A novel type-2 fuzzy membership function: Application to the prediction of noisy data

A novel, diamond-shaped type-2 fuzzy membership function is introduced in this study. The proposed type-2 fuzzy membership function has certain values on 0 and 1, but it has some uncertainties for the other membership values. It has been shown that the type-2 fuzzy system using this type of membership function introduced in this study has some noise reduction property in the presence of noisy inputs. The appropriate parameter selection to be able to achieve noise reduction property is also considered. A hybrid method consisting of particle swarm optimization (PSO) and gradient descent (GD) algorithm is used to optimize the parameters of the proposed type-2 fuzzy system. PSO is a derivative-free optimizer, and the possibility of the entrapment of this optimizer in local minimums is less than the gradient descent method. The proposed type-2 fuzzy system and the hybrid parameter estimation method are then tested on the prediction of a noisy, chaotic dynamical system. The simulation results show that the type-2 fuzzy predictor with the proposed novel membership functions shows a superior performance when compared to the other existing type-2 fuzzy systems in the presence of noisy inputs.