A Linear Diophantine Fuzzy Graph‐Theoretic Approach for Planar Dynamic Traffic Optimization

Dynamic urban traffic signal control systems face uncertainties such as fluctuating vehicle densities, unpredictable incidents, and varying driver behaviors, making precise decision‐making highly challenging. To address these complexities, fuzzy planar graphs have been employed for uncertainty modeling. However, linear Diophantine fuzzy planar graphs (LDFPGs) extend this framework by incorporating linear Diophantine constraints and hence provide a more structured and constraint‐aware approach. In this study, we introduce the concept of LDFPGs and formulate intelligent models to optimize urban traffic signal control under imprecise and dynamic conditions. A strong theoretical foundation is established by defining and characterizing linear Diophantine fuzzy multisets (LDFMSs), linear Diophantine fuzzy multigraphs (LDFMGs), and key notions such as considerable and strong multiedges, edge crossings, and the strength of multiedges. We also investigate the concept of strength for linear Diophantine fuzzy multiedges and analyze the structure of complete LDFMGs. Furthermore, the geometric and combinatorial duals associated with LDFPGs are explored. To demonstrate practical applicability, we propose an intelligent LDFPG‐based framework for dynamic traffic signal optimization and validate its effectiveness through comparative analysis. The findings highlight the potential of LDFPGs in developing efficient, adaptive, and reliable decision‐support systems for modern smart city traffic management.