Powerful and Powerless Fuzzy Graphs and it’s Application

Elham Darabian ¹ ( )
Rajab Ali Borzooei ² ( )

Submited date : 2025-08-01 Accepted date : 2025-09-22

Keywords: Fuzzy graph, Semi strong arc, Standard deviation, Modified fuzzy graph, Powerful fuzzy graph, Powerless fuzzy graph.,

Abstract :

In this article, we aim to enhance a fuzzy graph to achieve its optimal state and introduce a powerless or powerful fuzzy graph derived from it. To accomplish this, we will define a semi-strong arc and first determine modified fuzzy graphs that result from adjusting the value of an arc in the original fuzzy graph. Next, we will calculate the standard deviation of each fuzzy graph. To continue, we will identify the fuzzy graphs with the maximum and minimum standard deviations, designating them as the powerful and powerless fuzzy graphs, respectively. Finally, we will discuss an intriguing and significant application in identifying common injuries among high school students.

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