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

Sanchari Bera1, Osamah Ibrahim Khalaf2, Wing-Keung Wong3

  • 1Department of Applied Mathematics, Vidyasagar University, Midnapore - 721102, India.

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Summary

This study introduces m-polar interval-valued fuzzy hypergraphs (m-PIVFHGs), a novel fuzzy theory and hypergraph model for enhanced decision-making. The research details m-PIVFHG theory, properties, and a university application, improving upon existing fuzzy graph methods.

Keywords:
Fuzzy graphFuzzy hypergraphInterval-valued fuzzy graphm-Polar fuzzy graphm-Polar interval-valued fuzzy graph

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Area of Science:

  • Mathematics
  • Computer Science
  • Decision Science

Background:

  • Traditional fuzzy models lack precision in complex decision-making.
  • Hypergraph models offer structural representation but can be rigid.
  • Integrating fuzzy logic and hypergraphs can enhance data representation and analysis.

Purpose of the Study:

  • Introduce the novel concept of m-polar interval-valued fuzzy hypergraphs (m-PIVFHGs).
  • Explore the theoretical foundations, characteristics, and duality concepts of m-PIVFHGs.
  • Demonstrate the practical application of m-PIVFHGs in optimizing decision-making processes.

Main Methods:

  • Definition and theoretical exploration of m-PIVFHGs.
  • Analysis of membership degrees across multiple polarities within interval values.
  • Development and examination of cut and level concepts specific to m-PIVFHGs.
  • Application of m-PIVFHGs to a university decision-making optimization problem.

Main Results:

  • Established the theoretical framework for m-PIVFHGs.
  • Defined and analyzed unique characteristics, duality, and cut/level concepts.
  • Showcased improved decision-making precision and adaptability compared to traditional fuzzy graph methodologies.
  • Validated the practical utility through a real-world university application.

Conclusions:

  • m-PIVFHGs provide a robust framework for complex decision-making.
  • The model offers enhanced adaptability and precision over existing fuzzy graph approaches.
  • The study demonstrates significant potential for optimizing real-world decision-making scenarios.