Fuzzy numerical solution to the Malthusian model via Jγ-interactive arithmetic
DOI:
https://doi.org/10.5540/03.2023.010.01.0057Palavras-chave:
Fuzzy initial value problem, Generalized Hukuhara derivative, Euler’s method, Malthus model, Fuzzy InteractivityResumo
This work provides a numerical solution to the Malthusian model, considering the initial condition as a fuzzy value. The numerical solution is provided from Euler’s method, in which the operations built into the method are adapted to fuzzy numbers. This numerical solution is compatible with the analytical solution obtained from the generalized Hukuhara derivative. An example is presented to illustrate the methodology.
Downloads
Referências
B. Bede. Mathematics of Fuzzy Sets and Fuzzy Logic. 1st ed. 295. Berlin: Springer-Verlag Berlin Heidelberg, 2013.
B. Bede and L. Stefanini. “Generalized differentiability of fuzzy-valued functions.” In: Fuzzy Sets Syst. 230.1 (2013), pp. 119–141.
C. Carlsson, R. Fullér, and P. Majlender. “Additions of completely correlated fuzzy numbers”. In: Fuzzy Systems, 2004. Proceedings. 2004 IEEE International Conference on. Vol. 1. July 2004, pp. 535–539.
P. Diamond and P. Kloeden. “Metric Topology of Fuzzy Numbers and Fuzzy Analysis”. In: Fundamentals of Fuzzy Sets. Ed. by D. Dubois and H. Prade. Vol. 7. The Handbooks of Fuzzy Sets Series. Springer US, 2000, pp. 583–641.
E. Esmi, V. F. Wasques, and L. C. Barros. “Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions”. In: Fuzzy Sets and Systems 424 (2021), pp. 105–131.
E. Esmi et al. “Numerical solution for interval initial value problems based on interactive arithmetic”. In: Iranian Journal of Fuzzy Systems 19 (2022), pp. 1–12.
E. Esmi et al. “Solutions of higher order linear fuzzy differential equations with interactive fuzzy values”. In: Fuzzy Sets and Systems 419 (2021), pp. 122–140.
R. Fullér and P. Majlender. “On interactive fuzzy numbers”. In: Fuzzy Sets and Systems 143.3 (2004), pp. 355–369.
M. A. G. Ruggiero e V. L. R. Lopes. Cálculo Numérico: Aspectos Teóricos e Computacionais. 2nd ed. Pearson Universidades, 2000.
V. F. Wasques et al. “Numerical Solutions for Bidimensional Initial Value Problem with Interactive Fuzzy Numbers”. In: Fuzzy Information Processing. Springer International Publishing, 2018, pp. 84–95.
L. A. Zadeh. “The Concept of a Linguistic Variable and Its Application to Approximate Reasoning - I”. In: Information Sciences 8 (1975), pp. 199–249.
