Skip to main content
SpringerLink
Log in

A New Method for Solving Square Fuzzy Linear Systems

  • Conference paper
  • First Online:
Book cover Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 642))

Abstract

In this paper the exact algebraic characterization (w.r.t. a generalized \(\{1\}\)-inverse) of any solution of a general \(n\times n\) fuzzy linear system, whose coefficient matrix is a real matrix, singular or non-singular, is presented. A new method for obtaining exact solutions of a general \(n\times n\) fuzzy linear system is introduced. If the associated matrix is singular, infinitely many solutions are obtained, what is illustrated in given examples.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abbasbandy, S., Alavi, M.: A method for solving fuzzy linear systems. Iran. J. Fuzzy Syst. 2, 37–43 (2005)

    MathSciNet  MATH  Google Scholar 

  2. Abbasbandy, S., Otadi, M., Mosleh, M.: Minimal solution of general dual fuzzy linear systems. Chaos, Solitions Fractals 37, 1113–1124 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Allahviranlo, T., Kermani, M.A.: Solution of a fuzzy system of linear equation. Appl. Math. Comput. 175, 519–531 (2006)

    MathSciNet  Google Scholar 

  4. Allahviranlo, T., Ghanbari, M., Hosseinzadeh, A.A., Haghi, E., Nuraei, R.: A note on Fuzzy linear systems. Fuzzy Sets Syst. 177, 87–92 (2011)

    Article  MATH  Google Scholar 

  5. Allahviranlo, T., Ghanbari, M.: On the algebraic solution of fuzzy linear systems based on interval theory. Appl. Math. Model. 36, 5360–5379 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Asady, B., Abbasbandy, S., Alavi, M.: Fuzzy general linear systems. Appl. Math. Comput. 169, 34–40 (2005)

    MathSciNet  MATH  Google Scholar 

  7. Ben-Israel, A., Greville, T.N.E.: Generalized Inverses. Theory and Applications, Springer, New York (2003)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Cambell, S.L., Meyer, C.D.: Inverses of Linear Transformations. SIAM, Philadelphia (2009)

    Book  Google Scholar 

  10. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  11. Dubois, D., Prade, H.: Fundamentals of Fuzzy Sets. The Handbooks of Fuzzy Sets Series, vol. 1. Kluwer Academic Publishers (2000)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Jovović, I., Malešević, B.: A note of solutions of the matrix equations AXB=C. Ser. A: Appl. Math. Inform. Mech. 6, pp. 45–55 (2014). Scientific Publications of the State University of Novi Pazar

    Google Scholar 

  15. Lodwick, W.A., Dubois, D.: Interval linear systems as a necessary step in fuzzy linear systems. Fuzzy Sets Syst. 281, 227–251 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Miler Jerković, V., Malešević, B.: Block representation of generalized inverses of matrices. In: Proceedings of the Fifth Symposium on Mathematics and Applications, Organized by Faculty of Mathematics, University of Belgrade and Serbian Academy of Sciences and Arts, vol. 1, pp. 176–185 (2014)

    Google Scholar 

  17. Nikuie, M.: Singular fuzzy linear systems. App. Math. Comp. Intel. 2, 157–168 (2013)

    Google Scholar 

  18. Otadi, M., Mosleh, M.: Minimal solution of fuzzy linear systems. Iran. J. Fuzzy Syst. 12, 89–99 (2015)

    MathSciNet  MATH  Google Scholar 

  19. Penrose, R.: A generalized inverses for matrices. Math. Proc. Cambridge Philos. Soc. 51, 406–413 (1955)

    Article  MATH  Google Scholar 

  20. Perić, V.: Generalizirana reciproka matrice (in Serbo-Croatian). Matematika (Zagreb) 11, 40–57 (1982)

    MathSciNet  Google Scholar 

  21. Rohde, C.A.: Contribution of the theory, computation and application of generalized inverses (PhD disserattion), University of North Carolina at Releigh (1964)

    Google Scholar 

  22. Zimmermann, H.J.: Fuzzy Set Theory and Its Applications. Kluwer Academic Publishers (1992)

    Google Scholar 

Download references

Acknowledgements

The work presented in this paper was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia trough the projects: ON 175016 (first author), ON 174009 (second author) and ON 174032, III 44006 (third author).

Author information

Authors and Affiliations

  1. School of Electrical Engineering, University of Belgrade, Belgrade, Serbia

    Vera Miler Jerković & Branko Malešević

  2. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Biljana Mihailović

Authors
  1. Vera Miler Jerković
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Biljana Mihailović
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Branko Malešević
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Biljana Mihailović .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Department of Telecommunications and Information Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K. T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Jerković, V.M., Mihailović, B., Malešević, B. (2018). A New Method for Solving Square Fuzzy Linear Systems. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66824-6_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66823-9

  • Online ISBN: 978-3-319-66824-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation