Skip to main content
SpringerLink
Log in

On the solution of a class of fuzzy system of linear equations

  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

In this paper, we consider the system of linear equations \(A\tilde {x}=\tilde {b}\), where \(A\in \mathbb {R}^{n \times n}\) is a crisp H-matrix and \(\tilde {b}\) is a fuzzy n-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allahviranloo T 2004 Numerical methods for fuzzy system of linear equations. Appl. Mathematics and Computation, 155: 493–502

    Article  MATH  MathSciNet  Google Scholar 

  • Allahviranloo T 2005 Successive overrelaxation iterative method for fuzzy system of linear equations. Appl. Mathematics and Computation, 162: 189–196

    Article  MATH  MathSciNet  Google Scholar 

  • Allahviranloo T, Mikaeilvand N, Kiani NA and Shabestari R. 2008 Signed decomposition of fully fuzzy linear systems. Application and Appl. Math., 3: 77–88

    MATH  MathSciNet  Google Scholar 

  • Axelsson O 1996 Iterative solution methods, Cambridge University Press, Cambridge

  • Babbar N, Kumar A and Bansal A 2013a Linear programming approach to find the solution of fully fuzzy linear systems with arbitrary fuzzy coefficients. J. Intelligent & Fuzzy Systems, 25: 747–753

    MATH  MathSciNet  Google Scholar 

  • Babbar N, Kumar A and Bansal A 2013b Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers (m,α,β). Soft Computing, 17: 691–702

    Article  MATH  Google Scholar 

  • Dehghan M and Hashemi B 2006 Iterative solution of fuzzy linear systems. Appl. Mathematics and Computation, 175: 645–674

    Article  MATH  MathSciNet  Google Scholar 

  • Dehghan M, Hashemi B and Ghatee M 2006 Computational methods for solving fully fuzzy linear systems. Appl. Mathematics and Computation, 179: 328–343

    Article  MATH  MathSciNet  Google Scholar 

  • Dehghan M, Hashemi B and Ghatee M 2007 Solution of the fully fuzzy linear system using iterative techniques. Chaos Solitons Fractals, 34: 316–336

    Article  MATH  MathSciNet  Google Scholar 

  • Friedman M, Ming M and Kandel A 1998 Fuzzy linear systems. Fuzzy Sets and Systems, 96: 201–209

    Article  MATH  MathSciNet  Google Scholar 

  • Gong Z, Guo X and Liu K 2014 Approximate solution of dual fuzzy matrix equations. Information Sci., 266: 112–133

    Article  MathSciNet  Google Scholar 

  • Hadjidimos A 1978 Accelerated overrelaxation method. Mathematics of Computation, 32: 149–157

    Article  MATH  MathSciNet  Google Scholar 

  • Hashemi M S, Mirnia M K and Shahmorad S 2008 Solving fuzzy linear systems by using the Schur complement when coefficient matrix is an M-matrix. Iranian J. Fuzzy Systems, 5: 15–29

    MATH  MathSciNet  Google Scholar 

  • Ma M, Friedman M and Kandel A 2000 Duality in fuzzy systems. Fuzzy Sets and Systems 109: 55–58

  • Meurant G 1999 Computer solution of large linear systems, North-Holland, Amsterdam

  • Mosleh M, Otadi M and Khanmirzaie A 2009 Decomposition method for solving fully fuzzy linear systems. Iranian J. Optimization, 1: 188–198

    Google Scholar 

  • Nasseri S H, Sohrabi M and Ardil E 2008 Solving fully fuzzy linear systems by use of a certain decomposition of the coefficient matrix. Int. J. Computational and Mathematical Sci., 2: 140–142

    MathSciNet  Google Scholar 

  • Nasseri S H and Sohrabi M 2010 Gram-Schmidt approach for linear system of equations with fuzzy parameters. The J. Mathematics and Comput. Sci., 1: 80–89

    Google Scholar 

  • Nasseri S H and Zahmatkesh F 2010 Huang method for solving fully fuzzy linear system of equations. The J. Mathematics and Comput. Sci., 1: 1–5

    Google Scholar 

  • Salkuyeh D K 2011 On the solution of the fuzzy Sylvester matrix equation. Soft Computing, 15: 953–961

    Article  MATH  Google Scholar 

  • Senthilkumar P and Rajendran G 2011 New approach to solve symmetric fully fuzzy linear systems. Sādhanā, 36: 933–940

    MathSciNet  Google Scholar 

  • Wang K and Zheng B 2007 Block iterative methods for fuzzy linear systems. J. Appl. Mathematics and Computing, 25: 119–136

    Article  MATH  Google Scholar 

Download references

Acknowledgements

The author would like to thank the anonymous referee for the valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran

    DAVOD KHOJASTEH SALKUYEH

Authors
  1. DAVOD KHOJASTEH SALKUYEH
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to DAVOD KHOJASTEH SALKUYEH.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

SALKUYEH, D.K. On the solution of a class of fuzzy system of linear equations. Sadhana 40, 369–377 (2015). https://doi.org/10.1007/s12046-014-0313-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12046-014-0313-y

Keywords

Search

Navigation