从不完全偏好到通过Optimization进行排名
From Incomplete Preferences to Ranking via Optimization
摘要：
我们考虑的方法是基于离散最优化问题的解决方案，聚集的喜好。偏好由任意二元关系（可能加权）或不完整的成对比较矩阵表示。这一不完整的案件迄今实际上仍未得到探讨。我们研究了几种已知方法的性质，并提出了一种新的方法。特别是，我们测试这些方法是否遵守称为{ \it自一致单调性}的新公理。一些结果建立了相关的最优化问题的解决方案的特点。
英文摘要：
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices. This incomplete case remains practically unexplored so far. We examine the properties of several known methods and propose one new method. In particular, we test whether these methods obey a new axiom referred to as {\it Self-Consistent Monotonicity}. Some results are established that characterize solutions of the related optimization problems.
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