Granule description based on formal concept analysis

Abstract

Granule description is a fundamental problem in granular computing. Although the spirit of granular computing has been widely adopted in scientific researches, how to classify and describe granules in a concise and apt way is still an open, interesting and important problem. The main objective of our paper is to give a solution to this problem under the framework of granular computing. Firstly, by using stability index, we classify the granules into three categories: atomic granules, basic granules and composite granules. Secondly, in order to improve the conciseness and aptness of granules, we impose additional conditions on minimal generator to define a new term which is called the most apt minimal generator. And then, based on the most apt minimal generator, we put forward methods for the description of atomic granules and basic granules. Moreover, for composite granules, we continue to divide them into three subcategories: ∧-definable granules, (∧, ¬)-definable granules and (∧, ∨)-definable granules, and their respective descriptions are provided as well. Finally, some discussions are also made on indefinable granules.