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

Abstract

This paper explains the idea of t-intuitionistic fuzzy graphs as a powerful way to analyze and display relationships that are difficult to understand. The article also illustrates the ability of t-intuitionistic fuzzy graphs to establish complex relationships with multiple factors or dimensions of a physical situation under consideration. Moreover, the fundamental set operations of t-intuitionistic fuzzy graphs are proposed. The notions of homomorphism and isomorphism of t-intuitionistic fuzzy graphs are also introduced. Furthermore, the paper highlights a practical application of the proposed technique in the context of poverty reduction within a specific society. By employing t-intuitionistic fuzzy graphs, the research demonstrates the potential to address the multifaceted nature of poverty, considering various contributing factors and their interdependencies. This application showcases the versatility and effectiveness of t-intuitionistic fuzzy graphs as a tool for decision-making and policy planning in complex societal issues.

Figure 1

$0.70-\mathbb{IFG}{\mathcal{G}}_{0.7}$.

Figure 2

Complete $0.80-\mathbb{IFG}{\mathcal{G}}_{0.80}$.

Figure 3

$0.8-\mathbb{IFG}{\mathcal{G}}_1^{0.8}$.

Figure 4

$0.8-\mathbb{IFG}{\mathcal{G}}_2^{0.8}$.

Figure 5

$0.8-$$\mathbb{IFG}$ of ${\mathcal{G}}_1^{0.8}\times {\mathcal{G}}_2^{0.8}$.

Figure 6

$0.9-\mathbb{IFG}$ ${\mathcal{G}}_1^{0.9}$.

Figure 7

$0.9-\mathbb{IFG}$ ${\mathcal{G}}_2^{0.9}$.

Figure 8

Graphical representation of ${\mathcal{G}}_1^{0.9}\circ {\mathcal{G}}_2^{0.9}$.

Figure 9

$0.9-\mathbb{IFG}{\mathcal{G}}_1^{0.9}$.

Figure 10

$0.9-\mathbb{IFG}{\mathcal{G}}_2^{0.9}$.

Figure 11

Graphical representation of ${\mathcal{G}}_1^{0.9}\cup {\mathcal{G}}_2^{0.9}$.

Figure 12

Graphical representation of ${\mathcal{G}}_1^{0.9}+{\mathcal{G}}_2^{0.9}$.

Figure 13

$0.8-\mathbb{IFG}$ ${\mathcal{G}}_1^{0.8}$.

Figure 14

$0.8-\mathbb{IFG}{\mathcal{G}}_2^{0.8}$.

Figure 15

$0.8-$$\mathbb{IFG}$ ${\mathcal{G}}_1^{0.8}$.

Figure 16

$0.8-$$\mathbb{IFG}$ $\overline{{\mathcal{G}}_1^{0.8}}$.

Figure 17

Graphical representation of poverty reduction factors.

Figure 18

Graphical representation of score function of factor.