## 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 |

## Keywords

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

## ASJC Scopus subject areas

- Bioengineering
- Software