High order fuzzy time series method based on pi-sigma neural network

Fuzzy time series methods, which do not require the strict assumptions of classical time series methods, generally consist of three stages as fuzzification of crisp time series observations, determination of fuzzy relationships and defuzzification. All of these stages play a very important role on the forecasting performance of the model. An important stage of the fuzzy time series analysis is to determine the fuzzy relationships. Artificial neural networks seem to be very effective in determining fuzzy relationships that improve the accuracy of the forecasting performance. Several neuron models with different characteristics have been proposed so far. One of these models is Pi-Sigma neural network. An important advantage of Pi-Sigma neural network is that it requires fewer weights and nodes and has a lower number of computations when compared to multilayer perceptron. In this study, a new model for determining the fuzzy relationships for high order fuzzy time series forecasting which uses Pi-Sigma neural network is introduced. A modified particle swarm optimization model is used to train the Pi-Sigma network. We test the new model on two real datasets and we also perform a simulation study. The results are compared to the ones obtained by other techniques and show a better performance.