On t-intuitionistic fuzzy graphs: a comprehensive analysis and application in poverty reduction

Area of Science:

• Graph Theory
• Fuzzy Mathematics
• Decision Science

Background:

• Traditional graph models struggle with uncertainty and complex relationships.
• Intuitionistic fuzzy sets offer a framework to handle vagueness and hesitation.
• T-intuitionistic fuzzy graphs extend these concepts for more nuanced analysis.

Purpose of the Study:

• To introduce and define t-intuitionistic fuzzy graphs.
• To explore fundamental set operations, homomorphism, and isomorphism for these graphs.
• To demonstrate a practical application in socio-economic analysis, specifically poverty reduction.

Main Methods:

• Development of the theoretical framework for t-intuitionistic fuzzy graphs.
• Definition of set operations (union, intersection, complement) tailored for these graphs.
• Introduction of graph isomorphism and homomorphism concepts within this new framework.
• Application modeling using t-intuitionistic fuzzy graphs to represent poverty-related factors.

Main Results:

• Formal definitions and properties of t-intuitionistic fuzzy graphs established.
• Set operations and structural equivalences (homomorphism, isomorphism) are proposed.
• A practical model for poverty reduction analysis using t-intuitionistic fuzzy graphs is presented.
• The effectiveness of the approach in handling multi-dimensional societal issues is demonstrated.

Conclusions:

• T-intuitionistic fuzzy graphs provide a robust mathematical tool for complex relationship analysis.
• The proposed framework supports decision-making in intricate problems like poverty reduction.
• This research highlights the potential of fuzzy graph theory in applied social sciences.