### Abstract

Fuzzy control is at present still the most important area of real applications for fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, modeling a system by If . . . then rules. In the classical approaches it is necessary that observations on the actual state of the system partly match (fire) one or several rules in the model (fired rules), and the conclusion is calculated by the evaluation of the degrees of matching and the fired rules. Interpolation helps reducing the complexity as it allows rule bases with gaps. Various interpolation approaches are shown. It is proposed that dense rule bases should be reduced so that only the minimal necessary number of rules remain still containing the essential information in the original base, and all other rules are replaced by the interpolation algorithm that however can recover them with a certain accuracy prescribed before reduction. The interpolation method used for demonstration is the Lagrange-method supplying the best fitting minimal degree polynomial. The paper concentrates on the reduction technique that is rather independent from the style of the interpolation model, but cannot be given in the form of a tractable algorithm. An example is shown to illustrate possible results and difficulties with the method.

Original language | English |
---|---|

Pages (from-to) | 14-25 |

Number of pages | 12 |

Journal | IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics |

Volume | 27 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1997 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Artificial Intelligence
- Human-Computer Interaction

### Cite this

**Size reduction by interpolation in fuzzy rule bases.** / Kóczy, L.; Hirota, Kaoru.

Research output: Contribution to journal › Article

*IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics*, vol. 27, no. 1, pp. 14-25. https://doi.org/10.1109/3477.552182

}

TY - JOUR

T1 - Size reduction by interpolation in fuzzy rule bases

AU - Kóczy, L.

AU - Hirota, Kaoru

PY - 1997

Y1 - 1997

N2 - Fuzzy control is at present still the most important area of real applications for fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, modeling a system by If . . . then rules. In the classical approaches it is necessary that observations on the actual state of the system partly match (fire) one or several rules in the model (fired rules), and the conclusion is calculated by the evaluation of the degrees of matching and the fired rules. Interpolation helps reducing the complexity as it allows rule bases with gaps. Various interpolation approaches are shown. It is proposed that dense rule bases should be reduced so that only the minimal necessary number of rules remain still containing the essential information in the original base, and all other rules are replaced by the interpolation algorithm that however can recover them with a certain accuracy prescribed before reduction. The interpolation method used for demonstration is the Lagrange-method supplying the best fitting minimal degree polynomial. The paper concentrates on the reduction technique that is rather independent from the style of the interpolation model, but cannot be given in the form of a tractable algorithm. An example is shown to illustrate possible results and difficulties with the method.

AB - Fuzzy control is at present still the most important area of real applications for fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, modeling a system by If . . . then rules. In the classical approaches it is necessary that observations on the actual state of the system partly match (fire) one or several rules in the model (fired rules), and the conclusion is calculated by the evaluation of the degrees of matching and the fired rules. Interpolation helps reducing the complexity as it allows rule bases with gaps. Various interpolation approaches are shown. It is proposed that dense rule bases should be reduced so that only the minimal necessary number of rules remain still containing the essential information in the original base, and all other rules are replaced by the interpolation algorithm that however can recover them with a certain accuracy prescribed before reduction. The interpolation method used for demonstration is the Lagrange-method supplying the best fitting minimal degree polynomial. The paper concentrates on the reduction technique that is rather independent from the style of the interpolation model, but cannot be given in the form of a tractable algorithm. An example is shown to illustrate possible results and difficulties with the method.

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U2 - 10.1109/3477.552182

DO - 10.1109/3477.552182

M3 - Article

VL - 27

SP - 14

EP - 25

JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

SN - 1083-4419

IS - 1

ER -