New concepts on level graphs of vague graphs with application in medicine - Shi, Xiaolong; Jiang, Wubian; Khan, Aysha; Akhoundi, Maryam (Frontiers in Physics, 2023)
Vague graph (VG), belonging to FGs family has good capabilities when facing with problems that cannot be expressed by FGs. When an element membership is not clear, neutrality is a good option that can be well-supported by a VG. The previous definitions limitations in fuzzy graph have led us to offer new definitions in VGs. So, in this paper, we introduce the notion of vague edge graph ($VEG$) $\widehat{ζ}=(V,N)$, which $V$ is a crisp vertex set and $N$ is a vague relation (VR) on $M$, and present some of its properties. Using $λ$-level graphs (LGs) and $(λ,δ)$-LGs, we characterize VG $ζ=(M,N)$, that $M$ is a vague set (VS) on $V$ and $N$ is a VR on $V$. Medical diagnosis is one of the most sensitive and important issues in the medical sciences, and if it is not done property, then the patient will suffer irreparable damage. Therefore, an application of the VG in the diagnosis of the disease is expressed.