A study on information granularity in formal concept analysis based on concept-bases

摘要

As one of mature theories, formal concept analysis (FCA) possesses remarkable mathematical properties, but it may generate massive concepts and complicated lattice structure when dealing with large-scale data. With a view to the fact that granular computing (GrC) can significantly lower the difficulty by selecting larger and appropriate granulations when processing large-scale data or solving complicated problems, the paper introduces GrC into FCA, it not only helps to expand the extent and intent of classical concept, but also can effectively reduce the time complexity and space complexity of FCA in knowledge acquisition to some degree. In modeling, concept-base, as a kind of low-level knowledge, plays an important role in the whole process of information granularity. Based on concept-base, attribute granules, object granules and relation granules in formal contexts are studied. Meanwhile, supremum and infimum operations are introduced in the precess of information granularity, whose biggest distinction from traditional models is integrating the structural information of concept lattice. In addition, the paper also probes into reduction, core, and implication rules in granularity formal contexts. Theories and examples verify the reasonability and effectiveness of the conclusions drawn in the paper. In short, the paper not only can be viewed as an effective means for the expansion of FCA, but also is an attempt for the fusion study of the two theories.