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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References
Andonovski G, Muši G, Blaži S,Škrjanc I (2016) On-line evolving cloud-based model identification for production control. IFAC-PapersOnLine 49(5), 79–84. In: 4th IFAC Conference on Intelligent Control and Automation Sciences - ICONS 2016
Angelov P (2010) Evolving Takagi-Sugeno fuzzy systems from streaming data (eTS+). In: Angelov P, Filev DP, Kasabov N (eds) Evolving intelligent systems: methodology and applications. Wiley & IEEE Press, Hoboken, NJ, USA, pp 21–50
Angelov P, Filev D (2004) An approach to online identification of takagi-sugeno fuzzy models. IEEE Trans Syst Man Cybern Part B (Cybern) 34(1):484–498
Angelov P, Filev D (2005) A simplified method for learning evolving takagi-sugeno fuzzy models. In: IEEE international conference on fuzzy systems, pp 1068–1073
Angelov P, Zhou X (2006) Evolving fuzzy systems from data streams in real-time. In: International symposium on evolving fuzzy systems, pp 29–35, Ambleside, UK
Aström K, Wittenmark B (1996) Computer-controlled systems: theory and design, 3rd edn. Prentice Hall, Upper Saddle River
Carpenter G, Grossberg S, Rosen D (1991) A comparative study of general fuzzy min-max neural networks for pattern classification problems. Neural Comput 4:759–771
Davtalab R, Dezfoulian M (2014) Multi-level fuzzy min–max neural network classifier. IEEE Trans Neural Netw 25(3):470–482
Gabrys B, Bargiela A (2000) General fuzzy min–max neural network for clustering and classification. IEEE Trans Neural Netw 11(3):769–783
Hui Peng, Tohru Ozaki, Mori M, Hideo Shioya, Haggan-Ozaki V (2003) Modeling and control of nonlinear nitrogen oxide decomposition process. In: 42nd IEEE International Conference on Decision and Control, vol. 5, pp. 4770–4775 Vol.5. Maui, HW, USA
Jang J (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685
Jang J, Sun C, Mizutani E (1997) Neuro-fuzzy and soft computing. Prentice Hall, Upper Saddle River
Kasabov N, Song Q (2002) Denfis: dynamic evolving neural-fuzzy inference system and its application for time-series prediction. IEEE Trans Fuzzy Syst 10(2):144–154
Kasabov N (2001) Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning. IEEE Trans Syst Man Cybern Part B (Cybern) 31(6):902–918
Khuat T, Gabrys B (2020) A comparative study of general fuzzy min–max neural networks for pattern classification problems. Neural Comput 386:110–125
Kreinovich V, Mouzouris G, Nguyen H (1998) Fuzzy rule based modeling as a universal approximation tool. In: Nguyen H, Sugeno M(eds) Fuzzy systems: modeling and control, pp 135–195. Springer US, Boston, MA
Leite D, Škrjanc I, Gomide F (2020) An overview on evolving systems and learning from stream data. Evol Syst 11(2):181–198
Lemos A, Caminhas W, Gomide F (2011) Multivariable gaussian evolving fuzzy modeling system. IEEE Trans Fuzzy Syst 19(1):91–104
Lemos A, Caminhas W, Gomide F (2013) Evolving intelligent systems: Methods, algorithms and applications. In: Ramanna S, Jain LC, Howlett RJ (eds) Emerging paradigms in machine learning. Springer, Berlin, pp 117–159
Lughofer E (2008) FLEXFIS: a robust incremental learning approach for evolving Takagi-Sugeno fuzzy models. IEEE Trans Fuzzy Syst 16(6):1393–1410
Lughofer E (2011) Evolving fuzzy systems: methodologies, advanced concepts and applications, 1st edn. Springer, Berlin
Luna I, Ballini R (2012) Online estimation of stochastic volatility for asset returns. In: IEEE conference on computational intelligence for financial engineering and economics, pp 1–7
Nandedkar A, Biswas P (2007) A fuzzy min–max neural network classifier with compensatory neuron architecture. IEEE Trans Neural Netw 18(1):42–54
Porto A, Gomide F (2018) Evolving granular fuzzy min–max modeling. In: Barreto GA, Coelho R (eds) Fuzzy information processing. Springer, Cham, pp 37–48
Porto A, Gomide F (2018) Evolving granular fuzzy min–max regression. In: Melin P, Castillo O, Kacprzyk J, Reformat M, Melek W (eds) Fuzzy logic in intelligent system design: theory and applications. Springer, Cham, pp 162–171
Porto A, Gomide F (2019) Granular evolving min-max fuzzy modeling. In: Proceedings of the 11th conference of the european society for fuzzy logic and technology (EUSFLAT 2019), pp 14–21. Atlantis Press
Pratama M, Anavatti S, Angelov P, Lughofer E (2014) PANFIS: a novel incremental learning machine. IEEE Trans Neural Netw Learn Syst 25(1):55–68
Precup R, Angelov P, Costa B, Sayed-Mouchaweh M (2015) An overview on fault diagnosis and nature-inspired optimal control of industrial process applications. Comput Ind 74:75–94
Rubio J (2018) Error convergence analysis of the sufin and csufin. Appl Soft Comput 72:587–595
Shafieezadeh-Abadeh S, Kalhor A (2015) Evolving takagi–sugeno model based on online gustafson-kessel algorithm and kernel recursive least square method. Evol Syst 7(1):1–14
Simpson P (1993) Fuzzy min-max neural networks - part 2: Clustering. IEEE Trans Fuzzy Syst 1(1):32–45
Simpson P (1992) Fuzzy min-max neural networks - part 1. classification. IEEE Trans Neural Netw 3(5):776–786
Škrjanc I, Iglesias JA, Sanchis A, Leite D, Lughofer E, Gomide F (2019) Evolving fuzzy and neuro-fuzzy approaches in clustering, regression, identification, and classification: a survey. Inf Sci 490:344–368
Tagliaferri R, Eleuteri A, Meneganti M, Barone F (2001) Fuzzy min-max neural networks: from classification to regression. Soft Comput 5(1):69–76
Tan J, Quek C (2010) A bcm theory of meta-plasticity for online self-reorganizing fuzzy-associative learning. IEEE Trans Neural Netw 21(6):985–1003
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