基于生成树集合上不完整成对比较矩阵确定优先级向量的组合与采样方法
Combinatorial and Sampling Approaches to Determining the Priority Vector from an Incomplete Pairwise Comparison Matrix on the Set of Spanning Trees
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中文总结 AI 辅助
本文针对不完成对比较矩阵，提出基于生成树的组合与带序贯停止准则的蒙特卡洛采样方法，实现优先级向量的高效推导与精度保障。
中文摘要 AI 辅助
本文研究从不完成对比较矩阵推导优先级向量的组合方法与采样方法。研究表明，矩阵元素的信息显著组合与该矩阵诱导图的生成树存在一一对应关系。组合方法基于枚举所有生成树，并对从各生成树推导得到的优先级向量进行分量聚合。为降低计算复杂度，提出带序贯停止准则的蒙特卡洛采样方法，确保所得向量分量估计达到规定精度。
英文摘要
This paper considers combinatorial and sampling approaches to deriving a priority vector from an incomplete pairwise comparison matrix. It is shown that the informationally significant combinations of matrix elements are in one-to-one correspondence with spanning trees of the graph induced by the matrix. The combinatorial approach is based on the enumeration of all spanning trees and the componentwise aggregation of the priority vectors derived from them. To reduce computational complexity, a sampling Monte Carlo approach with a sequential stopping criterion is proposed, ensuring a prescribed accuracy for estimating the components of the resulting vector.
