### Abstract

Fuzzy rule based systems are important in many control engineering applications. In real problems, often the number of input variables is very high. Time complexity of the fuzzy control algorithms based on either the CRI or Mamdani's technique is too high for real time control. In the real situations, often a few or maximally a few dozen variables dominate the system in a certain area of the state space. This is why an experienced operator is able to control rather well, although overview of all the variables is virtually impossible. The subset of variables changes when the working point changes. Hierarchically structured rule bases are introduced where 'sub-rule bases' contain only subsets of the input variables. Fuzzy partition of the state space is applied for the structuring of the total input universe of discourse. While application of the corresponding sub-rule base in the 'middle' of a fuzzy subset of X is unambiguous, the 'twilight zones', i.e. areas belonging to different subsets to a greater than 0 degree form a serious theoretical problem. The idea of interpolation based on cylindric extensions of the subspaces is introduced and the necessary formulas are presented. Some examples are shown.

Original language | English |
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Title of host publication | 1993 IEEE International Conference on Fuzzy Systems |

Publisher | Publ by IEEE |

Pages | 402-405 |

Number of pages | 4 |

ISBN (Print) | 0780306155 |

Publication status | Published - 1993 |

Event | Second IEEE International Conference on Fuzzy Systems - San Francisco, CA, USA Duration: Mar 28 1993 → Apr 1 1993 |

### Other

Other | Second IEEE International Conference on Fuzzy Systems |
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City | San Francisco, CA, USA |

Period | 3/28/93 → 4/1/93 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*1993 IEEE International Conference on Fuzzy Systems*(pp. 402-405). Publ by IEEE.

**Interpolation in structured fuzzy rule bases.** / Kóczy, L.; Hirota, Kaoru.

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

*1993 IEEE International Conference on Fuzzy Systems.*Publ by IEEE, pp. 402-405, Second IEEE International Conference on Fuzzy Systems, San Francisco, CA, USA, 3/28/93.

}

TY - GEN

T1 - Interpolation in structured fuzzy rule bases

AU - Kóczy, L.

AU - Hirota, Kaoru

PY - 1993

Y1 - 1993

N2 - Fuzzy rule based systems are important in many control engineering applications. In real problems, often the number of input variables is very high. Time complexity of the fuzzy control algorithms based on either the CRI or Mamdani's technique is too high for real time control. In the real situations, often a few or maximally a few dozen variables dominate the system in a certain area of the state space. This is why an experienced operator is able to control rather well, although overview of all the variables is virtually impossible. The subset of variables changes when the working point changes. Hierarchically structured rule bases are introduced where 'sub-rule bases' contain only subsets of the input variables. Fuzzy partition of the state space is applied for the structuring of the total input universe of discourse. While application of the corresponding sub-rule base in the 'middle' of a fuzzy subset of X is unambiguous, the 'twilight zones', i.e. areas belonging to different subsets to a greater than 0 degree form a serious theoretical problem. The idea of interpolation based on cylindric extensions of the subspaces is introduced and the necessary formulas are presented. Some examples are shown.

AB - Fuzzy rule based systems are important in many control engineering applications. In real problems, often the number of input variables is very high. Time complexity of the fuzzy control algorithms based on either the CRI or Mamdani's technique is too high for real time control. In the real situations, often a few or maximally a few dozen variables dominate the system in a certain area of the state space. This is why an experienced operator is able to control rather well, although overview of all the variables is virtually impossible. The subset of variables changes when the working point changes. Hierarchically structured rule bases are introduced where 'sub-rule bases' contain only subsets of the input variables. Fuzzy partition of the state space is applied for the structuring of the total input universe of discourse. While application of the corresponding sub-rule base in the 'middle' of a fuzzy subset of X is unambiguous, the 'twilight zones', i.e. areas belonging to different subsets to a greater than 0 degree form a serious theoretical problem. The idea of interpolation based on cylindric extensions of the subspaces is introduced and the necessary formulas are presented. Some examples are shown.

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M3 - Conference contribution

AN - SCOPUS:0027147492

SN - 0780306155

SP - 402

EP - 405

BT - 1993 IEEE International Conference on Fuzzy Systems

PB - Publ by IEEE

ER -