In the industrial field, initially these architectures
were applied in modelling non-linear systems and
control engineering. Actually, however these
architectures are used in almost all knowledge areas
where a non-linear function should be approximated.
The actual neuro fuzzy systems application areas are
medicine, economy, control, mechanics, physics,
In this article it is presented, in a summarize way,
the last decade of investigation in the area of the
modelling non-linear functions through neuro-fuzzy
systems. Duo to the vast number of common tools it
continues to be difficult to compare conceptual the
different architectures and to evaluate comparatively
its performances. In generic terms the bibliography
points that neuro fuzzy systems that implement
Takagi-Sugeno type fuzzy inference systems get
accurate results than the approaches that implement
neuro fuzzy inference systems of Mamdani type,
although its bigger computational demanding. As a
guide line for implementing highly efficient neuro-
fuzzy systems they should have the following
characteristics; fast learning; adaptability on-line; to
adjust itself with the aim of obtaining the small
global error possible; small computational
The data acquisition and the pre-processing of input
training data are also very important for the success
of the application of the neuro-fuzzy architectures.
All the neuro-fuzzy architectures use the gradient
descent techniques of for the learning its internal
parameters. For a faster convergence of the
calculation of these parameters it would be
interesting to explore other efficient algorithms of
neural networks learning as the conjugated gradient
search in spite of the backpropagation algorithm.
 A. Abraham and Baikunth Nath, “ Hybrid
Intelligent Systems: A Review of a decade of
Research”, School of Computing and
Information Technology, Faculty of Information
Technology , Monash University, Autralia,
Technical Report Series, 5/2000, 2000, pp. 1-55.
 H. R. Berenji and P. Khedkar, “Learning and
Tuning Fuzzy Logic Controllers through
Reinforcements”, IEEE Transactions on Neural
Networks, 1992, Vol. 3, pp. 724-740.
 E. Czogala and J. Leski, “Neuro-Fuzzy
Intelligent Systems, Studies in Fuzziness and
Soft Computing”, Springer Verlag, Germany,
 M. Figueiredo and F. Gomide; "Design of Fuzzy
Systems Using Neuro-Fuzzy Networks", IEEE
Transactions on Neural Networks, 1999, Vol.
10, no. 4, pp.815-827.
 R. Jang, “Neuro-Fuzzy Modelling:
Architectures, Analysis and Applications”, PhD
Thesis, University of California, Berkley, July
 F. C. Juang, T. Chin Lin, “An On-Line Self
Constructing Neural Fuzzy Inference Network
and its applications”, IEEE Transactions on
Fuzzy Systems, 1998, Vol. 6, pp. 12-32.
 N. Kasabov e Qun Song, “Dynamic Evolving
Fuzzy Neural Networks with ‘m-out-of-n’
Activation Nodes for On-Line Adaptive
Systems”, Technical Report TR99/04,
Departement of Information Science, University
of Otago, 1999.
 B. Kosko, “Neural Networks and Fuzzy
Systems: A Dynamical System Approach to
Machine Intelligence”, Prentice Hall,
Englewood Cliffs, New Jersey, 1992.
 T. C. Lin, C. S. Lee, “Neural Network Based
Fuzzy Logic Control and Decision System”,
IEEE Transactions on Computers, 1991, Vol.
40, no. 12, pp. 1320-1336.
 D. Nauck, F. Klawon; R. Kruse,
“Foundations of Neuro-Fuzzy Systems”, J.
Wiley & Sons, 1997.
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for Function Approximation”, 4
Workshop Fuzzy-Neuro Systems, 1997.
 D. Nauck, “Beyond Neuro-Fuzzy Systems:
Perspectives and Directions”. Proc. of the Third
European Congress on Intelligent Techniques
and Soft Computing (EUFIT’95), Aachen, 1995.
 D. Nauck; “A Fuzzy Perceptron as a
Generic Model for Neuro-Fuzzy Approaches”.
Proc. Fuzzy-Systems, 2
 S. Sulzberger, N. Tschichold e S. Vestli,
“FUN: Optimization of Fuzzy Rule Based
Systems Using Neural Networks”, Proceedings
of IEEE Conference on Neural Networks, San
Francisco, March 1993, pp. 312-316.
 S. Tano, T. Oyama, T. Arnould, “ Deep
Combination of Fuzzy Inference and Neural
Network in Fuzzy Inference”, Fuzzy Sets and
Systems, 1996, Vol. 82(2), pp. 151-160.
 L. A. Zadeh; “Fuzzy Sets”, Information and
Control, 1965, Vol. 8, pp. 338-353.