Abstract
The authors 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 fuzy 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 "Uesu product", (3) decision analysis of the optimal fuzzy graph in the fuzzy graph sequence. By using the fuzzy node fuzzy graph theory and this new T-norm "Uesu product ", 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.
