Beta fuzzy logic systems approximation properties in the mimo case

Adel Alimi; Radhia Hassine; Mohamed Selmi

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 2, page 225-238
  • ISSN: 1641-876X

Abstract

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Many researches have been interested in the approximation properties of Fuzzy Logic Systems (FLS), which, like neural networks, can be seen as approximation schemes. Almost all of them tackled the Mamdani fuzzy model, which was shown to have many interesting approximation features. However, only in few cases the Sugeno fuzzy model was considered. In this paper, we are interested in the zero-order Multi-Input-Multi-Output (MIMO) Sugeno fuzzy model with Beta membership functions. This leads to Beta Fuzzy Logic Systems (BFLS). We show that BFLSs are universal approximators. We also prove that they possess the best approximation property and the interpolation characteristic.

How to cite

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Alimi, Adel, Hassine, Radhia, and Selmi, Mohamed. "Beta fuzzy logic systems approximation properties in the mimo case." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 225-238. <http://eudml.org/doc/207639>.

@article{Alimi2003,
abstract = {Many researches have been interested in the approximation properties of Fuzzy Logic Systems (FLS), which, like neural networks, can be seen as approximation schemes. Almost all of them tackled the Mamdani fuzzy model, which was shown to have many interesting approximation features. However, only in few cases the Sugeno fuzzy model was considered. In this paper, we are interested in the zero-order Multi-Input-Multi-Output (MIMO) Sugeno fuzzy model with Beta membership functions. This leads to Beta Fuzzy Logic Systems (BFLS). We show that BFLSs are universal approximators. We also prove that they possess the best approximation property and the interpolation characteristic.},
author = {Alimi, Adel, Hassine, Radhia, Selmi, Mohamed},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {interpolation property; Sugeno fuzzy model; universal approximation property; Beta function; best approximation property; MIMO systems; design of fuzzy controllers; optimization of membership functions; triangular membership functions; Kalman filter},
language = {eng},
number = {2},
pages = {225-238},
title = {Beta fuzzy logic systems approximation properties in the mimo case},
url = {http://eudml.org/doc/207639},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Alimi, Adel
AU - Hassine, Radhia
AU - Selmi, Mohamed
TI - Beta fuzzy logic systems approximation properties in the mimo case
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 2
SP - 225
EP - 238
AB - Many researches have been interested in the approximation properties of Fuzzy Logic Systems (FLS), which, like neural networks, can be seen as approximation schemes. Almost all of them tackled the Mamdani fuzzy model, which was shown to have many interesting approximation features. However, only in few cases the Sugeno fuzzy model was considered. In this paper, we are interested in the zero-order Multi-Input-Multi-Output (MIMO) Sugeno fuzzy model with Beta membership functions. This leads to Beta Fuzzy Logic Systems (BFLS). We show that BFLSs are universal approximators. We also prove that they possess the best approximation property and the interpolation characteristic.
LA - eng
KW - interpolation property; Sugeno fuzzy model; universal approximation property; Beta function; best approximation property; MIMO systems; design of fuzzy controllers; optimization of membership functions; triangular membership functions; Kalman filter
UR - http://eudml.org/doc/207639
ER -

References

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