Fuzzy nonlinear regression analysis using a random weight network

Modeling a fuzzy-in fuzzy-out system where both inputs and outputs are uncertain is of practical and theoretical importance. Fuzzy nonlinear regression (FNR) is one of the approaches used most widely to model such systems. In this study, we propose the use of a Random Weight Network (RWN) to develop a FNR model called FNR_RWN, where both the inputs and outputs are triangular fuzzy numbers. Unlike existing FNR models based on back-propagation (BP) and radial basis function (RBF) networks, FNR_RWN does not require iterative adjustment of the network weights and biases. Instead, the input layer weights and hidden layer biases of FNR_RWN are selected randomly. The output layer weights for FNR_RWN are calculated analytically based on a derived updating rule, which aims to minimize the integrated squared error between α-cut sets that correspond to the predicted fuzzy outputs and target fuzzy outputs, respectively. In FNR_RWN, the integrated squared error is solved approximately by Riemann integral theory. The experimental results show that the proposed FNR_RWN method can effectively approximate a fuzzy-in fuzzy-out system. FNR_RWN obtains better prediction accuracy in a lower computational time compared with existing FNR models based on BP and RBF networks.