Skip to main content
Springer Nature Link
Log in

An Evolutionary Approach for Approximating the Solutions of Systems of Linear Fuzzy Equations

  • Conference paper
Adaptive and Natural Computing Algorithms (ICANNGA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4431))

Included in the following conference series:

  • 2295 Accesses

Abstract

In this paper systems of linear equations Ax = b, where both A and b contain uncertain factors in terms of fuzziness are investigated. The classical solutions being vectors of fuzzy numbers are considered. The complex problem of finding the exact classical solutions is replaced by a corresponding optimization task with the cost function based on the Hausdorff metric. This cost function is next minimized with use of genetic algorithms. A number of numerical experiments are provided in order to verify the given approach. The results and some conclusions are also included.

This work is supported by the grant no. N519 020 31/3900 from the Polish Ministry of Science and Higher Education (Fund for Scientific Research in 2006-2007).

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alefeld, G., Herzberger, J.: Introduction to Interval Computation. Academic Press, London (1983)

    Google Scholar 

  2. Bertoluzza, C., Gil, M.A., Ralescu, D.A. (eds.): Statistical Modeling, Analysis and Management of Fuzzy Data. Physica-Verlag, New York (2002)

    MATH  Google Scholar 

  3. Buckley, J.J., Qu, Y.: Solving Systems of Linear Fuzzy Equations. Fuzzy Sets and Systems 43, 33–43 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Friedman, M., Ma, M., Kandel, A.: Fuzzy Linear Systems. Fuzzy Sets and Systems, 201–209 (1998)

    Google Scholar 

  5. Fuller, R., Giove, S.: A neuro-fuzzy approach to FMOLP problems. In: Proceedings of CIFT’94, pp. 97–101 (1994)

    Google Scholar 

  6. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Kluwer Academic Publishers, Boston (1989)

    MATH  Google Scholar 

  7. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1996)

    MATH  Google Scholar 

  8. Neumaier, A.: Interval Methods for Systems of Linear Equations. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  9. Wang, X., Zhong, Z., Ha, M.: Iteration Algorithms for Solving a System of Fuzzy Linear Equations. Fuzzy Sets and Systems 119, 121–128 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  10. Viet, N.H., Kleiber, M.: AI Methods in Solving Systems of Interval Linear Equations. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 150–159. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  12. Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning (I-III). Information Science 8, 199–250, 301–357; 9, 43–80 (1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland

    Nguyen Hoang Viet & Michał Kleiber

Authors
  1. Nguyen Hoang Viet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michał Kleiber
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Bartlomiej Beliczynski Andrzej Dzielinski Marcin Iwanowski Bernardete Ribeiro

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Viet, N.H., Kleiber, M. (2007). An Evolutionary Approach for Approximating the Solutions of Systems of Linear Fuzzy Equations. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2007. Lecture Notes in Computer Science, vol 4431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71618-1_63

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71618-1_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71589-4

  • Online ISBN: 978-3-540-71618-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics