Population Growth Models Using Fuzzy Ordinary Differential Equation

Diogo Sampaio da Silva; Roberto Antonio Cordeiro Prata

doi:10.5433/1679-0375.2025.v46.53167

Population Growth Models Using Fuzzy Ordinary Differential Equation

Authors

Diogo Sampaio da Silva Universidade Federal do Amazonas https://orcid.org/0009-0000-5597-1355
Roberto Antonio Cordeiro Prata Universidade Federal do Amazonas https://orcid.org/0000-0001-7578-1014

DOI:

https://doi.org/10.5433/1679-0375.2025.v46.53167

Keywords:

fuzzy mathematics, population growth models, ordinary differential equations, fuzzy numbers, mathematical modelling

Abstract

Fuzzy mathematics is a branch of mathematics that presents a new approach to the classical notion of set, enabling the generalization of concepts and results from classical mathematics. Using the concept of fuzzy number, a generalization of the real number, we study fuzzy ordinary differential equations, generating ampler solutions to differential equations that model population growth. In particular, we examined a model for the growth of microorganisms in milk. By applying the fuzzy solution we expanded the possible parameter values of the models and studied their relationships. In this context, we study the properties of interactive fuzzy numbers, as well as their applications in mathematical modeling. Through concrete examples, we illustrate the application of fuzzy mathematics and interactive fuzzy numbers
in real-world situations, highlighting their relevance in decision-making in contexts of uncertainty and imprecision.
Leveraging the solutions and parameters values reported in the literature, the theory of interactive fuzzy numbers was used to develop predictive models. These models encompass intervals centered around the values deterministically predicted values, incorporating deviations within the confidence interval obtained for one of the parameters in each model.

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Author Biographies

Diogo Sampaio da Silva, Universidade Federal do Amazonas

Master’s student in the Graduate Program in Mathematics at the Federal University of Amazonas (UFAM), Manaus, AM, Brazil.

Roberto Antonio Cordeiro Prata, Universidade Federal do Amazonas

Prof. Dr., Department of Mathematics, Federal University of Amazonas (UFAM), Manaus, AM, Brazil.

References

Barros, L. C., Bassanezi, R. C., & Lodwick, W. A. (2017). A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics Theory and Applications. Springer.

Bassanezi, R. (2002). Ensino - aprendizagem com Modelagem matemática. Contexto.

Cabral, V. M., & Barros, L. C. (2019). On differential equations with interactive fuzzy parameter via t-norms. Fuzzy Sets and Systems, 358, 97–107. https://doi.org/10.1016/j.fss.2018.07.010

Cabral, V. M., Prata, R. A. C., & Barros, L. C. (2015). f-correlated fuzzy numbers applied to HIV model with protease inhibitor therapy. Mathware & soft computing: The Magazine of the European Society for Fuzzy Logic and Technology, 22(1), 46–51.

Carlsson, C., Fullér, R., & Majlender, P. (2004). Additions of completely correlated fuzzy numbers. 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No. 04CH37542), 1, 535–539. https://doi.org/https://doi.org/10.1109/FUZZY.2004.1375791

Dubois, D., & Prade, H. (1981). Additions of interactive fuzzy numbers. IEEE Transactions on Automatic Control, 26(4), 926–936. https://doi.org/10.1109/TAC.1981.1102744

Gomes, L. T., Barros, L. C., & Bede, B. (2015). Fuzzy Differential Equations in Various Approaches. SBMAC-Springer. https://doi.org/10.1007/978-3-319-22575-3

Longhi, D. A., Dalcanton, F., Aragão, G. M. F., Carciofi, B. A. M., & Laurindo, J. B. (2013). Assessing the prediction ability of different mathematical models for the growth of Lactobacillus plantarum under non-isothermal conditions. Journal of Theoretical Biology, 335, 88–96. https://doi.org/10.1016/j.jtbi.2013.06.030

Longhi, D. A., Dalcanton, F., Aragão, G. M. F., Carciofi, B. A. M., & Laurindo, J. B. (2017). Microbial growth models: A general mathematical approach to obtain μmax and λ parameters from sigmoidal empirical primary models. Brazilian Journal of Chemical Engineering, 34(2), 369–375. https://ouci.dntb.gov.ua/en/works/lRX0pXW7/

Robazza, W., Teleken, J., & Gomes, G. (2010). Modelagem Matemática do Crescimento de Microrganismos em Alimentos. Trends in Computational and Applied Mathematics, 11(1), 101–110. https://doi.org/10.5540/tema.2010.011.01.0101

Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X

Zadeh, L. (1975). The concept of a linguistic variable and its application to approximate reasoning—II. Information Sciences, 8(4), 301–357. https://doi.org/10.1016/0020-0255(75)90046-8