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.

Neste trabalho, nós modelamos a reocupação de uma trilha de formigas cortadeiras. A modelagem matemática consiste em estudar o deslocamento de formigas cortadeiras em direção a uma região de atração e o retorno das mesmas para o formigueiro. Para conduzir esta pesquisa, nós utilizamos uma equação de difusão-convecção, na qual a dispersão e a velocidade nas direções horizontal (x) e vertical (y) são parâmetros fuzzy. Os especialistas afirmam que o feromônio é uma importante variável no que se refere à reocupação de uma trilha porque o mesmo pode interferir no comportamento das formigas cortadeiras, ocasionando alterações na dispersão e na velocidade do deslocamento. As simulações numéricas levaram em consideração o feromônio através de Sistemas Baseados em Regras Fuzzy (SBRF). Os resultados numéricos são compatíveis com o fenômeno biológico estudado.

In this paper we model the reoccupation of a trail by leaf-cutting ants. The mathematical modeling consists in studying the leaf-cutting ants' displacement towards an attraction area and their return to the nest. To carry out this research, we utilized the diffusion-advection equation, where the dispersion and velocity towards x and y are fuzzy parameters. The experts affirm that the pheromone is an important variable concerning trail reoccupation because it influences leaf-cutting ants dispersion and velocity of displacement. The numerical simulations took into account the pheromone through the Fuzzy Rule-Based System (FRBS). The numerical results are compatible with the biological phenomenon studied.