Iterative method for dual fuzzy linear systems

Zeng-feng Tian

Xian-bin Wu

pp. 297-304

in: Bing-yuan Cao, Cheng-yi Zhang, Tai-fu Li (eds), Fuzzy information and Engineering I, Berlin, Springer, 2009

Abstract

A simple iterative method for solving dual fuzzy linear system, x = Ax + u in which A is a real n×n matrix, x and u are unknown and given n-dimensional fuzzy vectors, and its convergence were obtained by X. Wang et al (Iteration algorithm for solving a system of fuzzy linear equations, Fuzzy Sets and Systems, 119(2001)121-128). However, only a sufficient condition to convergence of the iteration was given. In this paper, a metric of fuzzy vectors is defined and the completeness of fuzzy vector space with this metric is argued. In the complete metric space a sufficient and efficient condition to convergence of simple iteration and error estimation for using it to get solution of the dual fuzzy linear system are obtained.