An Information Freshness-Based Method for Quantum Bayesian Networks in the Consensus-Reaching Process Under Relative Deprivation

Group decision-making in social networks is often affected by psychological resistance and time-dependent information loss during the consensus-reaching process. Existing minimum-cost consensus models usually emphasize opinion distance, trust, and feedback mechanisms, but they pay limited attention to the joint effects of relative deprivation, cognitive concentration, and information freshness. To address this limitation, this paper develops an information freshness-based consensus-reaching method under relative deprivation. First, a quantum Bayesian-like network is constructed to describe the relative deprivation generated by horizontal and vertical reference comparisons, where interference terms are used to represent non-additive interactions among multiple comparison paths. Second, an entropy-based concentration assessment model is proposed under probabilistic linguistic term sets, in which entropy is used as an operational measure of the dispersion of decision makers’ probabilistic linguistic evaluations. Third, an information freshness update rule based on time decay and round increments is introduced to reflect information aging and renewal during repeated opinion adjustment. These three components are integrated into a quality-adjusted minimum opinion adjustment cost model, and a particle swarm optimization algorithm is designed to solve the resulting nonlinear constrained problem. A numerical example, a sensitivity analysis, an ablation comparison, and a robustness discussion are provided to illustrate the behavior of the proposed method. The results show that relative deprivation and concentration increase opinion adjustment resistance, while information freshness affects the trade-off between adjustment cost and consensus quality. The proposed framework offers a formal decision-support tool for consensus reaching under psychological and temporal uncertainty.