Iteration algorithms for solving a system of fuzzy linear equations. (English) Zbl 0974.65035

Wang, Xizhao; Zhong, Zimian; Ha, Minghu

Fuzzy Sets Syst. 119, No. 1, 121-128 (2001).

The iterative solution of a system of fuzzy linear equations \(x= Ax+u\) is discussed where \(A\) is a real \(n\times n\) matrix, \(x\) is the unknown vector and \(u\) is a given vector consisting of \(n\) fuzzy numbers. It is assumed that scale-multiplication and addition are defined by Zadeh’s extension principle. It is proved that there is a unique solution if \(\|A\|_\infty< 1\). Convergence conditions and error estimates for the simple iteration method are presented.

Reviewer: F.Szidarovszky (Tucson)

MSC:

65F10	Iterative numerical methods for linear systems
15B33	Matrices over special rings (quaternions, finite fields, etc.)
03E72	Theory of fuzzy sets, etc.

Keywords:

iteration algorithms; fuzzy numbers; convergence; system of fuzzy linear equations; Zadeh’s extension principle; error estimates

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