Iteration algorithms for solving a system of fuzzy linear equations

In this paper, we discuss the solution of a system of fuzzy linear equations, X = AX + U, and its iteration algorithms where A is a real n x n matrix, the unknown vector X and the constant U are all vectors consisting of n fuzzy numbers, and the addition, scale-multiplication are defined by Zadeh's extension principle. After introducing a metric between two fuzzy vectors, we prove that the system has unique solution if \\A\\(infinity) < 1 We also give the convergence and the error estimation for using simple iteration to obtain the solution. Finally, we give the convergence and the error estimation of successive iteration sequence for obtaining the solution. (C) 2001 Elsevier Science B.V. All rights reserved.