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Kaczmarz Method for Fuzzy Linear Systems

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Abstract

A Kaczmarz method is presented for solving a class of fuzzy linear systems of equations with crisp coefficient matrix and fuzzy right-hand side. The iterative scheme is established and the convergence theorem is provided. Numerical examples show that the method is effective.

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REFERENCES

  1. Friedman M., Ming M., Kandel A. "Fuzzy linear systems", Fuzzy Sets and Systems 96, 201-209 (1998).

    Article  MathSciNet  Google Scholar 

  2. Demenkov N.P., Mikrin E.A. "Identification of linear models by fuzzy basis functions", IFAC PapersOnLine 51–32, 574-579 (2018).

    Article  Google Scholar 

  3. Demenkov N.P., Mikrin E.A. "Methods of solving fuzzy systems of linear equations. Part 1. Complete Systems", Control Sciences 4, 3-14 (2019).

    Google Scholar 

  4. Demenkov N.P., Mikrin E.A. "Methods of solving fuzzy systems of linear equations. Part 2. Incomplete Systems", Control Sciences 5, 9-28 (2019).

    Google Scholar 

  5. Abbasbandy S., Ezzati R., Jafarian A. "LU decomposition method for solving fuzzy system of linear equations", Appl. Math. Comput. 172, 633-643 (2006).

    MathSciNet  MATH  Google Scholar 

  6. Abbasbandy S., Jafarian A. "Steepest descent method for system of fuzzy linear equations", Appl. Math. Comput. 175, 823-833 (2006).

    MathSciNet  MATH  Google Scholar 

  7. Abbasbandy S., Jafarian A., Ezzati R. "Conjugate gradient method for fuzzy symmetric positive definite system of linear equations", Appl. Math. Comput. 171, 1184-1191 (2005).

    MathSciNet  MATH  Google Scholar 

  8. Akram M., Allahviranloo T., Pedrycz W., Ali M. "Methods for solving LR-bipolar fuzzy linear systems", Soft Comput. 25, 85-108 (2021).

    Article  Google Scholar 

  9. Allahviranloo T. "Numerical methods for fuzzy system of linear equations", Appl. Math. Comput. 155, 493-502 (2004).

    MathSciNet  MATH  Google Scholar 

  10. Allahviranloo T. "Successive over relaxation iterative method for fuzzy system of linear equations", Appl. Math. Comput. 162, 189-196 (2005).

    MathSciNet  MATH  Google Scholar 

  11. Allahviranloo T. "The Adomian decomposition method for fuzzy system of linear equations", Appl. Math. Comput. 163, 553-563 (2005).

    MathSciNet  MATH  Google Scholar 

  12. Dehghan M., Hashemi B. "Iterative solution of fuzzy linear systems", Appl. Math. Comput. 175, 645-674 (2006).

    MathSciNet  MATH  Google Scholar 

  13. Ezzati R. "Solving fuzzy linear systems", Soft Comput. 15, 193-197 (2011).

    Article  MathSciNet  Google Scholar 

  14. Fariborzi Araghi M.A., Fallahzadeh A. "Inherited LU factorization for solving fuzzy system of linear equations", Soft Comput. 17, 159-163 (2013).

    Article  Google Scholar 

  15. Koam A.N.A., Akram M., Muhammad G., Hussain N. "LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations", Math. Probl. Eng. 2020, article 8384593 (2020).

    MathSciNet  MATH  Google Scholar 

  16. Li J., Li W., Kong X. "A new algorithm model for solving fuzzy linear systems", Southeast Asian Bull. Math. 34, 121-132 (2010).

    MathSciNet  Google Scholar 

  17. Miao S.-X., Zheng B., Wang K. "Block SOR methods for fuzzy linear systems", J. Appl. Math. Comput. 26, 201-218 (2008).

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  19. Wang K., Wu Y. "Uzawa-SOR method for fuzzy linear system", International Journal of Information and Computer Science 1, 36-39 (2012).

    Google Scholar 

  20. Wang K., Zheng B. "Symmetric successive overrelaxation methods for fuzzy linear systems", Appl. Math. Comput. 175, 891-901 (2006).

    MathSciNet  MATH  Google Scholar 

  21. Wang K., Zheng B. "Block iterative methods for fuzzy linear systems", J. Appl. Math. Comput. 25, 119-136 (2007).

    Article  MathSciNet  Google Scholar 

  22. Yin J.-F., Wang K. "Splitting iterative methods for fuzzy system of linear equations", Comput. Math. Model. 20, 326-335 (2009).

    Article  MathSciNet  Google Scholar 

  23. Zhang J.-J. "A new greedy Kaczmarz algorithm for the solution of very large linear systems", Appl. Math. Lett. 91, 207-212 (2019).

    Article  MathSciNet  Google Scholar 

  24. Bai Z.-Z. "On relaxed greedy randomized Kaczmarz methods for solving large sparse linear systems", Appl. Math. Lett. 83, 21-26 (2018).

    Article  MathSciNet  Google Scholar 

  25. Liu Y., Gu C.-Q. "Variant of greedy randomized Kaczmarz for ridge regression", Applied Numerical Mathematics 143, 223-246 (2019).

    Article  MathSciNet  Google Scholar 

  26. Niu Y.-Q., Zheng B. "A greedy block Kaczmarz algorithm for solving large-scale linear systems", Appl. Math. Lett. 104, article 106294 (2020).

    Article  MathSciNet  Google Scholar 

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Funding

Supported by Key Scientific Research Project of Colleges and Universities in Henan Province (20B110012), China.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    L. Bian & K. Wang

  2. Nanyang Vocational College of Agriculture, Nanyang, 473000, P. R. China

    S. Zhang & S. Wang

Authors
  1. L. Bian
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  2. S. Zhang
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  3. S. Wang
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  4. K. Wang
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Corresponding authors

Correspondence to L. Bian, S. Zhang, S. Wang or K. Wang.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 23–30.

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Bian, L., Zhang, S., Wang, S. et al. Kaczmarz Method for Fuzzy Linear Systems. Russ Math. 65, 20–26 (2021). https://doi.org/10.3103/S1066369X21120033

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  • DOI: https://doi.org/10.3103/S1066369X21120033

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