Skip to main content
Log in

M-Preconditioner for Solving Fuzzy Linear Systems

  • Numerical Methods
  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

An M-preconditioner is provided for solving fuzzy linear systems whose coefficient matrices are crisp M-matrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the M-preconditioned conjugate gradient (MPCG) method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

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

Access this article

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

  1. S. Abbasbandy, R. Ezzati, and A. Jafarian, “LU decomposition method for solving fuzzy system of linear equations,” Appl. Math. Comput., 172, 633–643 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Abbasbandy and A. Jafarian, “Steepest descent method for system of fuzzy linear equations,” Appl. Math. Comput., 175, 823–833 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Abbasbandy, A. Jafarian, and R. Ezzati, “Conjugate gradient method for fuzzy symmetric positive definite system of linear equations,” Appl. Math. Comput., 171, 1184–1191 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Allahviranloo, “Numerical methods for fuzzy system of linear equations,” Appl. Math. Comput., 155, 493–502 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  5. T. Allahviranloo, “Successive over relaxation iterative method for fuzzy system of linear equations,” Appl. Math. Comput., 162, 189–196 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Allahviranloo, “The Adomian decomposition method for fuzzy system of linear equations,” Appl. Math. Comput., 163, 553–563 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia (1994).

    Book  MATH  Google Scholar 

  8. M. Dehghan and B. Hashemi, “Iterative solution of fuzzy linear systems,” Appl. Math. Comput., 175, 645–674 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Ezzati, “Solving fuzzy linear systems,” Soft Comput., 15, 193–197 (2011).

    Article  MATH  Google Scholar 

  10. M. A. Fariborzi Araghi and A. Fallahzadeh, “Inherited LU factorization for solving fuzzy system of linear equations,” Soft Comput., 17, 159–163 (2013).

    Article  MATH  Google Scholar 

  11. M. Friedman, M. Ming, and A. Kandel, “Fuzzy linear systems,” Fuzzy Sets Syst., 96, 201–209 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  12. M. S. Hashemi, M. K. Mirnia, and S. Shahmorad, “Solving fuzzy linear systems by using the Schur complement when coefficient matrix is an M-matrix,” Iran. J. Fuzzy Syst., 5, 15–29 (2008).

    MathSciNet  MATH  Google Scholar 

  13. X.-Q. Jin, “M-preconditioner for M-matrices,” Appl. Math. Comput., 172, 701–707 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Li, W. Li, and X. Kong, “A new algorithm model for solving fuzzy linear systems,” Southeast Asian Bull. Math., 34, 121–132 (2010).

    MathSciNet  Google Scholar 

  15. S.-X. Miao, B. Zheng, and K. Wang, “Block SOR methods for fuzzy linear systems,” J. Appl. Math. Comput., 26, 201–218 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  16. S. H. Nasseri, M. Matinfar, and M. Sohrabi, “QR-decomposition method for solving fuzzy system of linear equations,” Int. J. Math. Comput., 4, 129–136 (2009).

    MathSciNet  Google Scholar 

  17. D. K. Salkuyeh, “On the solution of the fuzzy Sylvester matrix equation,” Soft Comput., 15, 953–961 (2011).

    Article  MATH  Google Scholar 

  18. K. Wang and Y. Wu, “Uzawa-SOR method for fuzzy linear system,” Int. J. Inform. Comput. Sci., 1, 36–39 (2012).

    Google Scholar 

  19. K. Wang and B. Zheng, “Symmetric successive overrelaxation methods for fuzzy linear systems,” Appl. Math. Comput., 175, 891–901 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  20. K. Wang and B. Zheng, “Block iterative methods for fuzzy linear systems,” J. Appl. Math. Comput., 25, 119–136 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  21. J.-F. Yin and K. Wang, “Splitting iterative methods for fuzzy system of linear equations,” Comput. Math. Model., 20, 326–335 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  22. Y. Zhu, J. Joutsensalo, and T. H¨am¨al¨ainen, “Solutions to fuzzy linear systems,” Information, 13, 23–30 (2010).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ke Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, S., Wang, S. & Wang, K. M-Preconditioner for Solving Fuzzy Linear Systems. Comput Math Model 26, 577–584 (2015). https://doi.org/10.1007/s10598-015-9294-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10598-015-9294-x

Keywords

Navigation