Fuzzy time series forecasting based on axiomatic fuzzy set theory

In fuzzy time series, a way of representing their original numeric data through a collection of fuzzy sets plays a pivotal role and impacts the prediction performance of the constructed forecasting models. An evident shortcoming of most existing models is that fuzzy sets (their membership functions) are developed in an intuitive manner so that not all aspects of the time series could be fully captured. In this study, using an idea of axiomatic fuzzy set clustering we take the distribution of data into account to position time series in the framework of fuzzy sets. The obtained clusters exhibit well-defined semantics. To produce numeric results of forecasting, we develop a method to determine the prototypes based on the corresponding fuzzy description of the clusters. The commonly used enrollment time series is applied to demonstrate how the proposed method works. The experimental results exploiting the Taiwan Stock Exchange Capitalization Weighted Stock Index demonstrate that the proposed method can effectively improve forecasting accuracy. Furthermore, the proposed approach is of a general form and as such can be easily integrated with various fuzzy time series models.