Advertisement

Fuzzy Solution of Interval Nonlinear Equations

  • Ludmila Dymova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6068)

Abstract

In [10,12], a new concept of interval and fuzzy linear equations solving based on the generalized procedure of interval extension called “interval extended zero” method has been proposed. The central for this approach is the treatment of “interval zero” as an interval centered around 0. It is shown that such proposition is not of heuristic nature, but is a direct consequence of interval subtraction operation. It is shown that the resulting solution of interval linear equation based on the proposed method may be naturally treated as a fuzzy number. In the current report, the method is extended to the case of nonlinear interval equations. It is shown that opposite to the known methods, a new approach makes it possible to get both the positive and negative solutions of quadratic interval equation.

Keywords

interval nonlinear equation fuzzy solution interval zero 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abbasbandy, S., Asady, B.: Newton’s method for solving fuzzy nonlinear equations. Applied Mathematics and Computation 159, 349–356 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Abbasbandy, S.: Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method. Applied Mathematics and Computation 170, 648–656 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Buckley, J.J., Qu, Y.: Solving linear and quadratic fuzzy equations. Fuzzy Sets and Systems 38, 43–59 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Buckley, J.J., Eslami, E.: Neural net solutions to fuzzy problems: The quadratic equation. Fuzzy Sets and Systems 86, 289–298 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Buckley, J.J., Eslami, E., Hayashi, Y.: Solving fuzzy equations using neural nets. Fuzzy Sets and Systems 86, 271–278 (1997)zbMATHCrossRefGoogle Scholar
  6. 6.
    Cleary, J.C.: Logical Arithmetic. Future Computing Systems 2, 125–149 (1987)Google Scholar
  7. 7.
    Dymova, L., Gonera, M., Sevastianov, P., Wyrzykowski, R.: New method for interval extension of Leontiefs input-output model with use of parallel programming. In: Proc. Int. Conf. on Fuzzy Sets and Soft Computing in Economics and Finance, St. Petersburg, pp. 549–556 (2004)Google Scholar
  8. 8.
    Jaulin, L., Kieffir, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, London (2001)zbMATHGoogle Scholar
  9. 9.
    Moore, R.E.: Interval analysis. Prentice-Hall, Englewood Cliffs (1966)zbMATHGoogle Scholar
  10. 10.
    Sevastjanov, P., Dymova, L.: Fuzzy solution of interval linear equations. In: Proc. of 7th Int. Conf. Paralel Processing and Applied Mathematics, Gdansk, pp. 1392–1399 (2007)Google Scholar
  11. 11.
    Sewastjanow, P., Dymowa, L.: On the Fuzzy Internal Rate of Return. In: Kahraman, C. (ed.) Fuzzy Engineering Economics with Applications, pp. 105–128. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Sevastjanov, P., Dymova, L.: A new method for solving interval and fuzzy equations: linear case. Information Sciences 17, 925–937 (2009)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ludmila Dymova
    • 1
  1. 1.Institute of Comp. & Information Sci.Czestochowa University of TechnologyCzestochowaPoland

Personalised recommendations