# 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

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topAlimi, 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 -

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