Optimal Fuzzy Graph Based on Fuzzy Node Fuzzy Graph Analysis

Abstract

We 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 firstly propose a fuzzy node fuzzy graph. Secondly, 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 ""quasi logical product"", (3) decision analysis of the optimal level in a partition tree, (4) 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, 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.