Abstract This paper proposes to analyze how the intervention measures such as lockdown, partial lockdown and no-lockdown help to impede the spread of the severe outbreak of COVID-19 in Brazil. A p-fuzzy model, considering as input variables, the infected population and the intervention measures and as output variable the level of infestation, is proposed. The numerical results show that intervention measures play a crucial role in determining the success of COVID-19 eradication programs, while the population is being vaccinated in stages. Therefore, the model proposed assists government decision making in order to minimize the spread of the pandemic.

Abstract The COVID-19 pandemic has spread widely through the world, since 2019. Then, the search for vaccines has become fundamental against the disease and has generated great expectations on population. In Brazil, the first case of COVID-19 was registered in February 2020 and the process of vaccination started in early 2021. In this context, considering the advance of vaccination and the behavior of epidemics, we present a study on the effect of population-wide vaccination on the evolution of the COVID-19 epidemic. To this end, we propose a new fuzzy system in order to model the COVID-19 epidemic evolution under the effect of vaccination in Brazil. This proposed model consists of a p-fuzzy system, where the input variables are the infected population and the vaccination rate. The output variable is the level of infection. Results of the proposed fuzzy system show that the level of infestation tends to decrease as the number of people vaccinated increases. Therefore, the population-wide vaccination strategy clearly contributes to suppressing the growth of the disease and to mitigating its impacts on society, including saving lives.

Abstract This paper proposes an automatic fuzzy classification system for glycemic index, which indicates the level of Diabetes Mellitus type 2. Diabetes is a chronic disease occurred when there is deficiency in insulin production or in its action, or both, causing complications. Neuro-fuzzy systems and Decision Trees are used to obtain, respectively, the numerical parameters of the membership functions and the linguistic based rules of the fuzzy classification system. The results goal to categorize the glycemic index into 4 classes: decrease a lot, decrease, stable and increase. Real database from [1] is used and the input attributes of the system are defined. In addition, the proposed automatic fuzzy classification system is compared with an “expert” fuzzy classification system, which is totally modeled using expert knowledge. From linguistic based rules obtained from fuzzy inference process, new scenarios are simulated in order to obtain a larger data set which provides a better evaluation of the classification systems. Results are promising, since they indicate the best treatment - intervention or comparative - for each patient, assisting in the decision-making process of the health care professional.

Neste trabalho consideramos o problema combinado, que acopla os problemas de dimensionamento de lotes e de corte de estoque, incluindo uma formulação matemática deste problema. Consideramos algumas propriedades da matriz de restrições deste modelo e como construir uma base esparsa para ela, utilizando um reordenamento estático das colunas. Resultados numéricos de uma implementação que realiza trocas de colunas básicas e verifica sua esparsidade, simulando o método simplex são apresentados. Experimentos numéricos também comprovam a robustez desta abordagem. Concluímos que a proposta de construção da base estática esparsa leva a bons resultados computacionais com relação à velocidade e robustez em comparação com abordagens que não consideram a estrutura esparsa da matriz.

In this work the combined problem is considered, which solves simultaneously the lot sizing and the cutting stock problems. We study some properties of the matrix of constraints and how to factorize the base without losing sparsity in the simplex method context, by a static reordering of the basic columns. Numerical results simulating simplex iterations and verify the sparsity of the factorizations are presented. Numerical experiments had also proven the robustness of this strategy. We conclude that the approach of constructing of the static sparse base reordering leads to very good computational results for both: speed and robustness, in comparison with approaches which do not consider the sparse structure of the matrix of constraints.