Abstract
Problem statement: In this study researchers propose a new fuzzy graph theoretic construct called fuzzy metagraph and a new method of clustering finding the similar fuzzy nodes in a fuzzy metagraph. Approach: We adopted T-norms (Triangular Norms) functions and join two or more T-norms to cluster the fuzzy nodes. Fuzzy metagraph is the fuzzyfication of the crisp Metagraphs using fuzzy Generating sets and the fuzzy edge set. We could efficiently analyze the inexact information and investigate the fuzzy relation by applying the fuzzy graph theory. Results: In this study researchers suggesting a new method of clustering of a new graph theoretic structure i.e., fuzzy metagraph and investigated fuzzy metanode and fuzzy metagraph structure. Conclusion/Recommendations: Our future research will be to explore all its useful operations on fuzzy metagraph. We will give the more application based implementation of fuzzy metagraph.
Highlights
An important concept in design of many information processing systems such as transaction processing systems, decision support systems, project management systems and workflow systems is that a graph structure
S = {X, X, E } where X is a fuzzy set on X is known Fuzzy MetaNode and E is a fuzzy edge set { ek, k = 1, 2, 3, ..., K} known as fuzzy edge set
Metagraph is a graphical model that visualized the process of any system and their formal analysis where the analysis will be accomplished by means of an algebraic representation of the graphical structure
Summary
An important concept in design of many information processing systems such as transaction processing systems, decision support systems, project management systems and workflow systems is that a graph structure. In this simplest form a graph consists of set a of elements (or nodes) and a set of ordered and unordered pairs of nodes (or edges). Since a fuzzy node fuzzy graph is complicated to analyze, we would transform it to a simple fuzzy graph by using T-norm family A Graph is defined by a pair G = {X, E} where X = {x1, x2, x3...xn } is a finite set of vertices and E a collection of edges that happen to connect these vertices. The concept of fuzzy graph is the fuzzyfication of the crisp graphs using fuzzy sets
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