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Comparison Between Numerical Solutions of Fuzzy Initial-Value Problems via Interactive and Standard Arithmetics

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Fuzzy Techniques: Theory and Applications (IFSA/NAFIPS 2019 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1000))

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Abstract

In this work we propose a numerical solution for an n-dimensional initial-value problem where the initial conditions are given by interactive fuzzy numbers. The concept of interactivity is tied to the notion of joint possibility distribution. The numerical solutions are given by the fourth order Runge-Kutta method adapted for the arithmetic operations of interactive fuzzy numbers via sup-J extension, which is a generalization of the Zadeh’s extension principle. We compare this method with the one based on the standard arithmetic. We show that the numerical solutions via interactive arithmetic are contained in the one via standard arithmetic. We provide an application to the SI epidemiological model to illustrate the results.

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Acknowledgment

The authors would like to thank the support of CNPq under grants no. 142414/2017-4 and 306546/2017-5, FAPESP under grant no. 2016/26040-7 and CAPES - Finance Code 001.

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Authors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, Brazil

    Vinícius Francisco Wasques, Estevão Esmi & Laécio C. Barros

  2. DigiPen Institute of Technology, Redmond, Washington, USA

    Barnabás Bede

Authors
  1. Vinícius Francisco Wasques
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  2. Estevão Esmi
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  3. Laécio C. Barros
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  4. Barnabás Bede
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Corresponding author

Correspondence to Vinícius Francisco Wasques .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA

    Ralph Baker Kearfott

  2. Center for Computing Research (CIC), Instituto Politecnico Nacional, Ciudad de Mexico, Mexico

    Ildar Batyrshin

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Marek Reformat

  4. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  5. Department of Computer Science, University of Texas at El Paso , El Paso, TX, USA

    Vladik Kreinovich

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Wasques, V.F., Esmi, E., Barros, L.C., Bede, B. (2019). Comparison Between Numerical Solutions of Fuzzy Initial-Value Problems via Interactive and Standard Arithmetics. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_62

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