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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 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=PQQP

with p i,j =max(0,a i,j ), q i,j =-min(0,a i,j ), i,j=1,,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
15A33Matrices over special rings
65F10Iterative methods for linear systems