Papers by Francielle Santo Pedro Simões
Neste trabalho estudamos sistemas de equações diferencias com parâmetros incertos e modelados por... more Neste trabalho estudamos sistemas de equações diferencias com parâmetros incertos e modelados por números fuzzy interativos através de duas abordagens distintas: a primeira via inclusão diferencial e a segunda via fuzziĄcação da solução determinística. Em ambos os casos a solução é fuzzy. Em seguida, a título de comparação, defuzziĄcamos a solução e a comparamos com a solução determinística. Notando que a operação produto é uma particular-norma, propomos que a interação entre espécies (e/ou indivíduos) seja modelada por-normas mais gerais. Neste caso, apesar da modelagem do sistema ser feita através de teoria de conjuntos fuzzy, as soluções dessas equações são determinísticas. A primeira abordagem é aplicada em um modelo para evolução de HIV positivo para populações em doença plenamente manifesta, enquanto a segunda é utilizada em modelos do tipo presa-predador de Lotka-Volterra e epidemiológico de transmissão direta.
A cross product of S-linearly correlated fuzzy numbers
IEEE International Conference on Fuzzy Systems, 2021
Solutions of Systems of Linear Fuzzy Differential Equations for a Special Class of Fuzzy Processes
Springer eBooks, Jul 28, 2021
Differential and Integral Calculus for Fuzzy Number-Valued Functions with Interactivity
Springer eBooks, Jul 26, 2021
Atlantis studies in uncertainty modelling, 2021
This paper introduces the notion of a bidimensional fuzzy initial value problem for a special cla... more 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 socalled 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 nonlinear classical initial value problem is provided. Lastly, an application on the preypredator is presented.
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, Feb 14, 2018
Resumo. Via de regra um modelo de dinâmica populacional envolve estudo da variação na quantidade ... more Resumo. Via de regra um modelo de dinâmica populacional envolve estudo da variação na quantidade de indivíduos de uma determinada população. As soluções desses sistemas são processos temporais, com ou sem memória, i.e., o presente está corralacionado ou não com o futuro. No nosso caso, propomos modelos de dinâmica populacional que são descritos por processos fuzzy autocorrelacionados, ou seja, apresentam interatividades locais modelada por meio da teoria de conjuntos fuzzy. Nesse sentido, veremos que em um problema de valor inicial com incerteza, saber que o campoé negativo nãoé suficiente para obter uma solução decrescente. Além disso,é preciso adotar certo controle na taxa de variação eé isso que faremos neste trabalho.
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, Aug 25, 2015
Apresentamos diversas definições de diferenças entre números fuzzy presentes na literatura: tradi... more Apresentamos diversas definições de diferenças entre números fuzzy presentes na literatura: tradicional, Hukuhara, generalizada de Hukuhara, generalizada, CIA e via distribuições. Exemplificamos através de um problema de transmissão direta e comparamos as diferentes abordagens.
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, Dec 12, 2014
Este trabalho trata das diversas possibilidades de modelar a taxa de interação em modelos de biom... more Este trabalho trata das diversas possibilidades de modelar a taxa de interação em modelos de biomatemática. Daremosênfase nos modelos do tipo presa-predador em que as taxas de predação são modeladas com t-normas. Essas são operações que generalizam o produto, que usualmenteé a operação utilizada para representar taxas de interação em modelos populacionais com duas ou mais espécies. Assim, apesar da modelagem do sistema ser feita através de lógica fuzzy, as soluções são determinísticas.
Advances in intelligent systems research, 2015
Several definitions of difference between fuzzy numbers are well established in literature: stand... more Several definitions of difference between fuzzy numbers are well established in literature: standard, Hukuhara, generalized Hukuhara, generalized, CIA and other differences based on joint possibility distributions. We present and compare them. An example of epidemiological model of a disease with direct transmission illustrates the different approaches. Finally, we briefly state some derivatives defined by using the cited differences.
A-Cross Product for Autocorrelated Fuzzy Processes: The Hutchinson Equation
Springer eBooks, Jul 28, 2021
Calculus for fuzzy functions with strongly linearly independent fuzzy coefficients
Fuzzy Sets and Systems, May 1, 2022
Abstract This paper establishes a theory of calculus for fuzzy-number-valued functions whose rang... more Abstract This paper establishes a theory of calculus for fuzzy-number-valued functions whose range is embedded in a specific Banach subspace of fuzzy numbers. These spaces are generated by strongly linearly independent (SLI) fuzzy numbers whose operations are induced by an isomorphism with R n . We use the notion of Frechet differentiability and Riemann integrability for these functions and present a fundamental theorem of calculus. Lastly, we develop a theory of fuzzy differential equations and provide an existence and uniqueness theorem.
Communications in computer and information science, 2020
This manuscript presents a model for HIV dynamics of seropositive individuals under antiretrovira... more This manuscript presents a model for HIV dynamics of seropositive individuals under antiretroviral treatment described from fuzzy set theory by two different approaches considering interactivity: differential equation with interactive derivative and differential equation with Fréchet derivative. It also establishes an identity between interactive derivative and fuzzy Fréchet derivative. With this identity, we establish when the solutions of the two differential equations coincide. Lastly, we present biological interpretations for both cases.
Higher Order Initial Value Problem with Interactive Fuzzy Conditions
In this manuscript we deal with non-homogeneous n-th order linear differential equations that hav... more In this manuscript we deal with non-homogeneous n-th order linear differential equations that have fuzzy initial conditions. We assume that the initial conditions are given by fuzzy numbers that satisfying a special type of relationship namely interactivity. In particular, we assume that the initial conditions are completely correlated fuzzy numbers. Based on this notion, we obtain solutions for linear fuzzy initial value problems by means of the extension principle. Finally, we show that endpoints of each α-level of the proposed solution can be determined by solving two associated classical initial value problems.
A Note on Caputo Fractional Derivative in the Space of Linearly Correlated Fuzzy Numbers
Springer eBooks, Sep 30, 2022
Information Sciences, Feb 1, 2020
In this manuscript we study integration and derivative theories for interactive fuzzy processes. ... more In this manuscript we study integration and derivative theories for interactive fuzzy processes. These theories are based on the Fréchet derivative and the Riemann integral. In addition, we present a connection between these two theories, i.e., some problems may be formulated in both ways. We establish the fundamental theorem of calculus, theorem of existence and the local uniqueness of the solution of fuzzy differential equations and some techniques to solve fuzzy initial value problems. To illustrate the usefulness of the developed theory, we investigate the radioactive decay model.
Trends in Computational and Applied Mathematics, May 24, 2023
The curve of cumulative cases of individuals infected by COVID-19 shows similar growth to the log... more The curve of cumulative cases of individuals infected by COVID-19 shows similar growth to the logistic curve in the period referring to each epidemic "wave", as each peak of active cases is called. Considering that in pandemic scenarios it is common to seek control measures based on previous experiences, in this paper we model the curve of cumulative cases through a logistic model with infected removal to include the control measures in the dynamics. This model is based on fractional differential equations to also include the memory effect. We study the scenario of the first two "waves" in the analyzed countries: Brazil, China, Italy, and Switzerland. Scenarios with and without control measures are compared, proving the importance of control measures such as isolation. Moreover, this model makes it possible to determine the portion of the population that did not participate in the dynamics of the spread of the disease, as well as to analyze how the number of infected people reduced in each country.
The Use of Triangular Norms in Epidemiological Models: A Comparative Study Using COVID-19 Data
IEEE Transactions on Fuzzy Systems, May 1, 2023
The use of t-norms in mathematical models of epidemics
We study different t-norms in epidemiological mathematical models. We explore the SI model, which... more We study different t-norms in epidemiological mathematical models. We explore the SI model, which encounter between individuals is originally modelled by the product operation (also a t-norm). We discuss the differences and advantages of using one or another t-norm. Finally, we compare the solutions provided by each approach.
Communications in computer and information science, 2020
This work presents an application of interactive fuzzy fractional differential equation, with Cap... more This work presents an application of interactive fuzzy fractional differential equation, with Caputo derivative, to an HIV model for seropositive individuals under antiretroviral treatment. The initial condition of the model is given by a fuzzy number and the differentiability is given by a fuzzy interactive derivative. A discussion about the model considering these notions are presented. Finally, a numerical solution to the problem is provided, in order to illustrate the results.
On fuzzy Laplace transform in linearly correlated fuzzy space
Soft Computing, Nov 24, 2022
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Papers by Francielle Santo Pedro Simões