## 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 |

## 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