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Interval-valued fuzzy [Formula: see text]-tolerance competition graphs.

Tarasankar Pramanik1, Sovan Samanta2, Madhumangal Pal3

  • 1Department of Mathematics, Khanpur Gangche High School (H.S.), Khanpur, Pandua, India.

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|December 6, 2016
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This study introduces interval-valued fuzzy tolerance competition graphs, extending fuzzy graph theory. These graphs offer a novel approach for applications like image matching.

Keywords:
CompetitionInterval-valued fuzzy graphsTolerance

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Area of Science:

  • Graph Theory
  • Fuzzy Mathematics
  • Computer Science

Background:

  • Fuzzy graphs are extensions of traditional graphs used in various fields.
  • Tolerance competition graphs provide a framework for modeling relationships with tolerance.
  • Existing fuzzy graph models lack the interval-valued approach for uncertainty.

Purpose of the Study:

  • To develop and define interval-valued fuzzy tolerance competition graphs (IVFPTCGs).
  • To explore the properties of products of IVFPTCGs.
  • To demonstrate the practical application of IVFPTCGs in image matching.

Main Methods:

  • Extending fuzzy sets to interval-valued fuzzy sets within the context of tolerance competition graphs.
  • Defining the product operation for two IVFPTCGs.
  • Analyzing hereditary properties related to the products of IVFPTCGs.

Main Results:

  • The paper successfully defines IVFPTCGs as an extension of fuzzy graphs.
  • New definitions for the product of two IVFPTCGs are established.
  • Hereditary properties of these products are investigated and represented.
  • A practical application in image matching is presented to validate the model.

Conclusions:

  • Interval-valued fuzzy tolerance competition graphs offer a more nuanced representation of complex relationships.
  • The defined products and their properties provide a foundation for further research in this area.
  • The image matching application demonstrates the utility of IVFPTCGs in real-world problems.