[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Resolution of a system of fuzzy polynomial equations using eigenvalue method

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, a system of fuzzy polynomial equations is studied. Two solution types are defined for this system, called solution and \(r\)-cut solution. Then sufficient and necessary conditions are proposed for existence of solution and \(r\)-cut solution of the system, respectively. The solution set of the system is also determined. Moreover, a new algorithm is designed to find all the solutions and all the \(r\)-cut solutions of the system based on the eigenvalue method. Finally, some examples are given to illustrate the concepts and the algorithm.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • Abbasi Molai A, Basiri A, Rahmany S (2013) Resolution of a system of fuzzy polynomial equations using the Gröbner basis. Inf Sci 220:541–558

    Article  MATH  MathSciNet  Google Scholar 

  • Basiri A, Faugère J-C (2003) Changing the ordering of Gröbner bases with LLL: case of two variables. In: Proceedings of ISSAC, ACM Press, New York, pp 23–29

  • Buckley JJ, Qu Y (1991) Solving fuzzy equations : a new solution concept. Fuzzy Sets Syst 39:291–301

    Article  MATH  MathSciNet  Google Scholar 

  • Cox D, Little J, O’Shea D (2004) Using algebraic geometry, 2nd edn. Springer, New York

    Google Scholar 

  • Cox D, Little J, O’Shea D (2007) Ideal, varieties, and algorithms: an introduction to computational algebra geometry and commutative algebra, 3rd edn. Springer-Varlag, New York

    Book  Google Scholar 

  • Dubois D, Prade H (1980) Systems of linear fuzzy constraints. Fuzzy Sets Syst 3:37–48

    Article  MATH  MathSciNet  Google Scholar 

  • Ezzati R (2011) Solving fuzzy linear systems. Soft Comput 15:193–197

    Article  MATH  Google Scholar 

  • Faugère J-C (June 1999) A new efficient algorithm for computing Gröbner bases (\({F}_{4}\)). J Pure Appl Algebr 139(1–3):61–88

  • Gvozdik A (1985) Solution of fuzzy linear equations. UDC 518(9):60–67

    MathSciNet  Google Scholar 

  • Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic. Theory and applications. Prentice Hall PTR, New Jersey

    MATH  Google Scholar 

  • Otadi M, Mosleh M (2011) Simulation and evaluation of dual fully fuzzy linear systems by fuzzy neural networks. Appl Math Model 35:5026–5039

    Article  MATH  MathSciNet  Google Scholar 

  • Rao S, Chen L (1998) Numerical solution of fuzzy linear equations in engineering analysis. Int J Numer Methods Eng 42:829–846

    Article  MATH  MathSciNet  Google Scholar 

  • Tian Z, Hu L, Greenhalgh D (2010) Perturbation analysis of fuzzy linear systems. Inf Sci 180:4706–4713

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh L (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8:199–249

    Article  MATH  MathSciNet  Google Scholar 

  • Zhao R, Govind R (1991) Solutions of algebraic equations involving generalized fuzzy numbers. Inf Sci 56:199–243

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran

    Hamed Farahani, Sajjad Rahmany, Abdolali Basiri & Ali Abbasi Molai

Authors
  1. Hamed Farahani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sajjad Rahmany
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdolali Basiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ali Abbasi Molai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Abbasi Molai.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farahani, H., Rahmany, S., Basiri, A. et al. Resolution of a system of fuzzy polynomial equations using eigenvalue method. Soft Comput 19, 283–291 (2015). https://doi.org/10.1007/s00500-014-1249-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-014-1249-1

Keywords

Search

Navigation