基于λ-强截集的广义模糊时间序列预测模型

Prediction Model of Generalized Fuzzy Time Series Based on λ Strong Cut Set

文章通过分析传统的加权模糊时间序列模型和广义模糊时间序列模型,指出了需要考虑的模糊状态的确定方法和建立模糊关系矩阵中的不足。结合模糊集理论中λ强截集的性质,重新定义所要考虑隶属度对应的模糊状态和模糊逻辑关系矩阵的建立过程,建立基于λ强截集的广义模糊时间序列模型。以Alabama大学22年的入学人数为例,利用均方误差MSE和泰尔不等系数TIC对比分析本文提出模型与传统加权模型和广义模型的预测精度以及考虑λ取不同阈值时模型预测精度的变化情况,验证本文建立模型的可行性和有效性。

By analyzing the traditional weighted fuzzy time series model and the generalized fuzzy time series, this paper points out a method for confirming fuzzy state and the insufficient of established fuzzy relationship matrix. Combining with the nature of λ strong cut set in fuzzy set theory, the paper redefines the fuzzy relation of the different membership degree and the corresponding fuzzy logic relation matrix construction procedure, and establishes a generalized fuzzy time series model based on λ strong cut set. Taking the enrollment of Alabama University for 22 years as an example, the paper uses mean square error （MSE） and Theil inequality coefficient （TIC） eontrastive analysis to come up with the prediction accuracy of proposed model, Iraditional weighted model and generalized model, as well as the changes of model prediction accuracy in consideration of λ as different thresholds, to test and verify the feasibility and effectiveness of the proposed model.