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Zheng, Bing; Wang, Ke

General fuzzy linear systems. (English) Zbl 1122.15005

Appl. Math. Comput. 181, No. 2, 1276-1286 (2006).
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.
Reviewer: Józef Drewniak (Rzeszów)

Cited in 5 Reviews
Cited in 22 Documents

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.)

Keywords:

linear system; fuzzy number; fuzzy coefficient; fuzzy solution; weak and strong solutions; positive matrix; generalized inverse; Moore-Penrose inverse; inconsistent system; approximate solution; least squares method

Citations:

Zbl 0929.15004
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\textit{B. Zheng} and \textit{K. Wang}, Appl. Math. Comput. 181, No. 2, 1276--1286 (2006; Zbl 1122.15005)
Full Text: DOI

References:

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