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

Abstract

This study introduces the novel concept of m-polar interval-valued fuzzy hypergraph (m-PIVFHG), an advancement that combines the strengths of fuzzy theory and hypergraph models to improve decision-making processes. m-PIVFHGs allow vertices to have degrees of membership across multiple polarities within sub-interval values of [0,1]. This offers better adaptability and precision than traditional models. This paper systematically explores the theoretical foundations of m-PIVFHGs, detailing their unique characteristics and presenting duality concepts with illustrative examples. It also defines various cut and level types specific to m-PIVFHGs and examines their properties. The practical utility of m-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.

Keywords

• Fuzzy graph
• Fuzzy hypergraph
• m-Polar fuzzy graph
• Interval-valued fuzzy graph
• m-Polar interval-valued fuzzy graph