The application of fuzzy set theory in the Saint Venant’s equations to study the flood wave propagation in the Potengi river, Rio Grande do Norte - Brazil, through the calculation of the flow as membership functions

Abstract

A mathematical model based on the equations of hydrodynamics combined with the fuzzy set theory was formulated, for the flood wave propagation in natural rivers. The model is able to evaluate the behavior of the control variables as membership functions. For the solution of the model governing partial differential equations, the Finite Difference Method was used, and for the solution of the resulting system of nonlinear algebraic equations, the Newton-Raphson Iteration Method was used. The results show that the use of Fuzzy Set Theory in the Hydrodynamic model could be an available alternative to determination of the uncertainty and to the Fuzzy Risk Analysis in the flood wave propagation.