一种新的七值逻辑中多准则决策辅助的偏好表示
Representation of preferences for multiple criteria decision aiding in a new seven-valued logic
AI总结：
本文提出在七值逻辑框架下表示多准则决策辅助中的偏好，通过构造七值偏好关系并利用多个超越关系或价值函数生成稳健推荐，以有效处理不确定性、不精确性和偏好不充分确定等问题。
摘要：
本文所考虑的七值逻辑自然产生于粗糙集框架之中，能够区分由不精确性导致的模糊性与由粗糙性导致的歧义性。最近，我们讨论了它在推理描述对象多属性分类的数据方面的效用。我们还证明了该逻辑作为一种特例包含了著名的Belnap四值逻辑。在此，我们展示七值逻辑以及由其派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，我们提出了新的超越关系和价值函数偏好模型形式，这些模型在考虑不完美偏好信息的情况下聚合多个准则。我们证明，我们的方法有效应对了MCDA偏好建模中的常见挑战，例如不确定性、不精确性以及表现和偏好的不充分确定。为此，我们提出了一种具体程序来构造七值偏好关系，并利用它来定义考虑稳健性关切的推荐，其方式是利用多个代表决策者偏好的超越关系或价值函数。此外，我们讨论了所提出的七值偏好结构的主要性质，并将其与MCDA中的当前方法进行比较，例如序数回归、稳健序数回归、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方向以及所提方法的潜在应用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
