In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article


1 Department of Mathematics, Payame Noor University (PNU) Tehran, Iran

2 Department of mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, Iran


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.


Main Subjects

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