Urban Traffic Flow and Intersection Safety Analysis through a Novel Picture Fuzzy Outerplanar Graph Approach

Abstract

Picture fuzzy sets provide a powerful framework for representing uncertainty by incorporating degrees of membership, neutrality, and non-membership simultaneously. Motivated by the limitations of classical fuzzy and intuitionistic fuzzy planar graph models in handling complex uncertain relationships, this paper introduces the concept of picture fuzzy outerplanar graphs (PFOGs) and investigates their structural properties. The study establishes the construction of picture fuzzy outerplanar subgraphs through vertex and edge deletion operations and characterizes the notions of maximal and maximum picture fuzzy outerplanar subgraphs. Several illustrative examples are presented to demonstrate the applicability of the proposed concepts. Furthermore, a series of theorems and corollaries are developed to reveal fundamental relationships among picture fuzzy outerplanar graphs and their associated substructures. The concept of a picture fuzzy dual graph is also introduced, and its important properties and connections with picture fuzzy outerplanar graphs are examined. Bycombining outerplanar graph theory with picture fuzzy information, the proposed framework offers a flexible mathematical tool for modeling systems involving uncertain and hesitant interactions. Potential applications include urban traffic network analysis, risk assessment of crossing-sensitive infrastructures, transportation planning, and decision-support systems operating under uncertainty. The results presented in this work extend the scope of fuzzy graph theory and provide a foundation for future investigations on advanced picture fuzzy graph structures and their illustrative example applications.