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Approximate Solution of LR Fuzzy Sylvester Matrix Equations

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  • Xiaobin Guo
  • Dequan Shang

Abstract

The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A, B are m × m and n × n crisp matrices, respectively, and C~ is an m × n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

Suggested Citation

  • Xiaobin Guo & Dequan Shang, 2013. "Approximate Solution of LR Fuzzy Sylvester Matrix Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:752760
    DOI: 10.1155/2013/752760
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    References listed on IDEAS

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    1. Dehghan, Mehdi & Hashemi, Behnam & Ghatee, Mehdi, 2007. "Solution of the fully fuzzy linear systems using iterative techniques," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 316-336.
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