A Novel Fuzzy Time Series Method Based on Dynamic Ridge Polynomial Neural Network With Penalty Term and Fuzzy Clustering Analysis

Due to the limitations of traditional time series models in handling semantic values and small-scale data, the concept of fuzzy time series forecasting has been introduced in academia. This model performs exceptionally well on fuzzy datasets, prompting many researchers to delve into this field. The general process of fuzzy time series analysis consists of the following stages: 1) domain partitioning; 2) formation of fuzzy sets for fuzzifying data; 3) extraction of fuzzy relationships; and 4) forecasting and defuzzification. Domain partitioning and the extraction of fuzzy relationships have always been crucial components of fuzzy time series forecasting. Until now, neural networks have been less commonly applied in the step of determining fuzzy relationships. Some researchers have attempted to utilize the Pi-Sigma neural network for the determination of fuzzy relationships. However, due to the fixed network structure that Pi-Sigma neural networks cannot adapt to changes over time, it has been indicated that it is not a universal approximator. Its performance in handling complex dynamic time series has not been satisfactory. In this paper, we utilize Fuzzy C-Means Clustering (FCM) to partition the domain into unequal-length intervals and employ a high-order dynamic neural network known as Dynamic Ridge Polynomial Neural Network (DRPNN). This network can start with a small basic structure and gradually increase its structural complexity as learning progresses until it achieves the required task accuracy, which demonstrates superior performance in handling complex time series data. During the training process, we employ a novel gradient descent training algorithm with penalty terms. We conducted tests on this algorithm using nine real-world datasets and performed Friedman and Bonferroni-Dunn tests to ensure that the proposed algorithm exhibits statistical performance superiority compared to other methods in the literature. The results indicate that our algorithm outperforms those from other studies.