Abstract
This paper introduces the concept of first-order systems of linear fuzzy differential equations for \(\mathcal {S}\)-linearly correlated fuzzy processes. These fuzzy processes have range embedded in Banach spaces of fuzzy numbers, and the fuzzy initial value problems studied are given in terms of the Fréchet derivative of these fuzzy functions. An equivalence between the first-order systems of linear fuzzy differential equations and a family of classical first-order systems of linear differential equations is established. Also, conditions on the existence and uniqueness of the solutions are presented. Lastly, an application on the multiple mass-spring system is provided.
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Acknowledgements
This research was partially supported by CNPq under grants nos. 306546/2017-5 and 142309/2019-2, and FAPESP under grant 2016/26040-7. The authors also would like to thank David Ernesto Caro Contreras for the simulation of the results presented in this work.
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Laiate, B., Esmi, E., Pedro, F.S., Barros, L.C. (2022). Solutions of Systems of Linear Fuzzy Differential Equations for a Special Class of Fuzzy Processes. In: Rayz, J., Raskin, V., Dick, S., Kreinovich, V. (eds) Explainable AI and Other Applications of Fuzzy Techniques. NAFIPS 2021. Lecture Notes in Networks and Systems, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-030-82099-2_20
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DOI: https://doi.org/10.1007/978-3-030-82099-2_20
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