Type-1 and Singleton Fuzzy Logic System Binary Classifier Trained by the BFGS Optimization Method

Mateus Gheorghe de Castro Ribeiro, Ivan F. M. Menezes

Abstract: This work implements the BFGS (Broyden-Fletcher-Goldfarb-Shanno) optimization method for training the type-1 and singleton fuzzy logic system applied to solve binary classification problems. The BFGS is a quasi-Newton method that approximates the second-order information using the gradient of the cost function. Additionally, the Golden Section method is used to obtain the step size for each line search in a descent direction. The effectiveness of the proposed method is demonstrated by using well-established classification metrics evaluated in popular datasets from the literature. Comparisons between the proposed approach and well-known gradient-based methods available are also provided, showing that the BFGS achieves improved performance in terms of accuracy, mean squared error, and the number of epoch demanded during the training phase.