebraic structures
15A33 Matrices over special rings

Keywords: linear system; fuzzy number; fuzzy coefficient; fuzzy solution; weak and strong solutions; positive matrix; generalized inverse; Moore-Penrose inverse; nonnegative matrix

Citations: Zbl 0929.15004

Cited in: Zbl 1242.15004

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