论文标题
成对比较的最佳序列：图形方法的图
Optimal sequences for pairwise comparisons: the graph of graphs approach
论文作者
论文摘要
在偏好建模中，必须确定问题制造商的问题及其安排的数量及其安排。我们专注于不完整的成对比较矩阵。首先，确定了最佳的不完整填充模式，从而导致权重向量最接近（平均）与完整情况下的情况最接近。这些结果是通过具有较大样本量的广泛数值模拟获得的。在表示图表的图中发现了最佳或接近最佳填充模式形成的序列的最佳填充序列。恒星图显示在跨越树中是最佳的，而最佳图总是接近两分。常规图似乎也对应于最佳情况，此外，规律性保留了所有最佳图，因为不同顶点的程度始终彼此尽可能近。结果的实际相关性包括案例，何时决策者可以在此过程的任何时期（例如在线问卷中）放弃问题。但是，发现的模式可能适用于广泛的偏好和信息理论模型。
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. First, optimal incomplete filling in patterns are identified, resulting in weight vectors being closest (on average) to that of the complete case. These results are obtained by extensive numerical simulations with large sample sizes. Optimal filling in sequences, formed by optimal or near optimal filling patterns, are found in the GRAPH of representing graphs. The star graph is revealed to be optimal among spanning trees, while the optimal graphs are always close to bipartite ones. Regular graphs appear to also correspond to optimal cases, furthermore regularity holds all optimal graphs, as the degrees of different vertices are always as close to each other as possible. The practical relevance of the results includes the cases when the decision maker can abandon the problem at any period of the process, e.g., in online questionnaires. However, the found patterns are potentially applicable in a wide range of models of preference and information theory.
