Modeling linguistic information is vital for qualitative decision making (QDM). Compared with single linguistic terms, the complex linguistic expressions (CLEs) are more powerful and flexible to express linguistic opinions under uncertainties. Among the existing types of CLEs, the linguistic terms with weakened hedges (LTWHs), which focus on the uncertainty of using single terms, can be used to model the linguistic expressions in natural languages. This paper concentrates on the application of LTWHs in the framework of QDM with preference relations. The concept of linguistic preference relations with hedges is presented after a new computational model of LTWHs is formed. Some consistency concepts, such as weak consistency and additive consistency, are then defined and their properties are studied. Theories and algorithms for consistency checking and improving are proposed. Finally, the availability of the proposed technique is demonstrated by a real application. Different from many studies related to consistency measures, we make use of fuzzy weighted digraphs to develop the theories and algorithms in a visible manner. Moreover, for consistency improving, the degree of consistency is measured by linguistic terms rather than numerical values so that the threshold of satisfactory consistency is interpretable.

中文翻译：

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语言偏好关系与对冲的一致性测度

建模语言信息对于定性决策 (QDM) 至关重要。与单一语言术语相比，复杂语言表达（CLE）在不确定性下表达语言观点的能力更强、更灵活。在现有的 CLE 类型中，弱对冲的语言术语 (LTWHs) 侧重于使用单个术语的不确定性，可用于对自然语言中的语言表达进行建模。本文重点研究LTWHs在具有偏好关系的QDM框架中的应用。在形成新的 LTWH 计算模型后，提出了与对冲的语言偏好关系的概念。然后定义了一些一致性概念，如弱一致性和加性一致性，并研究了它们的特性。提出了一致性检查和改进的理论和算法。最后，通过实际应用证明了所提出技术的可用性。与许多与一致性度量相关的研究不同，我们利用模糊加权有向图以可见的方式发展理论和算法。此外，为了提高一致性，一致性程度是通过语言术语而不是数值来衡量的，因此令人满意的一致性阈值是可以解释的。