Skip to main content
Log in

Solution of dual fuzzy polynomial equations by modified Adomian decomposition method

  • Original Article
  • Published:
Fuzzy Information and Engineering

Abstract

In this paper, we present some efficient numerical algorithm for solving dual fuzzy polynomial equations based on Newton’s method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of the algorithms.

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.

Similar content being viewed by others

References

  1. Adomian G (1989) Nonlinear stochastic system and approximations to physics. klower academic publisher, Dordrecht

    Book  Google Scholar 

  2. Adomian G, Rach R (1985) On the solution of algebraic equations by the decomposition method. Math. Anal. Appl. 105: 141–166

    Article  MATH  Google Scholar 

  3. Abbaoui K, Cherruault Y (1994) Convergence of Adomian’s method applied to nonlinear equations. Math. Comput. Model 20(9): 69–73

    Article  MathSciNet  MATH  Google Scholar 

  4. Abbasbandy S (2003) Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method. Appl. Math. Comput. 145: 887–893

    Article  MathSciNet  MATH  Google Scholar 

  5. Abbasbandy S (2005) Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method. Appl. Math. Comput. 170: 648–656

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheng S S L, Zadeh L A (1972) On fuzzy mapping and control. IEEE Transactions on Systems. Man and Cybernetics 2: 30–34

    Google Scholar 

  7. Dubois D, Prade H (1978) Operations on fuzzy numbers. Journal of Systems Science 9: 613–626

    Article  MathSciNet  MATH  Google Scholar 

  8. Nahmias S (1978) Fuzzy variables. Fuzzy Sets and Systems 12: 97–111

    Article  MathSciNet  Google Scholar 

  9. Cho Y J, Huang N J, Kang JM (2000) Nonlinear equations for fuzzy mapping in probabilistic normed spaces. Fuzzy Sets and Systems 110: 115–122

    Article  MathSciNet  MATH  Google Scholar 

  10. Fang J (2002) On nonlinear equations for fuzzy mapping in probabilistic normed spaces. Fuzzy Sets and Systems 131: 357–364

    Article  MathSciNet  MATH  Google Scholar 

  11. Ma J, Feng G (2003) An approach to H control of fuzzy dynamic systems. Fuzzy Sets and Systems 137: 367–386

    Article  MathSciNet  MATH  Google Scholar 

  12. Abbasbandy S, Asady B (2004) Newton’s method for solving fuzzy nonlinear equations. Appl. Math. Comput. 159: 349–356

    Article  MathSciNet  MATH  Google Scholar 

  13. Abbasbandy S, Jafarian A (2006) Steepest descent method for solving fuzzy nonlinear equations. Appl. Math. Comput. 175: 823–833

    Article  MathSciNet  MATH  Google Scholar 

  14. Nieto J J, Rodriguez-Lopez R (2005) Existence of extremal solutions for quadratic fuzzy equations. Fixed Point Theory and Applications 3: 321–342

    MathSciNet  Google Scholar 

  15. Abbasbandy S, Ezzati R (2006) Newton’s method for solving a system of fuzzy nonlinear equations. Appl. Math. Comput. 175: 1189–1199

    Article  MathSciNet  MATH  Google Scholar 

  16. Otadi M, Mosleh M (2011) Solution of fuzzy polynomial equations by modified Adomian decomposition method. Soft Computing 15: 187–192

    Article  MATH  Google Scholar 

  17. Allahviranloo T, Otadi M, Mosleh M (2007) Iterative method for fuzzy equations. Soft Computing 12: 935–939

    Article  Google Scholar 

  18. Tavassoli Kajani M, Asady B, Hadi Vencheh A (2005) An iterative method for solving dual fuzzy nonlinear equations. Appl. Math. Comput. 167: 316–323

    Article  MathSciNet  MATH  Google Scholar 

  19. Abbasbandy S, Otadi M (2006) Numerical solution of fuzzy polynomials by fuzzy neural network. Appl. Math. Comput. 181: 1084–1089

    Article  MathSciNet  MATH  Google Scholar 

  20. Abbasbandy S, Otadi M, Mosleh M (2008) Numerical solution of a system of fuzzy polynomials by fuzzy neural network. Inform. Sci. 178: 1948–1960

    Article  MATH  Google Scholar 

  21. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and application. Academic Press, New York

    Google Scholar 

  22. Zadeh L A (1965) Fuzzy sets. Inform. Control 8: 338–353

    Article  MathSciNet  MATH  Google Scholar 

  23. Zimmermann H J (1991) Fuzzy sets theory and its application. Kluwer Academic Press, Dordrecht

    Book  Google Scholar 

  24. Goetschel R, Voxman W (1986) Elementary calculus. Fuzzy Sets and Systems 18: 31–43

    Article  MathSciNet  MATH  Google Scholar 

  25. Abbaoui K, Cherruault Y, Seng V (1995) Practical formulae for the calculus of multi-variable Adomian polynomials. Comput. Model 22: 89–93

    Article  MathSciNet  MATH  Google Scholar 

  26. Buckley J J, Qu Y (1991) Solving fuzzy equations: a new solutions concept. Fuzzy Sets and Systems 39: 291–301

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maryam Mosleh.

About this article

Cite this article

Mosleh, M. Solution of dual fuzzy polynomial equations by modified Adomian decomposition method. Fuzzy Inf. Eng. 5, 45–56 (2013). https://doi.org/10.1007/s12543-013-0132-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12543-013-0132-6

Keywords

Navigation