提出基于顺序理论的模糊犹豫元素评分新方法，提升决策合理性。
An order-oriented approach to scoring hesitant fuzzy elements
- 以顺序理论为基，定义显式排序关系的评分框架
- 证明对称顺序下的评分满足强单调性和Gärdenfors条件
- 设计支配函数支持带阈值的群体决策应用
传统对犹豫模糊集的评分方法缺乏有序理论基础。本文提出统一框架，每个评分均相对于给定顺序定义。该顺序导向视角使评分机制更灵活且一致。我们考察了犹豫模糊元素（[0,1]中的非空子集）上的几种经典顺序，发现它们并不诱导格结构，与先前主张相反。相反，我们证明基于对称顺序定义的评分满足关键规范性准则，包括关于并集的强单调性及Gärdenfors条件。在此基础上，引入一类称为支配函数的排名函数，用于比较犹豫模糊元素相对于包含最小可接受阈值的控制集。针对有限集，给出两个具体例子：离散支配函数和相对支配函数。证明这些函数可用于构建典型犹豫模糊集上的模糊偏好关系，并支持群体决策。
原文摘要 · Abstract (English)
Traditional scoring approaches on hesitant fuzzy sets often lack a formal base in order theory. This paper proposes a unified framework, where each score is explicitly defined with respect to a given order. This order-oriented perspective enables more flexible and coherent scoring mechanisms. We examine several classical orders on hesitant fuzzy elements, that is, nonempty subsets in [0,1], and show that, contrary to prior claims, they do not induce lattice structures. In contrast, we prove that the scores defined with respect to the symmetric order satisfy key normative criteria for scoring functions, including strong monotonicity with respect to unions and the Gärdenfors condition. Following this analysis, we introduce a class of functions, called dominance functions, for ranking hesitant fuzzy elements. They aim to compare hesitant fuzzy elements relative to control sets incorporating minimum acceptability thresholds. Two concrete examples of dominance functions for finite sets are provided: the discrete dominance function and the relative dominance function. We show that these can be employed to construct fuzzy preference relations on typical hesitant fuzzy sets and support group decision-making.
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