基于FCM算法的高阶直觉模糊时间序列预测模型

The FCM Algorithm based High-order Intuitionistic Fuzzy Time Series Forecasting Model

针对现有模糊时间序列预测模型中有效论域划分和历史数据模糊化处理存在的不足,提出一种新的高阶直觉模糊时间序列预测模型.该模型首先将等分论域划分和基于FCM算法的非等分论域划分两种划分方法结合起来,较好地反映了历史数据内部或局部形态的关联特征.在此基础上,根据直觉模糊时间序列的数据特点,给出一种更具客观性的方法对历史数据直觉模糊化处理,较好地反映了历史数据“非此非彼”的模糊状态.然后结合“max-min”聚合运算,合理地选取要考虑的模糊状态,进而对预测结果去模糊化输出.在实验部分,该模型利用阿拉巴马大学学生招生人数和黄金期货收盘价格为实验数据,将预测结果与现有部分模型的预测结果进行对比分析,验证了新模型的可行性和有效性.

A new high-order intuitionistic fuzzy time series forecasting model is proposed in this paper to aiming at the shortcomings of the existing fuzzy time series forecasting models with effective universe of discourse partitioning and fuzzification preprocessing of historical data.The model firstly combines two partitioning methods of equal universe of discourse partitioning and non-equal universe of discourse partitioning based on the FCM algorithm, which better reflects the correlation characteristics of the internal or local patterns of historical data. On this basis, considering the historical data characteristics of intuitionistic fuzzy time series, a more objective method is proposed for intuitionistic fuzzy processing of historical data, which better reflects the fuzzy state of "neither this nor that" of historical data. At the same time, the intuitionistic fuzzy trend approximation factor is used to describe the membership of historical data to fuzzy sets instead of the traditional membership function, then combined with "max-min" aggregation operation, the fuzzy states to be considered are selected reasonably, and the forecasting results are defuzzied. In the experimental part, the model uses the enrollment of students in the University of Alabama and gold futures closing price as the experimental data, and compares the forecasting results with those of some existing models to verify the feasibility and superiority of the new model.