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 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.
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