Bidimensional Fuzzy Initial Value Problem of Autocorrelated Fuzzy Processes via Cross Product: The Prey-Predator Model

DOI

10.2991/asum.k.210827.024How to use a DOI?

Keywords

Fuzzy numbers, Strongly linearly independence, Autocorrelated fuzzy processes, Fréchet derivative, Cross product, Lotka-Volterra model

Abstract

This paper introduces the notion of a bidimensional fuzzy initial value problem for a special class of fuzzy functions. These functions, also called A-linearly correlated fuzzy processes, are a particular case of the so-called S-linearly correlated fuzzy processes, whose range is embedded in Banach spaces of fuzzy numbers. To this end, it recalls the notion of cross product and proves that this operation is the Zadeh’s extension of the linearization of the real-valued function given by the product of two real numbers. The equivalence between the bidimensional FIVP under the Fréchet derivative and a non-linear classical initial value problem is provided. Lastly, an application on the prey-predator is presented.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Beatriz Laiate
AU  - Laécio C. Barros
AU  - Francielle Santo Pedro
AU  - Estevão Esmi
PY  - 2021
DA  - 2021/08/30
TI  - Bidimensional Fuzzy Initial Value Problem of Autocorrelated Fuzzy Processes via Cross Product: The Prey-Predator Model
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 171
EP  - 178
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.024
DO  - 10.2991/asum.k.210827.024
ID  - Laiate2021
ER  -