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Iterative Method for Dual Fuzzy Linear Systems

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Book cover Fuzzy Information and Engineering

Part of the book series: Advances in Soft Computing ((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.

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Author information

Authors and Affiliations

  1. Composite Section, Junior College, Zhejiang Wanli University, Ningbo, 315101, Zhejiang, P.R. China

    Zeng-feng Tian & Xian-bin Wu

Authors
  1. Zeng-feng Tian
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  2. Xian-bin Wu
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Editor information

Editors and Affiliations

  1. Guangzhou Higher Education Mega Center, Guangzhou University, 230Wai Huan Xi Road, 510006, China

    Bing-yuan Cao

  2. Department of Mathematics, Hainan Normal University, Haikou, 571158, Hainan, P.R. China

    Cheng-yi Zhang

  3. Department of Electronic Information Engineering, Chongqing University of Science & Technology, 401331, Chongqing

    Tai-fu Li

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© 2009 Springer-Verlag Berlin Heidelberg

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Tian, Zf., Wu, Xb. (2009). Iterative Method for Dual Fuzzy Linear Systems. In: Cao, By., Zhang, Cy., Li, Tf. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88914-4_37

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  • DOI: https://doi.org/10.1007/978-3-540-88914-4_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88913-7

  • Online ISBN: 978-3-540-88914-4

  • eBook Packages: EngineeringEngineering (R0)

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