Soft Computing

, Volume 21, Issue 24, pp 7463–7472 | Cite as

Algebraic solution of fuzzy linear system as: \(\widetilde{A} \widetilde{X}+ \widetilde{B} \widetilde{X}=\widetilde{Y}\)

Methodologies and Application
  • 103 Downloads

Abstract

In this paper, fuzzy linear system as \(\widetilde{A} \widetilde{X}+ \widetilde{B} \widetilde{X}=\widetilde{Y}\) in which \(\widetilde{A}, \widetilde{B}\) are \(n \times n\) fuzzy matrices and \(\widetilde{X}, \widetilde{Y}\) are \(n \times 1\) fuzzy vectors is studied. A new method to solve such systems based on interval linear system, interval inclusion linear system is proposed. Numerical examples are given to illustrate the ability of the proposed method.

Keywords

Fuzzy linear system Interval linear system Interval inclusion linear system LR fuzzy number 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Abbasbandy S, Ezzati R, Jafarian A (2006) LU decomposition method for solving fuzzy system of equations. Appl Math Comput 172:633–643MATHMathSciNetGoogle Scholar
  2. Abbasbandy S, Jafarian A (2006) Steepest decent method for system of fuzzy linear equations. Appl Math Comput 175:823–833MATHMathSciNetGoogle Scholar
  3. Allahviranloo T (2004) Numerical methods for fuzzy system of linear equations. Appl Math Comput 155:493–502MATHMathSciNetGoogle Scholar
  4. Allahviranloo T (2005) Successive over relaxation iterative method for fuzzy system of linear equations. Appl Math Comput 162:189–196MATHMathSciNetGoogle Scholar
  5. Allahviranloo T, Salahshour S, Khezerloo M (2011) Maximal- and minimal symmetric solutions of fully fuzzy linear systems. J Comput Appl Math 235:4652–4662CrossRefMATHMathSciNetGoogle Scholar
  6. Allahviranloo T, Lotfi FH, Kiasari MK, Khezerloo M (2012) On the fuzzy solution of LR fuzzy linear systems. Appl Math Model 37(3):1170–1176CrossRefMATHMathSciNetGoogle Scholar
  7. Allahviranloo T, Ghanbari M (2012) On the algebraic solution of fuzzy linear systems based on interval theory. Appl Math Model 36(11):5360–5379CrossRefMATHMathSciNetGoogle Scholar
  8. Babakordi F, Allahviranlooa T, Adabitabar firozja M (2016) An efficient method for solving LR fuzzy dual matrix systems. J Intell Fuzzy Syst 30:575–581CrossRefMATHGoogle Scholar
  9. Friedman M, Ming M, Kandel A (1998) Fuzzy linear systems. Fuzzy Sets Syst 96:201–209CrossRefMATHMathSciNetGoogle Scholar
  10. Kaur J, Kumar A (2013) Mehar’s method for solving fully fuzzy linear programming problems with LR fuzzy parameters. Appl Math Model 37:7142–7153CrossRefMathSciNetGoogle Scholar
  11. Kumar A, Kaur J, Singh P (2011) A new method for solving fully fuzzy linear programming problems. Appl Math Model 35:817–823CrossRefMATHMathSciNetGoogle Scholar
  12. Neetu A, Kumar A, Bansal A (2013) Solving a fully fuzzy linear system with arbitrary triangular fuzzy numbers. Soft Comput 17:691–702CrossRefMATHGoogle Scholar
  13. Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets Syst 24:319–330CrossRefMATHMathSciNetGoogle Scholar
  14. Zimmermann HJ (1996) Fuzzy set theory and its applications, 3rd edn. Kluwer Academic, NorwellCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsScience and Research Branch, Islamic Azad UniversityTehranIran
  2. 2.Department of MathematicsGonbad Kavous UniversityGonbad KavousIran

Personalised recommendations