Perturbation analysis for a class of fuzzy linear systems

In this paper, the perturbation analysis is presented for a class of fuzzy linear systems which can be solved by an embedding method. We deduce the nonlinear upper perturbation bounds for the solutions, and discuss the normwise, mixed and componentwise condition numbers. The results show how the perturbations of the coefficient matrix and the right-hand vector impact the solutions to fuzzy linear systems.

[1]  Tofigh Allahviranloo,et al.  Successive over relaxation iterative method for fuzzy system of linear equations , 2005, Appl. Math. Comput..

[2]  Saeid Abbasbandy,et al.  LU decomposition method for solving fuzzy system of linear equations , 2006, Appl. Math. Comput..

[3]  Abraham Kandel,et al.  Fuzzy linear systems , 1998, Fuzzy Sets Syst..

[4]  Desmond J. Higham,et al.  Condition numbers and their condition numbers , 1995 .

[5]  Vimal Singh,et al.  Perturbation methods , 1991 .

[6]  Ke Wang,et al.  Inconsistent fuzzy linear systems , 2006, Appl. Math. Comput..

[7]  James J. Buckley,et al.  Solving fuzzy equations in economics and finance , 1992 .

[8]  Yimin Wei,et al.  Solving EP singular linear systems , 2004, Int. J. Comput. Math..

[9]  B. Zheng,et al.  Block iterative methods for fuzzy linear systems , 2007 .

[10]  James J. Buckley,et al.  Solving fuzzy equations , 1992 .

[11]  V. Mehrmann,et al.  Perturbation theory for matrix equations , 2003, IEEE Transactions on Automatic Control.

[12]  Mehdi Dehghan,et al.  Iterative solution of fuzzy linear systems , 2006, Appl. Math. Comput..

[13]  Ke Wang,et al.  General fuzzy linear systems , 2006, Appl. Math. Comput..

[14]  Ke Wang,et al.  Symmetric successive overrelaxation methods for fuzzy linear systems , 2006, Appl. Math. Comput..

[15]  Mei Han An,et al.  accuracy and stability of numerical algorithms , 1991 .

[16]  Fu Cheng Tang.  Perturbation techniques for fuzzy matrix equations , 2000, Fuzzy Sets Syst..

[17]  Tofigh Allahviranloo,et al.  The Adomian decomposition method for fuzzy system of linear equations , 2005, Appl. Math. Comput..

[18]  Iwona Skalna,et al.  Systems of fuzzy equations in structural mechanics , 2008 .

[19]  Saeid Abbasbandy,et al.  Conjugate gradient method for fuzzy symmetric positive definite system of linear equations , 2005, Appl. Math. Comput..

[20]  J. Buckley,et al.  Solving systems of linear fuzzy equations , 1991 .

[21]  Tofigh Allahviranloo,et al.  Numerical methods for fuzzy system of linear equations , 2004, Appl. Math. Comput..