Hassan, Iman Yakzan AbouKasabov, Nikola K2025-05-192025-05-192024-11-16Evolving Systems, ISSN: 1868-6478 (Print); 1868-6486 (Online), Springer Science and Business Media LLC, 16(1), 3-. doi: 10.1007/s12530-024-09630-41868-64781868-6486http://hdl.handle.net/10292/19233This paper introduces a novel framework, called here 'NeuDen' for the integration of neuromorphic evolving spiking neural networks (eSNN), that learn efficiently multiple time series in their temporal association and interaction as spike based information, with dynamic evolving neuro-fuzzy systems (deNFS), that learn incrementally extracted from the eSNN frequency-based (rate-based) feature vectors, to predict future time-series values and to produce interpretable fuzzy rules. The new framework aims to make the best out of the dominant characteristics of the two types of models. First, spike-time-dependent plasticity (STDP) learning is used in SNN to learn temporal interaction between multiple time series, connected to a dynamic eSNN (deSNN) as a regressor/classifier. Then, frequency-based feature-vectors are extracted from the trained deSNN for further learning, fuzzy inference and rule extraction in a deNFS, here exemplified by a popular DENFIS model, resulting in an accurate prediction results and explainable dynamic fuzzy rules. The NeuDen, framework and model, overcomes both the explainability problems of eSNN and the limitations of deNFS to model multiple streaming time series in their temporal interaction. NeuDen surpasses both deSNN and DENFIS by providing multiple regression models and achieving higher accuracy. NeuDen is demonstrated on benchmark data and on financial and economic time series, achieving from 3 to 100 times smaller RMSE when compared with other evolving systems. The proposed framework opens a new direction for the development of more efficient evolving systems by integrating eSNN with other Explainable Artificial Intelligence (XAI) techniques, such as other neuro-fuzzy systems, deep neural networks, and quantum classifiers for specific applications.© 2024 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s12530-024-09630-44605 Data Management and Data Science46 Information and Computing Sciences4602 Artificial Intelligence4611 Machine LearningMachine Learning and Artificial IntelligenceBioengineering4007 Control engineering, mechatronics and robotics4602 Artificial intelligence4611 Machine learningJournal ArticleOpenAccess10.1007/s12530-024-09630-4