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A New Method for Solving Nonlinear Interval and Fuzzy Equations

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Parallel Processing and Applied Mathematics (PPAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10778))

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Abstract

In this paper, a new concept called “interval extended zero” method which recently was used for solving interval and fuzzy linear equations is adapted to the solution of nonlinear interval and fuzzy equations. The known “test” example of quadratic fuzzy equation is used to perform the advantages of a new method. In this example, only the positive solution can be obtained using known methods, whereas generally a negative fuzzy root can exits too. The sources of this problem are clarified. 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 fuzzy equation. Generally, the developed method can be applied for solving a wide range of nonlinear interval and fuzzy equations if some initial constraints on the bounds of solution are known.

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Acknowledgement

The research has been supported by the grant financed by National Science Centre (Poland) on the basis of decision number DEC-2013/11/B/ST6/00960.

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Authors and Affiliations

  1. Institute of Computer and Information Sciences, Czestochowa University of Technology, Dabrowskiego 73, 42-201, Czestochowa, Poland

    Ludmila Dymova & Pavel Sevastjanov

Authors
  1. Ludmila Dymova
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  2. Pavel Sevastjanov
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Corresponding author

Correspondence to Pavel Sevastjanov .

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Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Dymova, L., Sevastjanov, P. (2018). A New Method for Solving Nonlinear Interval and Fuzzy Equations. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10778. Springer, Cham. https://doi.org/10.1007/978-3-319-78054-2_35

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  • DOI: https://doi.org/10.1007/978-3-319-78054-2_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78053-5

  • Online ISBN: 978-3-319-78054-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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