Granule description based on possible attribute analysis

Abstract

Concise granule descriptions for describable granules and approaching description methods for indescribable granules are fundamental issues in granular computing. The concept with only common attributes has been frequently investigated. To explore the granules with some special needs, we propose a new type of compound concepts in this paper: common-and-possible concept. Based on the definitions of concept-forming operations, the logical representations are derived for each of the following types of concepts: formal concept, property oriented concept, possible three-way concept, common-and-possible 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 four kinds of concepts.