p-Fuzzy Newton-Raphson Method

Autor(es)

Pinto, Nilmara J. B. ; Wasques, Vinicius F. ; Oliveira, Washington A. ; Barros, Laecio C.

• Tipo de documento: Artigo Científico
• Fonte: INTELLIGENT AND FUZZY SYSTEMS, VOL 3, INFUS 2024; v. 1090, p. 9-pg., 2024-01-01.

Resumo

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. (AU)

• Processo FAPESP: 20/09838-0 - BI0S - Brazilian Institute of Data Science
• Beneficiário: João Marcos Travassos Romano
• Modalidade de apoio: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia
• Processo FAPESP: 23/03927-0 - Equações diferenciais fuzzy e álgebra fuzzy com aplicações
• Beneficiário: Vinícius Francisco Wasques
• Modalidade de apoio: Auxílio à Pesquisa - Regular