标题： 多准则决策辅助的偏好表示在新的七值逻辑中 显示英文标题

标题： Representation of preferences for multiple criteria decision aiding in a new seven-valued logic

摘要： 在本文中考虑的七值逻辑自然地出现在粗糙集框架内，使得能够区分由于不精确性引起的模糊性与由于粗略性引起的歧义。最近，我们讨论了其在关于描述多属性分类对象的数据推理中的实用性。我们还表明，这种逻辑作为特殊情况包含了著名的贝尔纳普四值逻辑。在这里，我们展示了七值逻辑以及由此衍生的其他逻辑如何用于表示多准则决策辅助（MCDA）领域中的偏好。特别是，我们提出了新的优于和价值函数偏好模型形式，这些模型在考虑不完善的偏好信息的情况下聚合多个标准。我们证明了我们的方法有效解决了MCDA中偏好建模的常见挑战，如不确定性、不精确性和绩效及偏好的不明确性。为此，我们提出了一种特定的程序来构建七值偏好关系，并利用它来定义考虑鲁棒性问题的建议，通过使用多个优于或价值函数来表示决策者的偏好。此外，我们讨论了所提出的七值偏好结构的主要特性，并将其与MCDA中的现有方法进行比较，如序数回归、鲁棒序数回归、随机多属性可接受性分析、随机序数回归等。我们使用一个教学示例来说明和讨论我们方法的应用。最后，我们提出了未来研究的方向和所提出方法的潜在应用。 显示英文摘要

摘要： The seven-valued logic considered in this paper naturally arises within the rough set framework, allowing to distinguish vagueness due to imprecision from ambiguity due to coarseness. Recently, we discussed its utility for reasoning about data describing multi-attribute classification of objects. We also showed that this logic contains, as a particular case, the celebrated Belnap four-valued logic. Here, we present how the seven-valued logic, as well as the other logics that derive from it, can be used to represent preferences in the domain of Multiple Criteria Decision Aiding (MCDA). In particular, we propose new forms of outranking and value function preference models that aggregate multiple criteria taking into account imperfect preference information. We demonstrate that our approach effectively addresses common challenges in preference modeling for MCDA, such as uncertainty, imprecision, and ill-determination of performances and preferences. To this end, we present a specific procedure to construct a seven-valued preference relation and use it to define recommendations that consider robustness concerns by utilizing multiple outranking or value functions representing the decision maker s preferences. Moreover, we discuss the main properties of the proposed seven-valued preference structure and compare it with current approaches in MCDA, such as ordinal regression, robust ordinal regression, stochastic multiattribute acceptability analysis, stochastic ordinal regression, and so on. We illustrate and discuss the application of our approach using a didactic example. Finally, we propose directions for future research and potential applications of the proposed methodology.