标题： 区间值价值函数来自不确定偏好 显示英文标题

标题： Interval-valued Value Functions from Uncertain Preferences

摘要： 数值尺度（或优先级值）的构建是决策辅助研究中的一个常见主题。 然而，在实际情境中，不确定性以及有限的认知精度常常导致决策者提供区间判断而不是精确值。 在这种情况下，尽管从区间偏好中获得数值尺度可能是可行的，但这意味着信息的损失以及对输入信息的过度简化。 本文提出了一种从区间对比较中推导区间值价值尺度的一般框架。 这意味着要解决关于获取、确定代表性价值函数以及保持单调性和可解释性等属性的基本挑战。 我们首先提出了区间值偏好关系一致性的新定义。 我们证明了当一致性成立时，可以确定区间值价值函数，并建立了它们唯一性的条件。 此外，我们表明，我们的方法扩展并统一了经典模型，如模糊偏好关系、Saaty的偏好关系以及扑克牌方法。 在方法上，我们开发了优化模型，提供了在出现矛盾时引导决策者达成一致的程序。 该框架为构建单调区间值函数提供了连贯且可解释的基础，弥合了经典和区间值偏好模型之间的差距，并增强了决策的稳健性。 显示英文摘要

摘要： The construction of numerical value scales (or priority values) is a recurrent topic in decision-aiding research. However, in real contexts, uncertainty and limited cognitive precision often lead decision-makers to provide interval judgments rather than exact values. In this scenario, even though obtaining a numerical value scale from interval preferences could be feasible, it implies a loss of information and an oversimplification of the input information. This paper proposes a general framework for deriving interval-valued value scales from interval-valued pairwise comparisons. This implies addressing fundamental challenges regarding the elicitation, the determination of representative value functions, and the preservation of properties such as monotonicity and interpretability. We start by presenting a new definition for the consistency of an interval-valued preference relation. We show that when consistency holds, interval-valued value functions can be determined, and we establish conditions for their uniqueness. Furthermore, we show that our proposal extends and unifies classical models such as fuzzy preference relations, Saaty's preference relations, and the Deck of Cards Method. Methodologically, we develop optimization models that provide procedures to guide decision-makers towards consistency when contradictions arise. The framework provides a coherent and interpretable foundation for constructing monotonic interval value functions, bridging classical and interval-valued preference models, and enhancing robustness in decision-making.