Sistema p-Fuzzy aplicado às equações diferenciais parciais

Abstract

Describing mathematically natural phenomena in order to make predictions and decisions is one of the biggest challenges in mathematics. Several phenomena can be described through partial differential equations, however many of these phenomena present linguistic variables, i.e. vague and imprecise information. Such characteristics make phenomenon modeling through differential equations difficult due to their dependence on the precision of the parameters used. The purpose of this research is to demonstrate the feasibility and applicability of fuzzy partial systems (p-fuzzy) for the modeling of the phenomena described by partial differential equations. In particular, the method proposed made possible the mathematical treatment of the physical phenomenon of luminescence, therefore demonstrating the potential of fuzzy p systems in relation to those obtained without the fuzzy modeling approach. The p-fuzzy systems were obtained using the function ANFIS Matlab, which came from a data set and identifies the membership functions as well as the parameters of fuzzy rules based systems. Analyzing the results, it is possible to conclude that the p-fuzzy system is a useful tool for modeling specific phenomena that involve partial variation rates, including time evolution.