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Artificial neural networks (ANN) have been widely used in recent years to model non-linear time series since ANN approach is a responsive method and does not require some assumptions such as normality or linearity. An important problem with using ANN for time series forecasting is to determine the number of neurons in hidden layer. There have been some approaches in the literature to deal with the problem of determining the number of neurons in hidden layer. A new ANN model was suggested which is called multiplicative neuron model (MNM) in the literature. MNM has only one neuron in hidden layer. Therefore, the problem of determining the number of neurons in hidden layer is automatically solved when MNM is employed. Also, MNM can produce accurate forecasts for non-linear time series. ANN models utilized for non-linear time series have generally autoregressive structures since lagged variables of time series are generally inputs of these models. On the other hand, it is a wellknown fact that better forecasts for real life time series can be obtained from models whose inputs are lagged variables of error. In this study, a new recurrent multiplicative neuron neural network model is firstly proposed. In the proposed method, lagged variables of error are included in the model. Also, the problem of determining the number of neurons in hidden layer is avoided when the proposed method is used. To train the proposed neural network model, particle swarm optimization algorithm was used. To evaluate the performance of the proposed model, it was applied to a real life time series. Then, results produced by the proposed method were compared to those obtained from other methods. It was observed that the proposed method has superior performance to existing methods.

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Fuzzy inference systems have been commonly used for time series forecasting in the literature. Adaptive network fuzzy inference system, fuzzy time series approaches and fuzzy regression functions approaches are popular among fuzzy inference systems. In recent years, intuitionistic fuzzy sets have been preferred in the fuzzy modeling and new fuzzy inference systems have been proposed based on intuitionistic fuzzy sets. In this paper, a new intuitionistic fuzzy regression functions approach is proposed based on intuitionistic fuzzy sets for forecasting purpose. This new inference system is called an intuitionistic fuzzy time series functions approach. The contribution of the paper is proposing a new intuitionistic fuzzy inference system. To evaluate the performance of intuitionistic fuzzy time series functions, twenty-three real-world time series data sets are analyzed. The results obtained from the intuitionistic fuzzy time series functions approach are compared with some other methods according to a root mean square error and mean absolute percentage error criteria. The proposed method has superior forecasting performance among all methods.

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