Abstract
The paper introduces an evolving hyperbox granulation and functional fuzzy rule-based modeling approach within the framework of min–max learning. Evolving hyperbox fuzzy modeling is a per sample, one pass recursive learning mechanism suitable for on-line and real-time adaptive stream data-based modeling. Granulation of the data space is done as data are input, and undergoes continuous adaptation using expansion, contraction, and redundancy avoidance operations to encounter the number of hyperboxes that best matches the data, adjusting the granular structure of the data space whenever necessary. A functional fuzzy rule with Gaussian membership function in the rule antecedent, and affine function in the rule consequent is assigned to each hyperbox. The granular rule-based model developed during learning is transparent, understandable and easily interpretable. Hyperbox fuzzy modeling scales up well for data intensive applications because the models it develops are parsimonious, and min–max learning operates primarily with additions and comparisons. The use of evolving hyperbox fuzzy modeling approach to forecast a stock market index using actual time series data, to identify a synthetic high dimensional nonlinear system, and to predict a chaotic time series shows that it outperforms several state of the art evolving modeling counterparts.
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Acknowledgements
The authors are grateful to the Brazilian National Council for Scientific and Technological Development (CNPq) for a fellowship, and Grant 302467/2019-0, respectively. They also acknowledge the editors and the anonymous reviewers for the comments and suggestions that helped to improve the paper.
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Porto, A., Gomide, F. Evolving hyperbox fuzzy modeling. Evolving Systems 13, 423–434 (2022). https://doi.org/10.1007/s12530-022-09422-8
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DOI: https://doi.org/10.1007/s12530-022-09422-8