Sistemas p-fuzzy modificados para dinâmicas populacionais: modelagens e simulações

• Ano de defesa: 2012
• Autor(a) principal: Ferreira, Thiago Fernando
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Matemática; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: Teoria dos Conjuntos Fuzzy; Equações de Diferenças; Equações Diferenciais Ordinárias; Sistemas p-Fuzzy modificados; Sistemas p-Fuzzy modificados no tempo; Conjuntos difusos; Equações diferenciais ordinárias; Fuzzy set theory; Difference equations; Ordinary differential equations; Modified p-Fuzzy system; In-time modified p-Fuzzy systems; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufu.br/handle/123456789/16798; https://doi.org/10.14393/ufu.di.2012.224

The great challenge of mathematical modeling is to describe natural phenomena in order to make predictions and take decisions. The use of difference equations and ordinary differential equations has been an essential tool in modeling population-related phenomena. The feasibility and applicability of partially fuzzy systems (p-fuzzy) in modeling phenomena described by differential equations have already been studied. The proposal in this work is to present modified p-fuzzy systems (which membership functions are altered by a potency) and in-time modified p-fuzzy systems (in which the membership functions are altered at each iteration in time) which describe a better approximation to the deterministic solutions for some dynamic population models, than the p-fuzzy systems without modifications. The modified p-fuzzy systems were obtained numerically by means of programs in Matlab software, in order to determine the potency and function that adequately alter the potency, calculating the smallest error between the analytic solution and the modified p-fuzzy systems for some models in population dynamics. We verified that in-time modified p-fuzzy system for the pest control model is more convenient in relation to both the p-fuzzy without modifications and the one modified by the potency, since in this system the final result is the smallest pest population that survives to the control. After analyzing the attained results, it can be concluded that when the potency modified p-fuzzy system with either restrictive modifications (potency > 1) or expansive (0 < potency < 1), we accomplish a better approximation for the analytical solution for each model. For the pest control model, this approximation becomes greater when the modification is made to each and a very iteration, i.e., with in-time modified p-fuzzy system.