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A new approach to fuzzy initial value problem

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Abstract

In this paper, we consider a high-order linear differential equation with fuzzy initial values. We present solution as a fuzzy set of real functions such that each real function satisfies the initial value problem by some membership degree. Also we propose a method based on properties of linear transformations to find the fuzzy solution. We find out the solution determined by our method coincides with one of the solutions obtained by the extension principle method. Some examples are presented to illustrate applicability of the proposed method.

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Acknowledgments

We thank the anonymous reviewers and handling editor whose valuable comments and hints helped us to improve the quality of the paper

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Authors and Affiliations

  1. Baskent University, 06810 , Ankara, Turkey

    N. A. Gasilov & A. G. Fatullayev

  2. Computer Engineering Department, Ankara University, Ankara, Turkey

    Ş. E. Amrahov

  3. Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran

    A. Khastan

Authors
  1. N. A. Gasilov
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  2. A. G. Fatullayev
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  3. Ş. E. Amrahov
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  4. A. Khastan
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Corresponding author

Correspondence to N. A. Gasilov.

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Communicated by L. Spada.

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Gasilov, N.A., Fatullayev, A.G., Amrahov, Ş.E. et al. A new approach to fuzzy initial value problem. Soft Comput 18, 217–225 (2014). https://doi.org/10.1007/s00500-013-1081-z

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