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

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.

### MSC:

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

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