<p>Applied-mathematics and theoretical-computer-science viewpoints jointly frame large-scale group decision-making as a stochastic, graph-constrained optimization problem. Multi-granularity probabilistic linguistic preference relations encode agents’ uncertain utilities via discrete probability distributions over graded linguistic terms. Fuzzy social networks represent trust through real-valued adjacency matrices whose entries are updated by closed-form algebraic operations. A dynamic self-confidence mechanism recasts each agent’s belief mass as a state variable governed by a consensus-error gradient flow. The resulting algorithmic pipeline exhibits poly-logarithmic iteration complexity with respect to agent count, while the worst-case modification cost remains upper-bounded by a constant multiple of the initial inconsistency index. Empirical analysis of 38,900 online tourism reviews delivers a consensus level of 0.9873 within two iterations at a normalized cost of 0.006, outperforming seven state-of-the-art baselines. Beyond tourism, the framework applies to any multi-agent system whose preference topology is representable as an uncertain hyper-graph, including e-commerce recommenders, federated learning aggregators, and distributed medical-diagnosis platforms. Ongoing research incorporates online-learning regret minimizers to adapt model parameters under adversarial, non-stationary conditions.</p>