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Biquarterly Control and Optimization in applied Mathematics
Articles in Press
Current Issue
Journal Archive
Volume Volume 1 (2016)
Issue Issue 2
Issue Issue 1

Fuzzy Number-Valued Fuzzy Graph

Article 6, Volume 1, Issue 2, Autumn 2016, Page 77-86  XML PDF (465 K)
Document Type: بنیادی - نظری
Authors
siyamak firouzian 1 ; mohamad adabitabar firozja2
1Department of Mathematics, Payame Noor University (PNU) Tehran, Iran
2Department of mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, Iran
Abstract
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
Main Subjects
Mathematical Modeling
Statistics
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