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Horizontal Fuzzy Numbers for Solving Quadratic Fuzzy Equation

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Advances in Soft and Hard Computing (ACS 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 889))

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Abstract

The paper presents method for solving the quadratic equation with fuzzy coefficients. Based on the horizontal fuzzy numbers the solution of fuzzy quadratic equation can be obtained. Solutions with horizontal fuzzy numbers are multidimensional. Obtained solutions are compared with results of standard fuzzy arithmetic. In examples was shown that results with standard fuzzy arithmetic are overestimated or underestimated. Method with horizontal fuzzy numbers generates the granule of information about the solution. Obtained granule gives full information about the solution. Moreover, the granule of information gives possibility to indicate the crisp quadratic equation for crisp value of the solution.

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Author information

Authors and Affiliations

  1. Department of Mathematical Methods, Maritime University of Szczecin, Waly Chrobrego 1-2, 70-500, Szczecin, Poland

    Marek Landowski

Authors
  1. Marek Landowski
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Correspondence to Marek Landowski .

Editor information

Editors and Affiliations

  1. West Pomeranian University of Technology in Szczecin, Szczecin, Poland

    Jerzy Pejaś

  2. West Pomeranian University of Technology in Szczecin , Szczecin, Poland

    Imed El Fray

  3. West Pomeranian University of Technology in Szczecin, Szczecin, Poland

    Tomasz Hyla

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

    Janusz Kacprzyk

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Landowski, M. (2019). Horizontal Fuzzy Numbers for Solving Quadratic Fuzzy Equation. In: Pejaś, J., El Fray, I., Hyla, T., Kacprzyk, J. (eds) Advances in Soft and Hard Computing. ACS 2018. Advances in Intelligent Systems and Computing, vol 889. Springer, Cham. https://doi.org/10.1007/978-3-030-03314-9_4

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