p-Fuzzy Newton-Raphson Method

This work aims to find roots of real-valued functions via p-fuzzy systems. The expression “p-fuzzy” arises from partial knowledge about a system that is modeled by a Fuzzy Rule-Based Systems. In this paper, the Fuzzy Rule-Based System is considered to provide an approximation for the derivative of real-valued functions based solely on the function behavior, which is characterized by linguistic variables. The proposed method can be viewed as a modification of the classical Newton-Raphson method, where the derivative presented in the formula is replaced by the output produced by the Fuzzy Rule-Based System. The main advantage is to avoid the computation of the derivative of real-valued functions and deal only with linguistic variables. Some examples are given to show how the method works. Moreover, in these examples a brief comparison with the classical method is presented in order to observe which method provides a better approximation.