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Wang, Ke; Zheng, Bing

Inconsistent fuzzy linear systems. (English) Zbl 1122.15004

Appl. Math. Comput. 181, No. 2, 973-981 (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 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).
Reviewer: Józef Drewniak (Rzeszów)

Cited in 2 Reviews
Cited in 16 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; nonnegative matrix

Citations:

Zbl 0929.15004
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\textit{K. Wang} and \textit{B. Zheng}, Appl. Math. Comput. 181, No. 2, 973--981 (2006; Zbl 1122.15004)
Full Text: DOI

References:

[1] Friedman, M.; Ming, M.; Kandel, A., Fuzzy linear systems, Fuzzy Sets Syst., 96, 201-209 (1998) · Zbl 0929.15004
[2] Asady, B.; Abbasbandy, S.; Alavi, M., Fuzzy general linear systems, Appl. Math. Comput., 169, 34-40 (2005) · Zbl 1119.65325
[4] Cong-Xin, W.; Ming, M., Embedding problem of fuzzy number space: Part I, Fuzzy Sets Syst., 44, 33-38 (1991) · Zbl 0757.46066
[5] Ben-Israel, A.; Greville, T. N.E., Generalized Inverses: Theory and Applications (2003), Springer-Verlag: Springer-Verlag New York · Zbl 1026.15004
[6] Bapat, R. B., Structure of a nonnegative regular matrix and its generalized inverses, Linear Algebra Appl., 268, 31-39 (1998) · Zbl 0885.15015
[7] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1979), Academic Press: Academic Press New York · Zbl 0484.15016
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