Rule-based Evolving Fuzzy System for Time Series Forecasting: New Perspectives Based on Type-2 Fuzzy Sets Measures Approach

2025-02-05

AI Summary

To address the challenges of modeling high uncertainty and poor generalization in chaotic time series forecasting, this paper proposes an evolutionary type-2 fuzzy system, termed ePL-KRLS-FSM+. It is the first approach to embed a type-2 fuzzy measure into an evolutionary fuzzy modeling framework, integrating participatory learning (PL), kernel recursive least squares (KRLS), and dynamic fuzzification to simultaneously capture structural uncertainty and stochastic disturbances inherent in chaotic systems. Compared with state-of-the-art methods, ePL-KRLS-FSM+ reduces the number of rules by over 30%, significantly enhancing generalization consistency and robustness. Experimental evaluation on the Mackey–Glass and TAIEX benchmark datasets demonstrates superior prediction accuracy and stability—outperforming mainstream type-1 evolutionary fuzzy models and classical forecasting approaches across all error metrics.

Technology Category

Machine Learning: Evolutionary LearningMultiagent Systems: Multiagent Systems under UncertaintySearch and Optimization: Evolutionary Computation

Application Category

Web Mining and Content Analysis: Models for Web evolutionSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Handling uncertainty in time series data
• Improving chaotic data prediction accuracy
• Enhancing evolving fuzzy system performance

Innovation

• Type-2 fuzzy sets
• Participatory learning
• Kernel recursive least squares