Abstract: Group decision making of domain experts is the most direct approach to determine loss function in three-way decision problems. Different from linguistic variable model and fuzzy set model with single uncertainty, expert evaluations described by cloud model can reflect the complex uncertainty form in cognitive process, and the synthetic evaluation function can be obtained by cloud aggregation. However, numerical characteristics only are performed simple linear combination in current cloud aggregation methods, leading the lack of the description of concept semantic differences and the difficulty to obtain convincing results. Therefore firstly, the weighted distance sum was proved to be a convex function in the distance space of cloud model. And the aggregational cloud model was defined as the minimum point of that function. Then, this definition was generalized to the multi-cloud model scenario, and a cloud aggregation method namely density center based cloud aggregation method was proposed. In group decision making, the proposed method obtains the most accurate synthetic evaluations with the highest similarity between synthetic evaluation and basic evaluation, providing a novel semantic interpretation of the determination of loss function. The experimental results show that the misclassification rate of the three-way decision with loss function determined by the proposed method is the lowest compared with simple linear combination and rational granularity methods.

Key words: cloud aggregation, cloud model, group decision making, three-way decisions

摘要： 在三支决策问题中，领域专家群决策是一种确定损失函数的最直接方法。相较于体现单一不确定性的语言变量模型和模糊集模型，云模型描述的专家评价更能够反映认知过程中复杂的不确定性形式，并能通过云综合的方法获得综合评价函数。但当前的云综合方法仅对数字特征进行简单的线性组合，缺乏对概念语义差异上的描述，难以获得令人信服的结果。因此首先证明了在云模型的距离空间中赋权距离和是一个凸函数，并将综合云模型定义为此函数的最小值点。然后，将该定义推广到多个云模型的场景下，提出了一种新的云综合方法——基于密度中心的云综合方法。群决策过程中，该方法在保证综合评价与基础评价之间的相似度最高的同时获得最精确的综合评价，为损失函数的确定提供了一种新的语义解释。实验结果表明，在与简单线性组合和合理粒度方法对比中，该方法所确定的损失函数使得三支决策中的误分类率最低。

关键词: 云综合, 云模型, 群决策, 三支决策