Granule Description of Incomplete Data: A Cognitive Viewpoint

Granule description is one of the main challenges to realize explainable AI technologies through information granules. Specifically, granule description of incomplete data is still an open, interesting and important topic. In this study, this problem is studied systematically based on extent-intent view. Concretely, at first we define stable concepts and evanescent concepts in an incomplete formal context and propose their acquisition approaches, respectively. And then, we classify granules into two categories, i.e., basic granules and indefinable granules. After that, we present the descriptions of basic granules via stable concepts and evanescent concepts. Finally, we make some discussions on how to describe indefinable granules. The main contribution as well as the significant feature of this study is granule description of incomplete data based on ordinary formal concepts rather than approximate concepts. The analysis shows that the ordinary concept-based granule description is more concise and less complex than the approximate concept-based granule description, and meanwhile, the ordinary concept-based method can also maintain the same recall of granule description as that of the latter method. Our work will provide cognitive research method to the description of incomplete formal context with the help of concept cognition units.