Fuzzy Number-Valued Fuzzy Graph

Graph theory has an important role in the area of applications of networks and clusteringý. ýIn the case of dealing with uncertain dataý, ýwe must utilize ambiguous data such as fuzzy valueý, ýfuzzy interval value or values of fuzzy numberý. ýIn this studyý, ývalues of fuzzy number were usedý. ýInitiallyý, ýwe utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value fuzzy graph on nodes and arcsý. ýIn this studyý, ýsome properties of the graph on fuzzy number-value fuzzy graph were examinedý. ýFirstý, ýwe define the Cartesian productý, ýcompositioný, ýunion 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 definitionsý. ýWe also introduced the notion of homomorphismý, ýweak isomorphism,weak co-isomorphismý, ýisomorphismý, ýcompleteý, ýweak 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.