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On the properties of fuzzy differential equations under cross operations

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Abstract

This manuscript proposes a new framework for dealing with nonlinear fuzzy differential equations when the nonlinearity is given in terms of fuzzy arithmetic operations of product and division, here called \(\psi \)-cross operations. To this end, the fuzzy environment considered is given by finite-dimensional Banach spaces of fuzzy numbers, and the fuzzy functions involved are related to a calculus theory given in terms of the \(\psi \)-differentiability. The notion of power hedges with respect to the \(\psi \)-cross operations is introduced, and several algebraic properties are presented, such as the fuzzy product and division rules. Lastly, a study on polynomial fuzzy differential equations with an application to the fuzzy Abel equation is provided.

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Acknowledgements

The author would like to acknowledge the reviewers for the contribution to the content of this paper through the suggestions and questions raised in the revision process of the manuscript.

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  1. Department of Applied Mathematics, University of Campinas, Rua Sergio Buarque de Holanda, 651, Campinas, São Paulo, 13083-856, Brazil

    Beatriz Laiate

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  1. Beatriz Laiate
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Laiate, B. On the properties of fuzzy differential equations under cross operations. Comp. Appl. Math. 42, 293 (2023). https://doi.org/10.1007/s40314-023-02425-4

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