### Abstract

Generally, we could efficiently analyze the inexact information and investigate the fuzzy relation by applying the fuzzy graph theory^{[1]}. 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) decision analysis of the optimal fuzzy graph G_{λ0} in the fuzzy graph sequence {G_{λ}} and (5) its application to sociometry analysis. 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_{0} 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 | IEEE International Conference on Fuzzy Systems |

Pages | 1593-1597 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

Event | 2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011 - Taipei Duration: 2011 Jun 27 → 2011 Jun 30 |

### Other

Other | 2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011 |
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City | Taipei |

Period | 11/6/27 → 11/6/30 |

### Fingerprint

### Keywords

- contingency table
- fuzzy node fuzzy graph
- optimal fuzzy graph
- sociometry analysis
- T-norm

### ASJC Scopus subject areas

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

### Cite this

*IEEE International Conference on Fuzzy Systems*(pp. 1593-1597). [6007573] https://doi.org/10.1109/FUZZY.2011.6007573

**Relational structure analysis of fuzzy graph and its application : For analyzing fuzzy data of human relation.** / Uesu, Hiroaki; Nagashima, Kenichi; Chung, Hsunhsun; Tsuda, Ei.

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

*IEEE International Conference on Fuzzy Systems.*, 6007573, pp. 1593-1597, 2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011, Taipei, 11/6/27. https://doi.org/10.1109/FUZZY.2011.6007573

}

TY - GEN

T1 - Relational structure analysis of fuzzy graph and its application

T2 - For analyzing fuzzy data of human relation

AU - Uesu, Hiroaki

AU - Nagashima, Kenichi

AU - Chung, Hsunhsun

AU - Tsuda, Ei

PY - 2011

Y1 - 2011

N2 - Generally, we could efficiently analyze the inexact information and investigate the fuzzy relation by applying the fuzzy graph theory[1]. 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) decision analysis of the optimal fuzzy graph Gλ0 in the fuzzy graph sequence {Gλ} and (5) its application to sociometry analysis. 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 G0 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[1]. 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) decision analysis of the optimal fuzzy graph Gλ0 in the fuzzy graph sequence {Gλ} and (5) its application to sociometry analysis. 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 G0 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 - contingency table

KW - fuzzy node fuzzy graph

KW - optimal fuzzy graph

KW - sociometry analysis

KW - T-norm

UR - http://www.scopus.com/inward/record.url?scp=80053056952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053056952&partnerID=8YFLogxK

U2 - 10.1109/FUZZY.2011.6007573

DO - 10.1109/FUZZY.2011.6007573

M3 - Conference contribution

AN - SCOPUS:80053056952

SN - 9781424473175

SP - 1593

EP - 1597

BT - IEEE International Conference on Fuzzy Systems

ER -