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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.

65F10Iterative methods for linear systems
15B33Matrices over special rings (quaternions, finite fields, etc.)
03E72Fuzzy set theory
Full Text: DOI
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