在偏好建模中，确定需要向决策者提出的问题数量及其排列方式至关重要。我们聚焦于不完全成对比较矩阵，提出了最优填充模式：当底层表示图连通时，对于至多6个备选方案以及所有可能的比较次数，该模式能使（LLSM，对数最小二乘法）权重向量平均而言最接近完全情形下的结果。这些结果通过大样本量的大量数值模拟得到。许多最优填充结构可形成最优填充序列——即一个最优情形可通过向先前的最优情形添加一次比较得到——这些序列在图的图（graph of graphs）上呈现。研究发现星图在生成树中是最优的，而最优图始终接近二部图。正则图也对应最优情形，此外正则性对所有最优图都很重要，因为不同顶点的度数总是尽可能彼此接近。除了在给定决策问题中应用最优填充结构外，从业者还可在决策者可能在流程的任意阶段放弃问题的场景（例如在线问卷中）使用最优填充序列。
英文摘要：
In preference modelling, it is essential to determine the number of questions and their arrangements to ask from the decision maker. We focus on incomplete pairwise comparison matrices, and provide the optimal filling in patterns, which result in the closest (LLSM) weight vectors on average to the complete case for at most six alternatives and for all possible number of comparisons, when the underlying representing graph is connected. These results are obtained by extensive numerical simulations with large sample sizes. Many optimal filling structures resulted in optimal filling in sequences -- one optimal case can be reached by adding a comparison to a previous one -- which are presented on graph \color{black} of graphs. The star graph is revealed to be optimal among spanning trees, while the optimal graphs are always close to bipartite ones. Regular graphs also correspond to optimal cases, furthermore regularity is important for all optimal graphs, as the degrees of different vertices are always as close to each other as possible. Besides applying optimal filling structures in given decision making problems, practitioners can utilize the optimal filling sequences in the cases, when the decision maker can abandon the problem at any period of the process (e.g., in online questionnaires).
A DEMATEL-Based Completion Method for Incomplete Pairwise Comparison Matrix in AHP
Southwest University（西南大学）；Jinan University（暨南大学）；Vanderbilt University（范德堡大学）；The Hong Kong Polytechnic University（香港理工大学）；University of Portsmouth（朴茨茅斯大学）
The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices
Refined thresholds for inconsistency: The effect of the graph associated with incomplete pairwise comparisons
Corvinus University of Budapest (BCE), Institute of Operations and Decision Sciences, Department of Operations Research and Actuarial Sciences（布达佩斯考文纽斯大学）；Institute for Computer Science and Control (SZTAKI), Hungarian Research Network (HUN-REN)（匈牙利国家研究网络计算机科学与控制研究所）
Size independence of consistency index for pairwise comparison matrices in analytic hierarchy process
Faculty of Science and Engineering, Otemon Gakuin University（帝塚山学院大学理工学部）；Faculty of Applied Information Science, Hiroshima Institute of Technology（广岛工业大学应用信息科学部）
Inconsistency thresholds for incomplete pairwise comparison matrices
Corvinus University of Budapest (BCE)（布达佩斯考文纽斯大学）；Institute for Computer Science and Control (SZTAKI)（计算机科学与控制研究所）；Eötvös Loránd Research Network (ELKH)（厄特沃什·罗兰研究网络）
GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks
University of Oxford（牛津大学）；Amazon Web Services AI Shanghai Lablet（亚马逊云科技AI上海实验室）；The Alan Turing Institute（阿兰·图灵研究所）；Shanghai Jiao Tong University（上海交通大学）；Shanghai AI Laboratory（上海人工智能实验室）
