Rosana Motta Jafelice

On fuzzy solutions for partial differential equations

In this study we investigate heat, wave and Poisson equations as classical models of partial differential equations (PDEs) with uncertain parameters, considering the parameters as fuzzy numbers. The fuzzy solution is built from fuzzification of the deterministic solution. The continuity of the Zadeh extension is used to obtain qualitative properties on regular @a-cuts of the fuzzy solution. We prove the stability with respect to the initial boundary data, and show that as time goes to zero, the diameter of the fuzzy solution converges to zero and, as a consequence, to the cylindrical surface determined by the curve of the degree of membership. Numerical simulations are used to obtain a graphical representation of the fuzzy solution and a defuzzification of this solution is obtained using the center of gravity method. We theoretically show that the surface obtained by defuzzification with the plane determined by fixing time is indeed the solution of the same initial boundary problem for this time-point for the heat and Poisson equations and, in a particular case, for the wave equation. The deterministic solution and the defuzzified surface intercept are numerically compared using the Euclidean distance.

Methodology to determine the evolution of asymptomatic HIV population using fuzzy set theory

The aim of this paper is to o study the evolution of postive HIV population for manifestation of AIDS, the Acquired Immunodeficiency Syndrome.For this purpose, we suggest a methodology to combine a macroscopic HIV positive population model with an individual microscopic model. The first describes the evolution of the population whereas the second the evolution of HIV in each individual of the population. This methodology is suggested by the way that experts use to conduct public policies namely, to act at the individual level to observe and verify the manifest population.The population model we address is a differential equation system whose transference rate from asymptomatic to symptomatic population is found through a fuzzy rule-based system. The transference rate depends on the CD4-level, the main T lymphocyte attacked by the HIV retrovirus when it reaches the bloodstream. The microscopic model for a characteristic individual in a population is used to obtain the CD4-level at each time instant. From the CD4 - level, its fuzzy initial value, and the macroscopic population model, we compute the fuzzy values of the proportion of asymptomatic population at each time instant t using the extension principle. Next, centroid defuzzification is used to obtain a solution that represents the number of infected individuals. This approach provides a method to find a solution of a non-autonomous differential equation from an autonomous equation, a fuzzy initial value, the extension principle, and center of gravity defuzzification. Simulation experiments show that the solution given by the method suggested in this paper fits well to AIDS population data reported in the literature.

Fuzzy set-based model to compute the life expectancy of HIV infected populations

In this paper we study the influence of AIDS Acquired Immunodeficiency Syndrome - in the life expectancy of a population considering a classical population model completed with expert knowledge information via a fuzzy rule-based system. Medical experts recognize that the most important variables to characterize HIV infection are viral load and CD4+ level. In the model considered, we assume that AIDS has a direct influence in the mortality rate of a population and derive a fuzzy rule base system to capture this influence using viral load, CD4+ and a parameter that modify the transference rate, as variables. We determine the average number of individuals and the life expectancy for specific population groups with no anti-retroviral therapy. The values found are coherent with actual data reported by UN.

Postoperative vomiting in pediatric oncologic patients: prediction by a fuzzy logic model.

To report a fuzzy logic mathematical model to predict postoperative vomiting (POV) in pediatric oncologic patients and compare with preexisting scores.

Estudo da Concentração da Poluição do Ar com Parâmetro Fuzzy

O objetivo deste trabalho e modelar matematicamente uma fonte de poluicao, que consideramos como sendo a chamine de uma industria, que contamina a atmosfera com uma nuvem de poluicao que se espalha pela cidade de Uberlândia. [...]