Certain Types of Interval-Valued Fuzzy Graphs

Muhammad Akram · N. O. Alshehri · Wiesław A. Dudek

31 citations0/0 files storedJournal of Applied Mathematics

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Fuzzy and Soft Set Theory Advanced Algebra and Logic Advanced Mathematical Theories

Abstract

We propose certain types of interval-valued fuzzy graphs including balanced interval-valued fuzzy graphs, neighbourly irregular interval-valued fuzzy graphs, neighbourly total irregular interval-valued fuzzy graphs, highly irregular interval-valued fuzzy graphs, and highly total irregular interval-valued fuzzy graphs. Some interesting properties associated with these new interval-valued fuzzy graphs are investigated, and necessary and sufficient conditions under which neighbourly irregular and highly irregular interval-valued fuzzy graphs are equivalent are obtained. We also describe the relationship between intuitionistic fuzzy graphs and interval-valued fuzzy graphs.

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References

1965Fuzzy sets 1996Fuzzy sets 1986Intuitionistic fuzzy sets 2002On the relationship between some extensions of fuzzy set theory 2000Fuzzy Graphs and Fuzzy Hypergraphs 1987Some remarks on fuzzy graphs 2011Bipolar fuzzy graphs 1994Operations on fuzzy graphs

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