To capture collective opinions/evaluations in a collection of individual linguistic expressions, this study proposes an approach to construct order-2 information granules by extending the numerical data-based principles of justifiable granularity to a linguistic data-based one. First, the two key criteria of the principle of justifiable granularity, namely coverage and specificity, are formally defined in the context of order-2 information granules. Second, three order-2 information granules construction models by maximizing the product of coverage and specificity are developed for coping with one-dimensional direct linguistic expressions, linguistic preference relations, and multi-dimensional direct linguistic expressions, respectively. Third, considering that the developed order-2 information granules construction models exhibit a non-linear uncertain objective function and equality constraints, the constrained multi-swarm PSO without velocity is improved with the use of the constrained handling technique for effectively solving the models. Case studies on the considered three types of linguistic expressions show the applicability of the proposed models and ensuing algorithm. The superiority of the improved algorithm in handling the proposed models is demonstrated by comparison with the original one. The effectiveness of the proposed models in terms of abnormal corrective ability and balance of coverage and specificity is verified by comparing with a family of Top- methods. The originality of this study lies in the construction of an operational entity, namely order-2 information granule, that reflects the group opinion without specifying the formalism of individual linguistic expressions, which provides an effective and efficient way to aggregate ubiquitous linguistic information for subsequent computation, reasoning and decision-making.

中文翻译：

---

借助合理粒度原则构建语言表达的2阶信息粒

为了捕获个体语言表达集合中的集体意见/评估，本研究提出了一种通过将基于数值数据的合理粒度原则扩展到基于语言数据的原则来构建 2 阶信息粒度的方法。首先，合理粒度原则的两个关键标准，即覆盖率和特异性，是在2阶信息粒度的背景下正式定义的。其次，通过最大化覆盖率和特异性的乘积，开发了三种二阶信息粒构建模型，分别用于处理一维直接语言表达、语言偏好关系和多维直接语言表达。第三，考虑到所开发的二阶信息粒构建模型具有非线性不确定目标函数和等式约束，利用约束处理技术改进了无速度约束多群粒子群算法，以有效求解模型。对所考虑的三种语言表达类型的案例研究表明了所提出的模型和后续算法的适用性。通过与原始算法的比较，证明了改进算法在处理所提出的模型方面的优越性。通过与一系列 Top 方法进行比较，验证了所提出的模型在异常纠正能力以及覆盖率和特异性之间的平衡方面的有效性。本研究的独创性在于构建了一个操作实体，即二阶信息粒，它反映了群体意见，而不指定个体语言表达的形式主义，这为聚合普遍存在的语言信息以供后续计算提供了一种有效且高效的方法、推理和决策。