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Granular approximation of solutions of partial differential equations with fuzzy parameter

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Abstract

Fuzzy graph formed by a collection of fuzzy rules approximate solutions of partial differential equations with imprecise parameters in the form of fuzzy numbers. The fuzzy rules can be constructed by a judicious discretization of the variables domains, and using the extension principle on the fuzzy parameter. A detailed algorithm is developed, and numerical examples are offered using the heat, wave, and Poisson equations with triangular fuzzy numbers.

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Acknowledgements

The second author thanks CAPES, Brazilian Coordination of Higher Level Personnel Improvement for Grant 88881.119095/2016-01. The third and fourth authors thank CNPq, Brazilian National Council for Scientific and Technological Development for Grants 305862/2013-8, and 305906/2014-3, respectively. The authors are also grateful to the reviewers for the comments and suggestions that helped to improve the paper.

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Correspondence to Ana Maria Bertone.

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Bertone, A.M., Jafelice, R.M., Barros, L.C.d. et al. Granular approximation of solutions of partial differential equations with fuzzy parameter. Granul. Comput. 3, 1–7 (2018). https://doi.org/10.1007/s41066-017-0053-6

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  • DOI: https://doi.org/10.1007/s41066-017-0053-6

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