In this study we introduce two new concepts: (1) a new approach to construct clusters and (2) a methodology to compute similarities between numerical vectors based on clusters. The new approach to construct clusters is based on a variable‐distance threshold. There are several important domains where using commonly utilized fixed distance threshold clustering method might create clusters contradicting human expert reasoning. The domains where variable‐distance threshold clustering is more suitable are discussed and explained. In addition, we introduce a new concept for computing similarities between two numerical vectors, based on a membership in corresponding clusters. Such a concept constitutes an appropriate tool under greater degree of uncertainty where model structure is vague, and data are unreliable. First, we describe the procedure for construction of variable‐distance threshold clusters. Then we provide several models for computing the similarity between the two numerical vectors based on clusters. Several examples are included to illustrate the practical application of the models.

中文翻译：

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集群构建和相似性度量的新概念

在这项研究中，我们引入了两个新概念：（1）一种构造聚类的新方法，（2）一种基于聚类的数值向量之间的相似度计算方法。构建集群的新方法基于可变距离阈值。在几个重要领域中，使用常用的固定距离阈值聚类方法可能会创建与人类专家推理相矛盾的聚类。对可变距离阈值聚类更合适的领域进行了讨论和解释。另外，我们引入了一个新的概念，用于基于相应聚类中的成员资格来计算两个数值向量之间的相似度。在模型结构模糊，数据不可靠的情况下，这种概念构成了较大程度不确定性的适当工具。第一的，我们描述了构建可变距离阈值聚类的过程。然后，我们提供了几个模型，用于基于聚类计算两个数值向量之间的相似度。包括几个示例，以说明模型的实际应用。