Data Associations Between Two Hierarchy Trees

To study the data association, a structure called a hierarchy tree is constructed. It is based on the approach to hierarchical data processing, and constituted by different level partitions of a data set. This leads to the definition of the data association, thereby links two hierarchy trees together. The research on the data association focuses on the way to check whether data are associated with other data. The investigation includes the issues: the intuitive and formal methods for constructing hierarchy trees, the technique of making granules hierarchical, the sufficient and necessary condition for measuring the data association, the analysis of basing the closer data association on the closer data identity, the discussion of connecting numerical information with association closeness, etc. Crucially, the hierarchical data processing and numerical information are important characteristics of the research. As an applied example, two hierarchy trees are set up, demonstrating the hierarchical granulation process of two actual data sets. Data associations between the data sets are characterized by the approach developed in this paper, which provides the basis of algorithm design for the actual problem. In particular, since the research is relevant to granules and alterations of granularity, it may offer an avenue of research on granular computing.