Random weight network-based fuzzy nonlinear regression for trapezoidal fuzzy number data

Abstract

This paper proposes a random weight network (RWN)-based fuzzy nonlinear regression (FNR) model, abbreviated as TraFNRRWN, to solve the FNR problem in which both inputs and outputs are trapezoidal fuzzy numbers. TraFNRRWN is a special single hidden layer feed-forward neural network which does not require any iterative process to train the network weights. The input-layer weights of TraFNRRWN are randomly assigned and its output-layer weights are analytically determined by solving a constrained-optimization problem. In addition, a new strategy is used to construct the fuzzy membership degree function for the predicted fuzzy-out based on the derived output-layer weights of TraFNRRWN. A fuzzification method is developed to fuzzify the crisp numbers of data sets into trapezoidal fuzzy numbers. Twelve fuzzified data sets were used in the experiments to compare the performance of TraFNRRWN with five different FNR models. The experimental results have shown that TraFNRRWN obtained better prediction performance with less training time because it did not require time-consuming weight learning and parameter tuning.