Preferences are a fundamental ingredient in a variety of fields, ranging from economics to computer science, for deciding the best choices among possible alternatives. Contexts provide another important aspect to be considered in the selection of the best choices, since, very often, preferences are affected by context. In particular, the problem of preference propagation from more generic to more specific contexts naturally arises. Such a problem has only been addressed in a very limited way and always resorts to practical, ad hoc approaches. To fill this gap, in this article, we analyze preference propagation in a principled way and adopt an abstract context model without making any specific assumptions on how preferences are stated. Our framework only requires that the contexts form a partially ordered set and that preferences define a strict partial order on the objects of interest. We first formalize the basic properties that any propagation process should satisfy. We then introduce an algebraic model for preference propagation that relies on two abstract operators for combining preferences, and, under mild assumptions, we prove that the only possible interpretations for such operators are the well-known Pareto and Prioritized composition. We then study several propagation methods based on such operators and precisely characterize them in terms of the stated properties. We finally identify a method meeting all the requirements, on the basis of which we provide an efficient algorithm for preference propagation.

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上下文感知偏好传播的基础

偏好是从经济学到计算机科学等各个领域的基本要素，用于确定可能的替代方案中的最佳选择。在选择最佳选择时，上下文提供了另一个需要考虑的重要方面，因为偏好经常受到上下文的影响。特别是，问题偏好传播从更通用到更具体的上下文自然会出现。此类问题仅以非常有限的方式得到解决，并且总是诉诸实际的、临时的方法。为了填补这一空白，在本文中，我们以原则性的方式分析偏好传播，并采用抽象的上下文模型，而不对偏好的表达方式做出任何具体假设。我们的框架只要求上下文形成一个偏序集，并且偏好定义了对感兴趣对象的严格偏序。我们首先将任何传播过程应满足的基本属性形式化。然后，我们引入了一个偏好传播的代数模型，该模型依赖于两个抽象算子来组合偏好，并且在温和的假设下，我们证明此类算子唯一可能的解释是著名的帕累托和优先组合。然后，我们研究了几种基于此类算子的传播方法，并根据所述属性精确地表征它们。我们最终确定了一种满足所有要求的方法，在此基础上我们提供了一种有效的偏好传播算法。