Uma nova proposta para a implementação computacional do princípio de extensão de Zadeh

Abstract

This work presents a computational method that allows the application of the extension principle to obtain the slit diffraction pattern. This principle is a fuzzy logic tool that can treat mathematical expressions with an uncertainty in its parameters. The expressions tested describe oscillations and, since their resolution through traditional extension principle generates noisy data, we adopted a new method of resolution. This method is based on numerical methods for obtaining the roots of equations, and the resolution of the extension principle is performed analytically. To apply the new methodology we adopted slit diffraction, where we added uncertainty width parameter in order to obtain a given diffraction pattern. The results obtained on the defuzzification of the expressions with uncertainty were compared with the classical results, enabling a new analysis of the diffraction pattern