Meso-Granularity Labeled Method for Multi-Granularity Formal Concept Analysis

For the existing multi-granularity labeled formal contexts, the granular labeled values of all the attributes are organized by the union of some single-granularity labeled formal contexts. This may lead to the result that the subsequent related research problems mainly concern knowledge discovery on these single-granularity labeled formal contexts as well as their internal relationships. Consequently, it will not be beneficial for mining multilayer knowledge from multi-granularity labeled formal contexts. In this paper, we discuss meso-granularity labeled formal contexts in multi-granularity labeled formal contexts by restructuring granular labeled values of attributes of the original single-granularity labeled formal contexts, which makes knowledge discovery not limited to coarse and fine granular labeled data formed by data acquisition or representation, but absorbed from the combined data through cross-granularity. Firstly, we give the notion of a meso-granularity labeled formal context and its corresponding semantic interpretation. Secondly, we investigate generalization and specialization of meso-granularity labeled formal contexts, and prove that all the meso-granularity labeled formal contexts form a complete lattice under the generalization-specialization relation. Thirdly, we put forward a meso-granularity based knowledge discovery method for multi-granularity labeled formal decision contexts, and clarify the inference relationship between decision implications extracted from the coarse and fine meso-granularity labeled formal contexts. Finally, our experimental analysis demonstrates the effectiveness and advantages of the proposed meso-granularity labeled methods.