Abstract: There are limitations in establishing fuzzy logical relationship of the existing fuzzy time series forecasting methods, which makes it hard to adapt to the appearance of new relationship. In order to overcome the defects, an interval-similarity based fuzzy time series forecasting (ISFTS) algorithm was proposed. Firstly, based on fuzzy theory, an average-based method was used to redivide the intervals of the universe of discourse. Secondly, the fuzzy sets were defined and the historical data were fuzzified, then the third-order fuzzy logical relationships were established and a formula was used to measure the similarity between logical relationships. By computing the changing trend of future data, the fuzzy values were obtained. Finally, the fuzzy values were defuzzified and the forecasting values were obtained. The proposed algorithm makes up for the shortcomings in logical relationship of the existing forecasting algorithms because it forecasts the changing trend of future data. The experimental results show that the proposed algorithm ISFTS is superior to other forecasting algorithms on forecasting error, including Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). Therefore, the algorithm ISFTS is more adaptive in time series forecasting, especially in the case of large data.

Key words: fuzzy time series, fuzzy set, similarity, logical relationship, forecast

摘要： 针对现有模糊时间序列预测算法无法适应预测中新关系出现的问题，提出了一种基于区间相似度的模糊时间序列预测（ISFTS）算法。首先，在模糊理论的基础上，采用基于均值的方法二次划分论域的区间，在论域区间上定义相应模糊集将历史数据模糊化；然后建立三阶模糊逻辑关系并引入逻辑关系相似度的计算公式，计算未来数据变化趋势值得到预测的模糊值；最后对预测模糊值去模糊化得到预测的确定值。由于ISFTS算法是预测数据变化趋势，克服了目前预测算法的逻辑关系的缺陷。仿真实验结果表明，与同类的预测算法相比，ISFTS算法预测误差更小，在误差相对比(MAPE)、绝对误差均值(MAE)和均方根误差(RMSE)三项指标上均优于同类的对比算法，因此ISFTS算法在时间序列预测中尤其是大数据量情况下的预测具有更强的适应性。

关键词: 模糊时间序列, 模糊集, 相似度, 逻辑关系, 预测