### Abstract

Fuzzy signature sets (FSigSets) are extensions of the original fuzzy set concept, and also of the Vector Valued Fuzzy Set notion. In a FSigSet rule base the (input) universe of discourse X is mapped into a set of hierarchically grouped fuzzy sets, and each element of X has a 'membership degree' consisting of a rooted tree with membership degrees at each leaf and aggregations at the intermediate vertices. The structure of the tree is identical for each element in the case of homogenous FSigSets, and so are the aggregations, depending only on the position of the vertex. Interpolation in fuzzy rule bases allows the calculation of a conclusion in the output universe Y belonging to an observation even if there are gaps in the rule base and the observation does not intersect with any of the antecedent sets. The key question here is how to determine the degree of similarity, or inversely, the distance, of any observation from the surrounding antecedents of the rules in the base, so that the distance incorporates the information involved with the close connection of the features in the sub-groups, and the aggregations expressing the form of this connection. A solution is proposed, and a pair of numerical examples is presented.

Original language | English |
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Title of host publication | 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781509060344 |

DOIs | |

Publication status | Published - Aug 23 2017 |

Event | 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017 - Naples, Italy Duration: Jul 9 2017 → Jul 12 2017 |

### Other

Other | 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017 |
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Country | Italy |

City | Naples |

Period | 7/9/17 → 7/12/17 |

### Fingerprint

### Keywords

- Distance by aggragation
- Fuzzy rule bases
- Fuzzy rule interpolation
- Fuzzy Signature Sets

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Artificial Intelligence
- Applied Mathematics

### Cite this

*2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017*[8015393] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FUZZ-IEEE.2017.8015393

**Interpolation in homogenous fuzzy signature rule bases.** / Kóczy, L.

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

*2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017.*, 8015393, Institute of Electrical and Electronics Engineers Inc., 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017, Naples, Italy, 7/9/17. https://doi.org/10.1109/FUZZ-IEEE.2017.8015393

}

TY - GEN

T1 - Interpolation in homogenous fuzzy signature rule bases

AU - Kóczy, L.

PY - 2017/8/23

Y1 - 2017/8/23

N2 - Fuzzy signature sets (FSigSets) are extensions of the original fuzzy set concept, and also of the Vector Valued Fuzzy Set notion. In a FSigSet rule base the (input) universe of discourse X is mapped into a set of hierarchically grouped fuzzy sets, and each element of X has a 'membership degree' consisting of a rooted tree with membership degrees at each leaf and aggregations at the intermediate vertices. The structure of the tree is identical for each element in the case of homogenous FSigSets, and so are the aggregations, depending only on the position of the vertex. Interpolation in fuzzy rule bases allows the calculation of a conclusion in the output universe Y belonging to an observation even if there are gaps in the rule base and the observation does not intersect with any of the antecedent sets. The key question here is how to determine the degree of similarity, or inversely, the distance, of any observation from the surrounding antecedents of the rules in the base, so that the distance incorporates the information involved with the close connection of the features in the sub-groups, and the aggregations expressing the form of this connection. A solution is proposed, and a pair of numerical examples is presented.

AB - Fuzzy signature sets (FSigSets) are extensions of the original fuzzy set concept, and also of the Vector Valued Fuzzy Set notion. In a FSigSet rule base the (input) universe of discourse X is mapped into a set of hierarchically grouped fuzzy sets, and each element of X has a 'membership degree' consisting of a rooted tree with membership degrees at each leaf and aggregations at the intermediate vertices. The structure of the tree is identical for each element in the case of homogenous FSigSets, and so are the aggregations, depending only on the position of the vertex. Interpolation in fuzzy rule bases allows the calculation of a conclusion in the output universe Y belonging to an observation even if there are gaps in the rule base and the observation does not intersect with any of the antecedent sets. The key question here is how to determine the degree of similarity, or inversely, the distance, of any observation from the surrounding antecedents of the rules in the base, so that the distance incorporates the information involved with the close connection of the features in the sub-groups, and the aggregations expressing the form of this connection. A solution is proposed, and a pair of numerical examples is presented.

KW - Distance by aggragation

KW - Fuzzy rule bases

KW - Fuzzy rule interpolation

KW - Fuzzy Signature Sets

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U2 - 10.1109/FUZZ-IEEE.2017.8015393

DO - 10.1109/FUZZ-IEEE.2017.8015393

M3 - Conference contribution

BT - 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -