Abstract :
In this paper, the original fuzzy linear system is replaced by a matrix equation and a CG-type iterative method is considered, by which the exact solution can be obtained in finite steps in the absence of rounding error, even if the coefficient matrix of the matrix equation is singular or rectangular. In the paper [T. Allahviranloo, A comment on fuzzy linear systems, Fuzzy Sets Syst., 140(2003):559], the author pointed out that Theorem 3 of the paper [M. Friedman and M. Ming, Fuzzy Linear systems, Fuzzy Sets Syst., 96 (1998):201-209] cannot hold. In this paper, we think that this theorem is right and perfect its proof.
Keywords :
conjugate gradient methods; fuzzy set theory; fuzzy systems; conjugate gradient method; fuzzy linear systems; iterative method; matrix equation; Educational institutions; Equations; Fuzzy sets; Fuzzy systems; Information science; Iterative methods; Linear systems; Matrix decomposition; Roundoff errors; Vectors;
