Type-1 possibilistic fuzzy forecasting functions

Abstract

Type-1 Fuzzy Functions (T1FFs) were developed by Turksen as an alternative fuzzy inference system (FIS) and have been commonly used in forecasting problems. The main advantages of T1FFs are that they are free of rules and easy to implement. Thus, they have recently been an attractive tool for researchers. T1FFs start with clustering the inputs using the fuzzy c-means (FCM) clustering algorithm. Later, the degrees of membership and its nonlinear transformations are included into the input matrix for each cluster. Thus, as many input matrices are obtained as the number of clusters. Finally, the outputs are combined using the degrees of membership of the new observations. Because gathering objects in the same cluster as homogeneously as possible is an important task for a clustering algorithm, the possibilistic FCM is adapted to T1FFs in order to overcome the FCM’s limitations in the proposed method. We used 14 financial datasets and a beer consumption dataset to verify the forecasting performance of the proposed method. For example, the proposed method outperformed the other selected forecasting methods for the Taiwan Stock Exchange time-series datasets in terms of the mean of root mean square errors.