Relational structure analysis of fuzzy graph and its application: For analyzing fuzzy data of human relation

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.