Network design for bypass roads using interval valued fuzzy outerplanar graphs

This paper presents a novel approach to bypass road network design using interval valued fuzzy outerplanar graphs (IVFOGs), addressing the increasing demands of vehicular growth and evolving lifestyles. The uncertainty and variability inherent in urban traffic regulation are effectively managed through the application of interval valued fuzzy sets, which capture linguistic and imprecise traffic parameters. The study investigates the structural properties of IVFOGs and their corresponding duals, providing a solid theoretical foundation for modeling bypass networks. The concepts of vertex and edge deletion are explored to construct and analyze optimal bypass routes that avoid congested in urban centers. Furthermore, examples are provided to study the maximal and maximum interval valued fuzzy outerplanar graphs determined by both vertex and edge deletion. This framework enhances mobility, optimizes commuter travel time, and contributes to efficient road transport planning by offering a flexible, uncertainty-tolerant model tailored for real-world traffic scenarios.