Fuzzy Number-Valued Fuzzy Graph

Graph theory has an important role in the area of applications of networks and clustering‎. ‎In the case of dealing with uncertain data‎, ‎we must utilize ambiguous data such as fuzzy value‎, ‎fuzzy interval value or values of fuzzy number‎. ‎In this study‎, ‎values of fuzzy number were used‎. ‎Initially‎, ‎we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value fuzzy graph on nodes and arcs‎. ‎In this study‎, ‎some properties of the graph on fuzzy number-value fuzzy graph were examined‎. ‎First‎, ‎we define the Cartesian product‎, ‎composition‎, ‎union and join operators on fuzzy number-value fuzzy graphs and then prove some of their properties and and give some examples for every one of definitions‎. ‎We also introduced the notion of homomorphism‎, ‎weak isomorphism,weak co-isomorphism‎, ‎isomorphism‎, ‎complete‎, ‎weak complete and compliment on the fuzzy number fuzzy graphs and prove some of their properties and also present some examples for every one of them.

Keywords:

Fuzzy numbers‎ , ‎Relation‎ , ‎Fuzzy relation‎ , ‎Graph‎ , ‎Fuzzy graph