Polynomial Fuzzy Information Granule-Based Time Series Prediction

Abstract

Fuzzy information granulation transfers the time series analysis from the numerical platform to the granular platform, which enables us to study the time series at a different granularity. In previous studies, each fuzzy information granule in a granular time series can reflect the average, range, and linear trend characteristics of the data in the corresponding time window. In order to get a more general information granule, this paper proposes polynomial fuzzy information granules, each of which can reflect both the linear trend and the nonlinear trend of the data in a time window. The distance metric of the proposed information granules is given theoretically. After studying the distance measure of the polynomial fuzzy information granule and its geometric interpretation, we design a time series prediction method based on the polynomial fuzzy information granules and fuzzy inference system. The experimental results show that the proposed prediction method can achieve a good long-term prediction.