This paper proposes to establish the distance between partial preference orderings based on two very different approaches. The first approach corresponds to the brute force method based on combinatorics. It generates all possible complete preference orderings compatible with the partial preference orderings and calculates the Frobenius distance between all fully compatible preference orderings. Unfortunately, this first method is not very efficient in solving high-dimensional problems because of its big combinatorial complexity. That is why we propose to circumvent this problem by using a second approach based on belief functions, which can adequately model the missing information of partial preference orderings. This second approach to the calculation of distance does not suffer from combinatorial complexity limitation. We show through simple examples how these two theoretical methods work.

翻译：本文提出基于两种截然不同的方法建立部分偏好排序间的距离度量。第一种方法对应于基于组合数学的暴力方法，该方法生成与部分偏好排序兼容的所有可能完全偏好排序，并计算所有完全兼容偏好排序间的弗罗贝尼乌斯距离。然而，由于巨大的组合复杂度，第一种方法在解决高维问题时效率较低。为此，我们提出采用第二种基于置信函数的方法来规避此问题，该方法能够恰当地建模部分偏好排序中的缺失信息。第二种距离计算方法不受组合复杂度限制。我们通过简单示例展示了这两种理论方法的工作原理。