## 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 M. Friedman [Fuzzy Sets Syst. 96, 201–209 (1998; Zbl 0929.15004)] and M. Friedman, A. Kandel and M. Ma [Fuzzy Sets Syst. 109, 55–58 (2000; Zbl 0945.15002)], where the associated matrix $$S$$ was introduced, $S = \left[\begin{matrix} P & Q \\ Q & P \end{matrix}\right]$ 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:

 65F30 Other matrix algorithms (MSC2010) 15A06 Linear equations (linear algebraic aspects) 08A72 Fuzzy algebraic structures 15B33 Matrices over special rings (quaternions, finite fields, etc.) 65F10 Iterative numerical methods for linear systems

### Citations:

Zbl 0929.15004; Zbl 0945.15002
Full Text:

### References:

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