Intuitionistic Fuzzy Linear Systems

  • Hafida Atti
  • Bouchra Ben AmmaEmail author
  • Said Melliani
  • S. Chadli
Part of the Studies in Computational Intelligence book series (SCI, volume 862)


In this work we present a method for solving intuitionistic fuzzy linear systems by four crisp linear systems. Also necessary and sufficient conditions for existence of intuitionistic fuzzy solution are given. A numerical examples are illustrated the efficiency of the proposed method.


Intuitionistic fuzzy linear systems Intuitionistic fuzzy numbers Nonnegative matrix 


  1. 1.
    Allahviranloo, T.: Numerical method for fuzzy system of linear equations. Appl Math Comput. 153, 493–502 (2004)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Asady, B., Abbasbandy, S., Alavi, M.: Fuzzy general linear systems. Appl. Math. Comput. 169(1), 34–40 (2005)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Abbasbandy, S., Alavi, M.: A method for solving fuzzy linear systems. Iran. J. Fuzzy Syst. 2(2), 37–43 (2005)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Abbasbandy, S., Allahviranloo, T., Ezzati, R.: A method for solving fuzzy linear general systems. J. Fuzzy Math. 15(4), 881–889 (2007)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Atanassov, K.T.: Intuitionistic fuzzy sets. VII ITKRs session, Sofia (deposited in Central Science and Technical Library of the Bulgarian Academy of Sciences (1697/84) (1983)Google Scholar
  6. 6.
    Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)CrossRefGoogle Scholar
  7. 7.
    Friedman, M., Min, Ma., Kandel, A.: Fuzzy linear systems, Fuzzy Sets Syst. 96, 201–209 (1998)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ezzati, R.: Solving linear systems. Soft Comput. 15(1), 193–197 (2011)CrossRefGoogle Scholar
  9. 9.
    Keyanpour1, M., Akbarian, T.: Solving intuitionistic fuzzy nonlinear equations. J. Fuzzy Set Valued Anal. 1–6 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Najariyan1, M., Mazandarani, M., John, R.: Type-2 fuzzy linear systems. Granul. Comput. 2:175–186 (2017)CrossRefGoogle Scholar
  11. 11.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Hafida Atti
    • 1
  • Bouchra Ben Amma
    • 1
    Email author
  • Said Melliani
    • 1
  • S. Chadli
    • 1
  1. 1.Laboratory of Applied Mathematics and Scientific Computing, Faculty of Sciences and TechnologiesSultan Moulay Slimane UniversityBeni MellalMorocco

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