This study focuses on linguistic information operational realization through information granulation in group decision-making (GDM) scenarios where the preference information offered by decision-makers over alternatives is described using distributed linguistic preference relations (DLPRs). First, an information granulation model is proposed to arrive at the operational realization of linguistic information in the GDM with DLPRs. The information granulation is formulated as a certain optimization problem where a combination of consistency degree of individual DLPRs and consensus degree among individuals is regarded as the underlying performance index. Then, considering that the proposed model is a constrained optimization problem (COP) with an adjustable parameter, which is difficult to be effectively solved using general optimization methods, we develop a novel approach towards achieving the optimal solution, referred to as penalty function-based co-evolutionary particle swarm optimization (PFCPSO). Within the PFCPSO setting, the designed penalty function is used to transform the COPs into unconstrained ones. Besides, the penalty factors and the adjustable parameter, as well as the decision variables of the optimization problems, are simultaneously optimized through the co-evolutionary mechanism of two populations in co-evolutionary particle swarm optimization (CPSO). Finally, a comprehensive evaluation problem about car brands is studied using the proposed model and the newly developed PFCPSO approach, which demonstrates their applicability. Two comparative studies are also conducted to show the effectiveness of the proposals. Overall, this study exhibits two facets of originality: the presentation of the linguistic information granulation model, and the development of the PFCPSO approach for solving the proposed model.

本研究侧重于通过群体决策 (GDM) 场景中的信息颗粒化实现语言信息操作，其中决策者提供的对替代方案的偏好信息使用分布式语言偏好关系 (DLPR) 进行描述。首先，提出了一种信息粒度模型，以使用 DLPR 在 GDM 中实现语言信息的操作实现。信息粒度被表述为一个特定的优化问题，其中将个体 DLPR 的一致性程度和个体之间的共识程度的组合作为底层性能指标。然后，考虑到所提出的模型是一个参数可调的约束优化问题（COP），使用一般优化方法难以有效解决，我们开发了一种实现最优解的新方法，称为基于惩罚函数的协同进化粒子群优化 (PFCPSO)。在 PFCPSO 设置中，设计的惩罚函数用于将 COP 转换为无约束的。此外，通过协同进化粒子群优化（CPSO）中两个种群的协同进化机制，同时优化惩罚因子和可调参数，以及优化问题的决策变量。最后，使用所提出的模型和新开发的 PFCPSO 方法研究了关于汽车品牌的综合评价问题，证明了它们的适用性。还进行了两项比较研究，以显示建议的有效性。总的来说，这项研究展示了两个方面的原创性：