Abstract:Multi-granularity formal concept analysis is an important tool for data mining and knowledge discovery. However, there is no standard to select an optimal formal context in the existing multi-granularity formal concept analysis theory, which leads to the fact that multiple single-granularity formal contexts have to be studied separately one by one for achieving the task of knowledge discovery, leaving the formal contexts with multi-granularity attributes unexplored. In this paper, how to combine attribute blocks of the granularity tree of a multi-granularity formal context is studied, and information entropy is used as a criterion to judge whether a combined formal context is good or not, so as to evaluate the performance of the obtained optimal granularity selection results. Firstly, based on a granularity tree, the notion of a generalized meso-granularity pruning formal context is proposed, which can not only realize inter-layer cross-granularity combination but also cross-layer combination of attribute blocks. Secondly, information entropy of a generalized mesogranularity pruning formal context is defined to evaluate its advantages and disadvantages, and an optimal granularity selection algorithm is designed. Then, information entropy is used to measure the importance of multi-granularity pruning class-attribute block and granularity tree. Finally, experimental analysis shows the effectiveness of the proposed methods of optimal granularity selection and importance measurement of granularity tree based on information entropy.