Fuzzy Graph Theory and Neuromorphic Graph Models for Uncertain Mathematical Systems

Abstract

Uncertain mathematical systems frequently involve ambiguous graph relationships, incomplete connectivity structures, nonlinear uncertainty propagation, and dynamically evolving graph interactions that cannot be effectively represented using classical deterministic graph theory. To address these limitations, this research proposed a hybrid Fuzzy-Neuromorphic Graph Framework (FNGF) integrating fuzzy graph theory, adaptive neuromorphic spike propagation, entropy-aware graph optimization, and spectral graph stability analysis within a unified mathematical architecture. The proposed framework incorporates adaptive fuzzy membership modeling, spike-driven graph learning, synaptic graph optimization, and entropy-guided graph sparsification mechanisms for intelligent uncertainty-aware graph computation. Experimental evaluations were conducted using 5000 synthetically generated uncertain graph instances under varying graph perturbation levels and uncertainty densities. The proposed framework achieved uncertainty classification accuracies of 97.82%, 94.12%, and 90.37% under low, medium, and high graph noise environments, respectively. Furthermore, the framework demonstrated 95.84% graph stability prediction accuracy, approximately 60.29% entropy reduction, and nearly 79% reduction in graph computational energy consumption compared to conventional graph neural systems. The entropy-aware graph pruning mechanism significantly improved graph sparsification and graph robustness against topological perturbations, while sparse spike-driven graph propagation substantially enhanced adaptive convergence efficiency. The proposed framework establishes a mathematically rigorous, scalable, interpretable, and energy-efficient intelligent graph architecture suitable for future uncertain intelligent systems, adaptive optimization environments, neuromorphic communication systems, and large-scale uncertainty-aware computational networks.