### Abstract

We show in this paper that the set of functions, consisting of polytopic or TS models constructed from finite number of components, is nowhere dense in the approximation model space, if that is defined as a subset of continuous functions. This topological notion means that the given set of functions lies "almost discretely" in the space of approximated functions. As a consequence, by means of the mentioned models we cannot approximate in general continuous functions arbitrarily well, if the number of components are restricted. Thus, only functions satisfying certain conditions can be approximated by such models, or alternatively, we need unbounded number of components. The possible solutions are outlined in the paper.

Original language | English |
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Title of host publication | Proceedings of the IEEE International Conference on Systems, Man and Cybernetics |

Editors | A. El Kamel, K. Mellouli, P. Borne |

Pages | 150-153 |

Number of pages | 4 |

Volume | 7 |

Publication status | Published - 2002 |

Event | 2002 IEEE International Conference on Systems, Man and Cybernetics - Yasmine Hammamet, Tunisia Duration: Oct 6 2002 → Oct 9 2002 |

### Other

Other | 2002 IEEE International Conference on Systems, Man and Cybernetics |
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Country | Tunisia |

City | Yasmine Hammamet |

Period | 10/6/02 → 10/9/02 |

### Fingerprint

### Keywords

- Function approximation
- Polytopic model
- TS model

### ASJC Scopus subject areas

- Hardware and Architecture
- Control and Systems Engineering

### Cite this

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics*(Vol. 7, pp. 150-153)

**Polytopic and TS models are nowhere dense in the approximation model space.** / Tikk, D.; Baranyi, P.; Patton, Ron J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE International Conference on Systems, Man and Cybernetics.*vol. 7, pp. 150-153, 2002 IEEE International Conference on Systems, Man and Cybernetics, Yasmine Hammamet, Tunisia, 10/6/02.

}

TY - GEN

T1 - Polytopic and TS models are nowhere dense in the approximation model space

AU - Tikk, D.

AU - Baranyi, P.

AU - Patton, Ron J.

PY - 2002

Y1 - 2002

N2 - We show in this paper that the set of functions, consisting of polytopic or TS models constructed from finite number of components, is nowhere dense in the approximation model space, if that is defined as a subset of continuous functions. This topological notion means that the given set of functions lies "almost discretely" in the space of approximated functions. As a consequence, by means of the mentioned models we cannot approximate in general continuous functions arbitrarily well, if the number of components are restricted. Thus, only functions satisfying certain conditions can be approximated by such models, or alternatively, we need unbounded number of components. The possible solutions are outlined in the paper.

AB - We show in this paper that the set of functions, consisting of polytopic or TS models constructed from finite number of components, is nowhere dense in the approximation model space, if that is defined as a subset of continuous functions. This topological notion means that the given set of functions lies "almost discretely" in the space of approximated functions. As a consequence, by means of the mentioned models we cannot approximate in general continuous functions arbitrarily well, if the number of components are restricted. Thus, only functions satisfying certain conditions can be approximated by such models, or alternatively, we need unbounded number of components. The possible solutions are outlined in the paper.

KW - Function approximation

KW - Polytopic model

KW - TS model

UR - http://www.scopus.com/inward/record.url?scp=0037731725&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037731725&partnerID=8YFLogxK

M3 - Conference contribution

VL - 7

SP - 150

EP - 153

BT - Proceedings of the IEEE International Conference on Systems, Man and Cybernetics

A2 - El Kamel, A.

A2 - Mellouli, K.

A2 - Borne, P.

ER -