Isomorphic Property and Some Operations of Picture Fuzzy Graphs

Abstract

In this paper picture fuzzy graph has shown more advantage in handling vagueness and uncertainty than fuzzy set. We have applied concept of picture fuzzy set to fuzzy set. Picture fuzzy graph is generalization of fuzzy graph. The concept of picture fuzzy graph has discussed here. In this paper complement and Ring sum operation of picture fuzzy graphs has discussed isomorphic property of picture fuzzy graphs. We have used picture Fuzzy graph play important role in representation of many uncertain decision making problem in daily life since Picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, e.g. number theory, coding theory, cryptography, computer science, operation research, also we are using certain concepts of bipolar fuzzy directed hypergraphs Finally we have proved the Ring sum of two picture fuzzy graphs is also a picture fuzzy graph.