Neo-fuzzy neuron learning using backfitting algorithm

  • Jérôme MendesEmail author
  • Francisco Souza
  • Rui Araújo
  • Saeid Rastegar
Original Article


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.


Fuzzy 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.


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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Jérôme Mendes
    • 1
    Email author
  • Francisco Souza
    • 1
  • Rui Araújo
    • 1
  • Saeid Rastegar
    • 1
  1. 1.Department of Electrical and Computer Engineering (DEEC-UC), Institute of Systems and Robotics (ISR-UC)University of Coimbra, Pólo IICoimbraPortugal

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