m-Polar interval-valued fuzzy hypergraphs and its application in decision-making problems

This study introduces the novel concept of <i>m</i>-<i>polar interval-valued fuzzy hypergraph</i> (<i>m</i>-PIVFHG), an advancement that combines the strengths of fuzzy theory and hypergraph models to improve decision-making processes. <i>m</i>-PIVFHGs allow vertices to have degrees of membership across multiple polarities within sub-interval values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo></mml:math> . This offers better adaptability and precision than traditional models. This paper systematically explores the theoretical foundations of <i>m</i>-PIVFHGs, detailing their unique characteristics and presenting duality concepts with illustrative examples. It also defines various cut and level types specific to <i>m</i>-PIVFHGs and examines their properties. The practical utility of <i>m</i>-PIVFHGs is demonstrated through a real-world application aimed at optimizing decision-making in a university setting, showcasing significant improvements over existing fuzzy graph methodologies.