New concepts on level graphs of vague graphs with application in medicine

Vague graphs (VGs), belonging to the fuzzy graph (FG) family, have good capabilities when facing problems that cannot be expressed by FGs. When an element membership is unclear, neutrality is a good option that can be well-supported by a VG. The previous definitions limitations in FG have led us to offer new definitions in VGs. Therefore, this study introduces the notion of vague edge graph (VEG) (Formula presented.), in which V is a crisp vertex set and N is a vague relation (VR) on M, presenting some of its properties. Using λ-level graphs (LGs) and (λ, δ)-LGs, we characterize VG ζ = (M, N), where 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. If it is not done properly, the patient will suffer irreparable damage. Therefore, an application of VG in the diagnosis of the disease is expressed.