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Connectivity Concepts in Intuitionistic Fuzzy Incidence Graphs with Application.

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Summary
This summary is machine-generated.

This study introduces intuitionistic fuzzy incidence graphs (IFIGs), a powerful extension of fuzzy incidence graphs (FIGs). IFIGs incorporate non-membership values, enabling more reliable analysis and novel applications like investment selection.

Keywords:
BridgesCut-verticesFuzzy graphFuzzy incidence graphFuzzy setIntuitionistic fuzzy graphIntuitionistic fuzzy incidence graphIntuitionistic fuzzy set

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Area of Science:

  • Graph Theory
  • Fuzzy Mathematics
  • Decision Making

Background:

  • Fuzzy incidence graphs (FIGs) lack non-membership values, limiting their applicability.
  • Intuitionistic fuzzy graphs (IFGs) address this by including both membership and non-membership values.
  • A need exists for a graph structure that combines incidence concepts with intuitionistic fuzzy sets.

Purpose of the Study:

  • To introduce and define intuitionistic fuzzy incidence graphs (IFIGs) as a generalization of FIGs.
  • To explore connectivity concepts within IFIGs, including intuitionistic fuzzy cut-vertices and bridges.
  • To develop the concepts of intuitionistic incidence gain and loss for paths and vertex pairs.

Main Methods:

  • Formal definition of IFIGs and their properties.
  • Extension of existing graph connectivity concepts (cut-vertices, bridges) to the intuitionistic fuzzy incidence context.
  • Introduction of new metrics: intuitionistic incidence gain and loss.

Main Results:

  • IFIGs are established as a more comprehensive structure than FIGs due to the inclusion of non-membership values.
  • Novel concepts analogous to intuitionistic fuzzy cut-vertices, intuitionistic incidence cut-vertices, intuitionistic fuzzy bridges, and intuitionistic incidence bridges are defined.
  • The notions of intuitionistic incidence gain and loss are introduced for enhanced path analysis.

Conclusions:

  • IFIGs offer a more reliable and valuable framework compared to FIGs for complex modeling.
  • The developed concepts are essential for analyzing connectivity and relationships in systems where uncertainty is represented by both membership and non-membership.
  • IFIGs provide a practical tool for applications, such as investment selection, that require non-membership information.