AUTHOR=Shi Xiaolong , Jiang Wubian , Khan Aysha , Akhoundi Maryam 

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

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1130765

DOI=10.3389/fphy.2023.1130765

ISSN=2296-424X

ABSTRACT=<p>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 (<italic>VEG</italic>) <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>ζ</mml:mi></mml:mrow><mml:mo stretchy="false">̂</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula>, in which <italic>V</italic> is a crisp vertex set and <italic>N</italic> is a vague relation (VR) on <italic>M</italic>, presenting some of its properties. Using <italic>λ</italic>-level graphs (LGs) and (<italic>λ</italic>, <italic>δ</italic>)-LGs, we characterize VG <italic>ζ</italic> = (<italic>M</italic>, <italic>N</italic>), where <italic>M</italic> is a vague set (VS) on <italic>V</italic> and <italic>N</italic> is a VR on <italic>V</italic>. 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.</p>