Iterative Method for Dual Fuzzy Linear Systems

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


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.


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


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Zeng-feng Tian
    • 1
  • Xian-bin Wu
    • 1
  1. 1.Composite Section, Junior CollegeZhejiang Wanli UniversityNingboP.R. China

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