### Abstract

We could generally analyze the inexact information efficiently and investigate the fuzzy relation by applying the fuzzy graph theory. We would extend the fuzzy graph theory, and propose a fuzzy node fuzzy graph. And we transform it to a fuzzy graph by using T-norm family. In this paper, we would discuss about four subjects, (1) fuzzy node fuzzy graph, (2) new T-norm "quasi logical product", (3) decision analysis of the optimal fuzzy graph in the fuzzy graph sequence {G _{λ} }. By using the fuzzy node fuzzy graph theory and this new T-norm, we could clarify the relational structure of fuzzy information, and by using the decision of an optimal level on a partition tree, we could analyze the clustering relation among nodes. Moreover, we would illustrate its practical effectiveness with the case study concerning sociometry analysis.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 84-91 |

Number of pages | 8 |

Volume | 5179 LNAI |

Edition | PART 3 |

DOIs | |

Publication status | Published - 2008 |

Event | 12th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2008 - Zagreb Duration: 2008 Sep 3 → 2008 Sep 5 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Number | PART 3 |

Volume | 5179 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 12th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2008 |
---|---|

City | Zagreb |

Period | 08/9/3 → 08/9/5 |

### Fingerprint

### Keywords

- Fuzzy node fuzzy graph
- Sociometry analysis
- T-norm

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(PART 3 ed., Vol. 5179 LNAI, pp. 84-91). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5179 LNAI, No. PART 3). https://doi.org/10.1007/978-3-540-85567-5-11

**Structure analysis of fuzzy node fuzzy graph and its application to sociometry analysis.** / Uesu, Hiroaki.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*PART 3 edn, vol. 5179 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 3, vol. 5179 LNAI, pp. 84-91, 12th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2008, Zagreb, 08/9/3. https://doi.org/10.1007/978-3-540-85567-5-11

}

TY - GEN

T1 - Structure analysis of fuzzy node fuzzy graph and its application to sociometry analysis

AU - Uesu, Hiroaki

PY - 2008

Y1 - 2008

N2 - We could generally analyze the inexact information efficiently and investigate the fuzzy relation by applying the fuzzy graph theory. We would extend the fuzzy graph theory, and propose a fuzzy node fuzzy graph. And we transform it to a fuzzy graph by using T-norm family. In this paper, we would discuss about four subjects, (1) fuzzy node fuzzy graph, (2) new T-norm "quasi logical product", (3) decision analysis of the optimal fuzzy graph in the fuzzy graph sequence {G λ }. By using the fuzzy node fuzzy graph theory and this new T-norm, we could clarify the relational structure of fuzzy information, and by using the decision of an optimal level on a partition tree, we could analyze the clustering relation among nodes. Moreover, we would illustrate its practical effectiveness with the case study concerning sociometry analysis.

AB - We could generally analyze the inexact information efficiently and investigate the fuzzy relation by applying the fuzzy graph theory. We would extend the fuzzy graph theory, and propose a fuzzy node fuzzy graph. And we transform it to a fuzzy graph by using T-norm family. In this paper, we would discuss about four subjects, (1) fuzzy node fuzzy graph, (2) new T-norm "quasi logical product", (3) decision analysis of the optimal fuzzy graph in the fuzzy graph sequence {G λ }. By using the fuzzy node fuzzy graph theory and this new T-norm, we could clarify the relational structure of fuzzy information, and by using the decision of an optimal level on a partition tree, we could analyze the clustering relation among nodes. Moreover, we would illustrate its practical effectiveness with the case study concerning sociometry analysis.

KW - Fuzzy node fuzzy graph

KW - Sociometry analysis

KW - T-norm

UR - http://www.scopus.com/inward/record.url?scp=57749197554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57749197554&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85567-5-11

DO - 10.1007/978-3-540-85567-5-11

M3 - Conference contribution

AN - SCOPUS:57749197554

SN - 3540855661

SN - 9783540855668

VL - 5179 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 84

EP - 91

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -