Skip to main content
SpringerLink
Log in

Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers \(( {m,\alpha ,\beta }) \)

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

In this paper, we discuss some new numerical methods to solve a fully fuzzy linear system (FFLS) with triangular fuzzy numbers of the form \( ( {m,\alpha ,\beta }) \). Almost every existing method that intends to solve a FFLS confines the coefficient matrix and the solutions to be non-negative fuzzy numbers. The main intent of the proposed methods is to remove these restrictions and widen the scope of fuzzy linear systems in scientific applications. The methods are illustrated with the help of numerical examples and are conceptually easy to understand and apply in real life situations.

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

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T (2004a) Numerical methods for fuzzy system of linear equations. Appl Math Comput 155:493–502

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T (2004b) Successive overrelaxation iterative method for fuzzy system of linear equations. Appl Math Comput 162:189–196

    Article  MathSciNet  Google Scholar 

  • Allahviranloo T (2005) The adomian decomposition method for fuzzy system of linear equations. Appl Math Comput 163:553–563

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T, Ghanbari M (2010) Solving fuzzy linear system by homotopy perturbation method. Int J Comput Cogn 8:24–30

    Google Scholar 

  • Allahviranloo T, Mikarilvand N, Kiani NA, Shabestari RH (2008) Signed decomposition of fully fuzzy linear systems. Appl Appl Math 3:77–88

    MathSciNet  MATH  Google Scholar 

  • Buckley JJ, Qu Y (1991) Solving systems of linear fuzzy equations. Fuzzy Sets Syst 43:33–43

    Article  MathSciNet  MATH  Google Scholar 

  • Dehghan M, Hashemi B (2006a) Solution of the fully fuzzy linear system using the decomposition procedure. Appl Math Comput 182:1568–1580

    Article  MathSciNet  MATH  Google Scholar 

  • Dehghan M, Hashemi B (2006b) Iterative solution of fuzzy linear systems. Appl Math Comput 175:645–674

    Article  MathSciNet  MATH  Google Scholar 

  • Dehghan M, Hashemi B, Ghatee M (2006) Computational methods for solving fully fuzzy linear systems. Appl Math Comput 179:328–343

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Friedman M, Ming M, Kandel A (1998) Fuzzy linear systems. Fuzzy Sets Syst 96:201–209

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman M, Ming M, Kandel A (2000) Duality in fuzzy linear systems. Fuzzy Sets Syst 109:55–58

    Article  MATH  Google Scholar 

  • Gao J (2009) A unified iterative scheme for solving fully fuzzy linear system. Global Congr Intell Syst 1:431–435

    Google Scholar 

  • Kaufmann A, Gupta MM (1985) Introduction to fuzzy arithmetic: theory and applications. Van Nostrand Reinhold, New York

    MATH  Google Scholar 

  • Kumar A, Neetu Bansal A (2010) A new method to solve fully fuzzy linear system with trapezoidal fuzzy numbers. Can J Sci Eng Math 1:45–56

    Google Scholar 

  • Liu HK (2010) On the solution of fully fuzzy linear systems. World Acad Sci Eng Technol Math Comput Sci 6:29–33

    Google Scholar 

  • Mosleh M, Otadi M (2010) Regular splitting method for approximating linear system of fuzzy equations. Int J Contemp Math Sci 5:263–274

    MathSciNet  MATH  Google Scholar 

  • Mosleh M, Abbasbandy S, Otadi M (2007) Full fuzzy linear systems of the form Ax + b = Cx + d. In: First joint congress on fuzzy and intelligent systems, Ferdowsi University of Mashhad, Iran. http://www.docstoc.com/docs/6566376/Full-fuzzy-linear-systems-of-the-form-Axb=Cxd

  • Mosleh M, Otadi M, Khanmirzaie A (2009) Decomposition method for solving fully fuzzy linear systems. Iran J Optim 1:188–198

    Google Scholar 

  • Muzzioli S, Reynaerts H (2006) Fuzzy linear systems of the form \( {\text{A}}_{1} {\text{x}} + {\text{b}}_{1} = {\text{A}}_{2} {\text{x}} + {\text{b}}_{2} . \)Fuzzy Sets Syst 157:939–951

  • Nasseri SH, Sohrabi M (2010) Gram–Schmidt approach for linear system of equations with fuzzy parameters. J Math Comput Sci 1:80–89

    Google Scholar 

  • Nasseri SH, Zahmatkesh F (2010) Huang method for solving fully fuzzy linear system of equations. J Math Comput Sci 1:1–5

    Google Scholar 

  • Nasseri SH, Sohrabi M, Ardil E (2008) Solving fully fuzzy linear systems by use of a certain decomposition of the coefficient matrix. Int J Comput Math Sci 2:140142

    MathSciNet  Google Scholar 

  • Nasseri SH, Matinfar M, Kheiri Z (2009) Greville’s method for the fully fuzzy linear system of equations. Adv Fuzzy Sets Syst 4:301–311

    MathSciNet  MATH  Google Scholar 

  • Sun X, Guo S (2009) Solution to general fuzzy linear system and its necessary and sufficient condition. Fuzzy Inf Eng 3:317–327

    Article  MathSciNet  Google Scholar 

  • Yin JF, Wang K (2009) Splitting iterative methods for fuzzy system of linear equations. Comput Math Model 20:326–335

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank to the “Editor-in-Chief” and the anonymous referees for various suggestions which have led to an improvement in both the quality and clarity of the paper. I, Dr. Amit Kumar, want to acknowledge the innocent inner blessings of Mehar. I believe that Mehar is an angel for me and without Mehar’s blessings it was not possible to think of the idea proposed in this paper. Mehar is a lovely daughter of Parmpreet Kaur (Research Scholar under my supervision).

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Applications, Thapar University, Patiala, 147004, India

    Neetu Babbar & Amit Kumar

  2. Computer Science and Engineering Department, Thapar University, Patiala, 147004, India

    Abhinav Bansal

Authors
  1. Neetu Babbar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abhinav Bansal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abhinav Bansal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Babbar, N., Kumar, A. & Bansal, A. Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers \(( {m,\alpha ,\beta }) \) . Soft Comput 17, 691–702 (2013). https://doi.org/10.1007/s00500-012-0941-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-012-0941-2

Keywords

Search

Navigation