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Numerical methods for fuzzy system of linear equations. (English) Zbl 1067.65040
The paper deals with systems of linear equations $Ax = b$ with fuzzy right-hand side ($b$ and $x$ are vectors of fuzzy numbers). It is a continuation of papers by {\it M. Friedman} [Fuzzy Sets Syst. 96, 201--209 (1998; Zbl 0929.15004)] and {\it M. Friedman}, {\it A. Kandel} and {\it M. Ma} [Fuzzy Sets Syst. 109, 55--58 (2000; Zbl 0945.15002)], where the associated matrix $S$ was introduced, $$S = \left[\matrix P & Q \\ Q & P \endmatrix\right]$$ with $p_{i,j} =\max(0,a_{i,j})$, $q_{i,j} = -\min(0,a_{i,j})$, $i,j =1,\dots,n$, where the system $Sy=c$ is crisp (real matrix and vectors). If the matrix $A$ is diagonally dominant, then $S$ has also this property (Theorem 3.2). Therefore, approximate solutions can be obtained by Jacobi iterations or Gauss-Seidel iterations.

MSC:
65F30Other matrix algorithms
15A06Linear equations (linear algebra)
08A72Fuzzy algebraic structures
15B33Matrices over special rings (quaternions, finite fields, etc.)
65F10Iterative methods for linear systems
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References:
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