# Iterative Method for Dual Fuzzy Linear Systems

• Zeng-feng Tian
• Xian-bin Wu
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 54)

## 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.

## Keywords

Fuzzy numbers Iterative method Dual fuzzy linear system Fuzzy vector space Spectral radius

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