Granule Description based on Compound Concepts
  Concise granule descriptions for describable granules and approaching
description methods for indescribable granules are challenging and important
issues in granular computing. The concept with only common attributes has been
frequently studied. To investigate the granules with some special needs, we
propose two new types of compound concepts in this paper: bipolar concept and
common-and-necessary concept. Based on the definitions of concept-forming
operations, the logical formulas are derived for each of the following types of
concepts: formal concept, three-way concept, object oriented concept, bipolar
concept and common-and-necessary concept. Furthermore, by utilizing the logical
relationship among various concepts, we have derived concise and unified
equivalent conditions for describable granules and approaching description
methods for indescribable granules for all five kinds of concepts.
