Uncertainty theory adopts the belief degree and uncertainty distribution to ensure good alignment with a decision-maker’s uncertain preferences, making the final decisions obtained from the consensus-reaching process closer to the actual decision-making scenarios. Under the constraints of the uncertain distance measure and consensus utility, this article explores the minimum-cost consensus model under various linear uncertainty distribution-based preferences. First, the uncertain distance is used to measure the deviation between individual opinions and the consensus through uncertainty distributions. A nonlinear analytical formula is derived to avoid the computational complexity of integral and piecewise function operations, thus reducing the calculation cost of the uncertain distance measure. The consensus utility function defined in this article characterizes the adjustment value and degree of aggregation of individual opinions. Three new consensus models are constructed based on the consensus utility and linear uncertainty distribution. The results show that, in complex group decision-making contexts, the uncertain consensus models are more flexible than traditional minimum-cost consensus models: compared with the high volatility of the adjusted opinions in traditional deterministic consensus models with crisp number-based preferences, the variation trends of both individual adjusted opinions and the collective opinion with a linear uncertainty distribution are much smoother and the fitting range is closer to reality. The introduction of the consensus utility not only reflects the relative changes of individual opinions, but also accounts for individual psychological changes during the opinion-adjustment process. Most importantly, it reduces the cost per unit of consensus utility, facilitates the determination of the optimal threshold for the consensus utility, and improves the efficiency of resource allocation.

不确定性理论采用置信度和不确定性分布，以确保与决策者的不确定性偏好保持良好的一致性，从而使从达成共识的过程中获得的最终决策更接近实际决策场景。在不确定距离度量和共识效用的约束下，本文探索了基于各种线性不确定性分布的偏好下的最小成本共识模型。首先，不确定性距离用于通过不确定性分布来度量个人意见和共识之间的偏差。推导了非线性解析公式，以避免积分和分段函数运算的计算复杂性，从而降低了不确定距离测度的计算成本。本文定义的共识效用函数表征了个人意见的调整值和汇总程度。基于共识效用和线性不确定性分布，构建了三个新的共识模型。结果表明，在复杂的群体决策环境中，不确定的共识模型比传统的最小成本共识模型更灵活：与传统的确定性共识模型（具有清晰的基于数字的偏好）相比，调整后的观点具有很高的波动性，具有线性不确定性分布的个体调整意见和集体意见的变化趋势更加平滑，拟合范围也更接近实际。共识效用的引入不仅反映了个人意见的相对变化，而且还可以解释意见调整过程中的个人心理变化。最重要的是，它降低了单位共识效用的成本，有助于确定共识效用的最佳阈值，并提高了资源分配的效率。