Universal Approximators: New Approach for the Curve Fit of the COVID-19 Infected Population

Authors

DOI:

https://doi.org/10.5540/tcam.2022.023.02.00213

Keywords:

Mathematical Modeling, Fuzzy clustering. Takagi-Sugeno-Kang inference methods, Regression analysis

Abstract

Fuzzy systems that include Takagi-Sugeno inference method with linear outputs, are widely known to have the ability to uniformly approximate any polynomial with high precision and, as a consequence, any continuous function, by applying the approximation theorem of Weierstrass. There is one more advantage for these methods which is to obtain an explicit expression of the defuzzified output as a function of the system’s inputs. The purpose of this study is to describe the dynamics of a data set collected through the behavior of the tangential envelope and the local concavity of a curve to be adjusted. The functions that define the envelope and its concavity are identified by means of a hybrid system that combines a fuzzy clustering with the qualities of the Takagi-Sugeno inference method. The analyzed data set represents the world population of confirmed infected people by the infectious disease caused by the coronavirus of severe acute respiratory syndrome, named COVID-19. The proposed fuzzy method, in two versions, first and second order, are compared with curves built through the least square method with the maximum of the absolute value of the difference between the fit values and the data, normalized at each instant. In these comparisons, both fuzzy approaches proposed in this study are the ones that best match the data collected, being the fuzzy approximation of second order the best of all.

Author Biographies

A. M. A. Bertone, Federal University of Uberlandia

Math college.


J. B. Martins, Federal Institute of Triangulo Mineiro Campus Uberaba Technology Park.

Computing department.

R. S. M. Jafelice, Federal University of Uberlandia

Math College

References

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Published

2022-06-27

How to Cite

Bertone, A. M. A., Martins, J. B., & Jafelice, R. S. M. (2022). Universal Approximators: New Approach for the Curve Fit of the COVID-19 Infected Population. Trends in Computational and Applied Mathematics, 23(2), 213–222. https://doi.org/10.5540/tcam.2022.023.02.00213

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Section

Original Article