### Abstract

The classical approaches in fuzzy control (Zadeh and Mamdani) deal with dense rule bases. When this is not the case, i.e. in sparse rule bases one has to choose another method. Fuzzy rule interpolation (proposed first by Koczy and Hirota) offers a possibility to construct fuzzy controllers (KH-controllers) under such conditions. On the other hand there is a great demand in finding a stable interpolating method among researchers in the field of mathematical (numerical) analysis. We would like to approximate a function that is only known at distinct points (e.g. where it can be measured). In practice the stability of these method is a natural requirement. The classical methods generally do not fulfill this condition, only with some strong restriction concerning the measured points. If we neglect the classical form of the approximating function (polynomial and trigonometrical), we can get better behaving approximation. The function of the KH-controller approximating function (which is a simple fractional function) fulfills the stability condition.

Original language | English |
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Title of host publication | IEEE International Conference on Fuzzy Systems |

Publisher | IEEE |

Pages | 93-98 |

Number of pages | 6 |

Volume | 1 |

Publication status | Published - 1997 |

Event | Proceedings of the 1997 6th IEEE International Conference on Fussy Systems, FUZZ-IEEE'97. Part 1 (of 3) - Barcelona, Spain Duration: Jul 1 1997 → Jul 5 1997 |

### Other

Other | Proceedings of the 1997 6th IEEE International Conference on Fussy Systems, FUZZ-IEEE'97. Part 1 (of 3) |
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City | Barcelona, Spain |

Period | 7/1/97 → 7/5/97 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality

### Cite this

*IEEE International Conference on Fuzzy Systems*(Vol. 1, pp. 93-98). IEEE.

**Stability of interpolative fuzzy KH-controllers.** / Joo, Istvan; Kóczy, L.; Tikk, D.; Várlaki, P.

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

*IEEE International Conference on Fuzzy Systems.*vol. 1, IEEE, pp. 93-98, Proceedings of the 1997 6th IEEE International Conference on Fussy Systems, FUZZ-IEEE'97. Part 1 (of 3), Barcelona, Spain, 7/1/97.

}

TY - GEN

T1 - Stability of interpolative fuzzy KH-controllers

AU - Joo, Istvan

AU - Kóczy, L.

AU - Tikk, D.

AU - Várlaki, P.

PY - 1997

Y1 - 1997

N2 - The classical approaches in fuzzy control (Zadeh and Mamdani) deal with dense rule bases. When this is not the case, i.e. in sparse rule bases one has to choose another method. Fuzzy rule interpolation (proposed first by Koczy and Hirota) offers a possibility to construct fuzzy controllers (KH-controllers) under such conditions. On the other hand there is a great demand in finding a stable interpolating method among researchers in the field of mathematical (numerical) analysis. We would like to approximate a function that is only known at distinct points (e.g. where it can be measured). In practice the stability of these method is a natural requirement. The classical methods generally do not fulfill this condition, only with some strong restriction concerning the measured points. If we neglect the classical form of the approximating function (polynomial and trigonometrical), we can get better behaving approximation. The function of the KH-controller approximating function (which is a simple fractional function) fulfills the stability condition.

AB - The classical approaches in fuzzy control (Zadeh and Mamdani) deal with dense rule bases. When this is not the case, i.e. in sparse rule bases one has to choose another method. Fuzzy rule interpolation (proposed first by Koczy and Hirota) offers a possibility to construct fuzzy controllers (KH-controllers) under such conditions. On the other hand there is a great demand in finding a stable interpolating method among researchers in the field of mathematical (numerical) analysis. We would like to approximate a function that is only known at distinct points (e.g. where it can be measured). In practice the stability of these method is a natural requirement. The classical methods generally do not fulfill this condition, only with some strong restriction concerning the measured points. If we neglect the classical form of the approximating function (polynomial and trigonometrical), we can get better behaving approximation. The function of the KH-controller approximating function (which is a simple fractional function) fulfills the stability condition.

UR - http://www.scopus.com/inward/record.url?scp=0030718092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030718092&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0030718092

VL - 1

SP - 93

EP - 98

BT - IEEE International Conference on Fuzzy Systems

PB - IEEE

ER -