论文标题
不完整的分析层次结构过程和Bradley-Terry模型：（IN）一致性和信息检索
The incomplete Analytic Hierarchy Process and Bradley-Terry model: (in)consistency and information retrieval
论文作者
论文摘要
偏好建模，排名，投票和多准则决策的几种方法包括成对比较。通常，一次比较两个对象更简单，此外，某些关系（例如，运动匹配的结果）是自然而然的。本文研究并比较了成对比较模型和随机的布拉德利 - 泰式模型。事实证明，它们提供相同的优先级向量，以进行一致（完整或不完整）比较。对于不完整的比较，考虑了所有填充水平。最近的结果确定了小型项目（最多n = 6）的乘法/添加/相互对成对比较的最佳子集和序列。本文的仿真表明，如果布拉德利 - 托莱（Bradley-terry）和瑟斯通（Thurstone）模型，相同的子集和序列也是最佳的。令人惊讶的是，这表明存在更普遍的结果。信息和偏好理论的进一步模型受未来的研究，以确定输入数据的最佳子集。
Several methods of preference modeling, ranking, voting and multi-criteria decision making include pairwise comparisons. It is usually simpler to compare two objects at a time, furthermore, some relations (e.g., the outcome of sports matches) are naturally known for pairs. This paper investigates and compares pairwise comparison models and the stochastic Bradley-Terry model. It is proved that they provide the same priority vectors for consistent (complete or incomplete) comparisons. For incomplete comparisons, all filling in levels are considered. Recent results identified the optimal subsets and sequences of multiplicative/additive/reciprocal pairwise comparisons for small sizes of items (up to n = 6). Simulations of this paper show that the same subsets and sequences are optimal in case of the Bradley-Terry and the Thurstone models as well. This, somehow surprising, coincidence suggests the existence of a more general result. Further models of information and preference theory are subject to future investigation in order to identify optimal subsets of input data.
