Planarity of Intuitionistic Pythagorean Fuzzy Graphs and its Application in Decision Making

Source abstract

This paper introduces the concept of Intuitionistic Pythagorean Fuzzy Graphs (IPFGs) and outlines their key characteristics as a means of addressing such uncertain scenarios by examining Pythagorean uncertain planarity values using weak, strong, and significant edges. An Intuitionistic Pythagorean Fuzzy Graph is a generalization of a traditional graph that can solve certain problems beyond the capabilities of both classical graph theory and fuzzy graph theory. The approach based on Pythagorean fuzzy graphs offers greater flexibility in handling human judgment data compared to other fuzzy models. This paper defines the concept of planarity in an Intuitionistic Pythagorean Fuzzy Graph using the notions of intersecting value and Intuitionistic Pythagorean Fuzzy Planarity Value. The upper and lower bounds of this planarity value are then established through a series of interrelated theorems. Finally, the weak and strong planarity of an Intuitionistic Pythagorean Fuzzy Graph is delineated, and the results of the analysis are discussed. The paper poses a challenge that demonstrates the application of the proposed concept.