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On the solution of the fuzzy Sylvester matrix equation

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Abstract

In this paper, we consider the fuzzy Sylvester matrix equation \(AX+XB=C,\) where \(A\in {\mathbb{R}}^{n \times n}\) and \(B\in {\mathbb{R}}^{m \times m}\) are crisp M-matrices, C is an \(n\times m\) fuzzy matrix and X is unknown. We first transform this system to an \((mn)\times (mn)\) fuzzy system of linear equations. Then, we investigate the existence and uniqueness of a fuzzy solution to this system. We use the accelerated over-relaxation method to compute an approximate solution to this system. Some numerical experiments are given to illustrate the theoretical results.

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Acknowledgments

The author would like to thank the anonymous referee and editor Dr. Brunella Gerla for their insightful and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran

    Davod Khojasteh Salkuyeh

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  1. Davod Khojasteh Salkuyeh
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Correspondence to Davod Khojasteh Salkuyeh.

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Salkuyeh, D.K. On the solution of the fuzzy Sylvester matrix equation. Soft Comput 15, 953–961 (2011). https://doi.org/10.1007/s00500-010-0637-4

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