Neo-fuzzy neuron learning using backfitting algorithm
- 543 Downloads
This paper proposes an automatic and simple approach to design a neo-fuzzy neuron for identification purposes. The proposed approach uses the backfitting algorithm to learn multiple univariate additive models, where each additive model is a zero-order T-S fuzzy system which is a function of one input variable, and there is one additive model for each input variable. The multiple zero-order T-S fuzzy models constitute a neo-fuzzy neuron. The structure of the model used in this paper allows to have results with good interpretability and accuracy. To validate and demonstrate the performance and effectiveness of the proposed approach, it is applied on 10 benchmark data sets and compared with the extreme learning machine (ELM), support vector regression (SVR) algorithms, and two algorithms for design neo-fuzzy neuron systems, an adaptive learning algorithm for a neo-fuzzy neuron systems (ALNFN), and a fuzzy Kolmogorov’s network (FKN). A statistical paired t test analysis is also presented to compare the proposed approach with ELM, SVR, ALNFN, and FKN with the aim to see whether the results of the proposed approach are statistically different from ELM, SVR, ALNFN, and FKN. The results indicate that the proposed approach outperforms ELM and FKN in all data sets and outperforms SVR and ALNFN in almost all data sets that they were statistically different in almost all data sets and that in most data sets the number of fuzzy rules selected by cross-validation was small obtaining a model with a small complexity and good interpretability capability.
KeywordsFuzzy identification Neo-fuzzy neuron learning Zero-order T-S fuzzy system Additive models Backfitting algorithm
Jérôme Mendes, Francisco Souza, and Saeid Rastegar have been supported by Fundação para a Ciência e a Tecnologia (FCT) under grants SFRH/BPD/99708/2014, SFRH/BPD/112774/2015, and SFRH/BD/89186/2012, respectively.
Compliance with ethical standards
Conflict of interest
We declare that no conflict of interest exits in the submission of this manuscript, and the manuscript is approved by all authors for publication.
- 1.Bodyanskiy Y, Kokshenev I, Kolodyazhniy V (2003) An adaptive learning algorithm for a neo-fuzzy neuron. In: Proceedings of the 3rd conference of the European society for fuzzy logic and technology (EUSFLAT 2003), pp 375–379Google Scholar
- 5.Chang CC, Lin CJ (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol 2:27:1–27:27. Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
- 11.Delve repository of University of Toronto. http://www.cs.toronto.edu/~delve/data/datasets.html
- 13.Hu Z, Bodyanskiy YV, Tyshchenko OK, Boiko OO (2016) Adaptive forecasting of non-stationary nonlinear time series based on the evolving weighted neuro-neo-fuzzy-ANARX-model. Int J Inf Technol Comput Sci (IJITCS) 8(10):1–10Google Scholar
- 14.Hu Z, Bodyanskiy YV, Tyshchenko OK, Boiko OO (2016) An evolving cascade system based on a set of neo-fuzzy nodes. Int J Intell Syst Appl (IJISA) 8(9):1–7Google Scholar
- 20.Lichman M (2013) UCI machine learning repository. http://archive.ics.uci.edu/ml
- 23.Miki T, Yamakawa T (1999) Analog implementation of neo-fuzzy neuron and its on-board learning. In: Mastorakis N E (ed) Computational Intelligence and Applications. WSES Press, Piraeus, Greece. pp 144–149Google Scholar
- 30.Torgo L. Regression datasets. http://www.dcc.fc.up.pt/~ltorgo/Regression/DataSets.html
- 36.Yamakawa T, Uchino E, Miki T, Kusanag H (1992) A neo-fuzzy neuron and its applications to system identification and prediction of the system behavior. In: Proceedings of the 2nd international conference on fuzzy logic and neural networks. Iizuka, pp 477–483Google Scholar
- 37.Ying H (1997) General Miso Takagi-Sugeno fuzzy systems with simplified linear rule consequent as universal approximators for control and modeling applications. In: IEEE international conference on systems, man, and cybernetics. Computational cybernetics and simulation, vol 2, pp 1335–1340Google Scholar