基于不动点的模糊时间序列模型  

A Fuzzy Time Series Model Based on Fixed Points

作　　者：刘智 LIU Zhi(Department of Basic,Shenyang University of Technology,Liaoyang 111003,China)

机构地区：[1]沈阳工业大学基础部,辽宁辽阳111003

出　　处：《数学的实践与认识》2023年第3期190-199,共10页Mathematics in Practice and Theory

基　　金：辽宁省教育厅科学研究经费项目(LJKZ0164);过程工业综合自动化国家重点实验室基础研究基金(2013ZCX02)。

摘　　要：模糊时间序列在解决模糊性和不确定性数据方面表现出明显的优势.为了提高模型的预测精度,将数学理论中不动点理论与时间序列模型相结合,提出了分式函数、逆分式函数、预测函数的定义,并且证明了预测函数值收敛定理.在这些理论基础上,建立了一种基于不动点的模糊时间序列模型,进一步完善了模糊时间序列理论.预测结果表明,该模型具有预测精度较高、理论完整、鲁棒性强、应用范围广的特点.Fuzzy time series has obvious advantages in solving the problem of fuzzy and uncertain data.In order to improve the prediction precision of the model,this paper combines the fixed point theory in mathematical theory with the time series model,puts forward the definitions of fractional function,inverse fractional function and prediction function,and proves the convergence theorem of prediction function value.On the basis of these theories,a fuzzy time series model based on fixed points is established in this paper,which further improves the fuzzy time series theory.The prediction results show that this model has the characteristics of high prediction accuracy,complete theory,strong robustness and wide application.

关 键 词：模糊时间序列 不动点 预测 

分 类 号：O211.61[理学—概率论与数理统计] O177.91[理学—数学]