Ridge estimation for regression models with crisp inputs and Gaussian fuzzy output

This paper deals with ridge estimation of fuzzy multiple linear and nonlinear regression models with crisp inputs and Gaussian fuzzy output. Using ridge regression learning algorithm in the Lagrangian dual space, we describe a ridge estimation of fuzzy multiple linear regression model of Xu and Li (Fuzzy Sets and Systems 119 (2001) 215). It allows us to perform nonlinear regression for Xu and Liʹs model by constructing a fuzzy linear regression function in a high dimensional feature space. Experimental results are then presented which indicate the performance of this algorithm.