New concepts for cluster construction and similarity measurement

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.