University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 23 4 2026 08 01 Integrating Fuzzy Logic into Transformer-Based Models for Long-Term Multivariate Time Series Forecasting: A Novel Approach to Fuzzy Positional Encoding 1 20 9972 10.22111/ijfs.2026.54871.9725 EN Mitra Ahmadipor Department of Computer Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. 0009-0001-7895-1397 Masoud Saeed Department of Computer Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran Mahdi Eftekhari Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran Journal Article 2026 02 20 Long-term multivariate time series forecasting is one of the most challenging problems in machine learning. Among the proposed solutions, deep learning networks—particularly transformer-based models—have demonstrated superior performance. However, these models are vulnerable to noise, uncertainty, and abrupt changes, and often lack interpretability. To address these limitations, this study introduces a novel hybrid architecture called FuzzyPE-KAN, which integrates fuzzy logic into the transformer framework. The proposed architecture incorporates: (1) a learnable Gaussian noise-based fuzzy attention mechanism that enhances robustness against noise; (2) a learnable fuzzy positional encoding relying on Gaussian membership functions and multilayer perceptrons to effectively model the inherently vague and graded nature of time; and (3) complete replacement of feed-forward layers with Kolmogorov–Arnold Networks to dramatically reduce the number of parameters and improve interpretability. The proposed architecture was applied to five state-of-the-art baseline models (Transformer, Informer, PatchTST, Crossformer, and iTransformer) and evaluated on eight standard benchmark datasets (ETTh1/2, ETTm1/2, Weather, Electricity, Traffic, and Exchange Rate). Results indicate that the proposed variants achieve an average improvement of 26–49% in Mean Squared Error and 17–29% in Mean Absolute Error across most scenarios compared to the baseline models. The most substantial gains were observed on the Exchange Rate dataset (78% improvement), Weather (71.28%), ETTh2 (76.41%), and ETTm2 (78.66%). This research demonstrates that the simultaneous integration of fuzzy logic and Kolmogorov–Arnold Networks within a transformer architecture not only enhances accuracy and robustness but also elevates model interpretability to a significant level, paving the way for real-world applications in finance, energy, and healthcare domains. https://ijfs.usb.ac.ir/article_9972_776f2b58453662febc67686e6b699c3d.pdf