### Abstract

Generally, we could efficiently analyze the inexact information 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. Since a fuzzy node fuzzy graph is complicated to analyze, we would transform it to a simple fuzzy graph by using T-norm family. In addition, to investigate the relations between nodes, we would define the fuzzy contingency table. In this paper, we would discuss about five subjects, (1) new T-norm "Uesu product", (2) fuzzy node fuzzy graph, (3) fuzzy contingency table, (4) entropy measures of fuzziness and (5) decision analysis of the optimal fuzzy graph G_{λ0} in the fuzzy graph sequence {G_{λ}}. By using the fuzzy node fuzzy graph theory, the new T-norm and the fuzzy contingency table, we could clarify the relational structure of fuzzy information. According to the decision method in section 2, we could find the optimal fuzzy graph G_{λ0} in the fuzzy graph sequence {G _{λ}}, and clarify the structural feature of the fuzzy node fuzzy graph. 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 | Proceedings - 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012 |

Pages | 301-306 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2012 |

Event | 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012 - Kaohsiung City Duration: 2012 Sep 26 → 2012 Sep 28 |

### Other

Other | 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012 |
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City | Kaohsiung City |

Period | 12/9/26 → 12/9/28 |

### Fingerprint

### Keywords

- fuzzy node fuzzy graph
- sociometry analysis
- T-norm
- T-norm family

### ASJC Scopus subject areas

- Bioengineering
- Software

### Cite this

*Proceedings - 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012*(pp. 301-306). [6337682] https://doi.org/10.1109/IBICA.2012.32

**Analysis of similarity coefficients in fuzzy node fuzzy graph and its application.** / Uesu, Hiroaki; Kanagawa, Shuya; Shinkai, Kimiaki; Nagashima, Kenichi.

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

*Proceedings - 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012.*, 6337682, pp. 301-306, 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012, Kaohsiung City, 12/9/26. https://doi.org/10.1109/IBICA.2012.32

}

TY - GEN

T1 - Analysis of similarity coefficients in fuzzy node fuzzy graph and its application

AU - Uesu, Hiroaki

AU - Kanagawa, Shuya

AU - Shinkai, Kimiaki

AU - Nagashima, Kenichi

PY - 2012

Y1 - 2012

N2 - Generally, we could efficiently analyze the inexact information 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. Since a fuzzy node fuzzy graph is complicated to analyze, we would transform it to a simple fuzzy graph by using T-norm family. In addition, to investigate the relations between nodes, we would define the fuzzy contingency table. In this paper, we would discuss about five subjects, (1) new T-norm "Uesu product", (2) fuzzy node fuzzy graph, (3) fuzzy contingency table, (4) entropy measures of fuzziness and (5) decision analysis of the optimal fuzzy graph Gλ0 in the fuzzy graph sequence {Gλ}. By using the fuzzy node fuzzy graph theory, the new T-norm and the fuzzy contingency table, we could clarify the relational structure of fuzzy information. According to the decision method in section 2, we could find the optimal fuzzy graph Gλ0 in the fuzzy graph sequence {G λ}, and clarify the structural feature of the fuzzy node fuzzy graph. Moreover, we would illustrate its practical effectiveness with the case study concerning sociometry analysis.

AB - Generally, we could efficiently analyze the inexact information 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. Since a fuzzy node fuzzy graph is complicated to analyze, we would transform it to a simple fuzzy graph by using T-norm family. In addition, to investigate the relations between nodes, we would define the fuzzy contingency table. In this paper, we would discuss about five subjects, (1) new T-norm "Uesu product", (2) fuzzy node fuzzy graph, (3) fuzzy contingency table, (4) entropy measures of fuzziness and (5) decision analysis of the optimal fuzzy graph Gλ0 in the fuzzy graph sequence {Gλ}. By using the fuzzy node fuzzy graph theory, the new T-norm and the fuzzy contingency table, we could clarify the relational structure of fuzzy information. According to the decision method in section 2, we could find the optimal fuzzy graph Gλ0 in the fuzzy graph sequence {G λ}, and clarify the structural feature of the fuzzy node fuzzy graph. 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

KW - T-norm family

UR - http://www.scopus.com/inward/record.url?scp=84870706207&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870706207&partnerID=8YFLogxK

U2 - 10.1109/IBICA.2012.32

DO - 10.1109/IBICA.2012.32

M3 - Conference contribution

AN - SCOPUS:84870706207

SP - 301

EP - 306

BT - Proceedings - 3rd International Conference on Innovations in Bio-Inspired Computing and Applications, IBICA 2012

ER -