An Optimization Technique for Solving a Class of Ridge Fuzzy Regression Problems

In this paper, a hybrid scheme based on recurrent neural networks for approximate coefficients (parameters) of ridge fuzzy regression model with LR-fuzzy output and crisp inputs is presented. Here a neural network is first constructed based on some concepts of convex optimization and stability theory. The suggested neural network model guarantees to find the approximate parameters of the ridge fuzzy regression problem. The existence and convergence of the trajectories of the neural network are studied. The Lyapunov stability for the neural network is also shown. To assess the ridge fuzzy regression estimator, the mean squared prediction error with three different well known distances are used. In order to depict the performance of the proposed ridge technique in the presence of multicollinear data, a Monte Carlo simulation is presented. To further determine, an example of a situation in which one variable is a perfect linear combination of the other variable is used to test the applicability of the proposed method. In this study, the performance of the model is evaluated by error parameters and visualized in the Taylor diagram. The predictive ability of the model thus obtained is examined by cross- validation to investigate how well the model fits and predicts every observations.