用改进的模糊系统预测混沌时间序列,精度更高且规则更少。
Rule-based Evolving Fuzzy System for Time Series Forecasting: New Perspectives Based on Type-2 Fuzzy Sets Measures Approach
- 结合核递归最小二乘与类型2模糊集,动态生成并度量模糊规则。
- 在麦基-玻璃方程和台湾股市指数上误差最低,规则数更少。
- 适合处理高度不确定的复杂时间序列,如金融与混沌数据。
真实世界数据常含不确定性与外部变量相关的变化,称为随机性。另一种随机来源是混沌,它是混沌时间序列的重要组成部分。现有方法中,演化模糊系统(eFSs)因其自主处理数据和复杂问题的能力,已被证明是强大的时间序列预测模型。但类型2模糊集在高度不确定场景下优于类型1模糊集。本文提出ePL-KRLS-FSM+,一种融合参与式学习(PL)、核递归最小二乘法(KRLS)、类型2模糊逻辑与数据到模糊集转换的演化模糊建模方法。该方法可更优地处理数据不确定性,提升混沌数据预测精度。模型在两个复杂数据集上评估:不同混沌程度的麦基-玻璃延迟微分方程,以及台湾市值加权股票指数(TAIEX)。性能对比主流规则型eFS模型与经典方法,基于误差指标、运行时间和最终规则数分析。结果表明,该模型具有竞争力,表现稳定,优于类型1模型,并在误差和规则数量上均达到最低水平。
原文摘要 · Abstract (English)
Real-world data contain uncertainty and variations that can be correlated to external variables, known as randomness. An alternative cause of randomness is chaos, which can be an important component of chaotic time series. One of the existing methods to deal with this type of data is the use of the evolving Fuzzy Systems (eFSs), which have been proven to be a powerful class of models for time series forecasting, due to their autonomy to handle the data and highly complex problems in real-world applications. However, due to its working structure, type-2 fuzzy sets can outperform type-1 fuzzy sets for highly uncertain scenarios. We then propose ePL-KRLS-FSM+, an enhanced class of evolving fuzzy modeling approach that combines participatory learning (PL), a kernel recursive least squares method (KRLS), type-2 fuzzy logic and data transformation into fuzzy sets (FSs). This improvement allows to create and measure type-2 fuzzy sets for better handling uncertainties in the data, generating a model that can predict chaotic data with increased accuracy. The model is evaluated using two complex datasets: the chaotic time series Mackey-Glass delay differential equation with different degrees of chaos, and the main stock index of the Taiwan Capitalization Weighted Stock Index - TAIEX. Model performance is compared to related state-of-the-art rule-based eFS models and classical approaches and is analyzed in terms of error metrics, runtime and the number of final rules. Forecasting results show that the proposed model is competitive and performs consistently compared with type-1 models, also outperforming other forecasting methods by showing the lowest error metrics and number of final rules.
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