Granule description in knowledge granularity and representation

Abstract

Granule description is an important problem in knowledge granularity and representation. In the theoretical study of granule description, two basic sub-problems need to be solved: (1) check whether a target granule is definable, and try to offer an exact description for the target granule if definable; (2) an appropriate approximate description should also be provided to the target granule if indefinable. Up to now, there have been some preliminary studies on these two sub-problems. However, the existing findings are not enough or incomplete since sufficient and necessary conditions of definable granules have not been explored, and there have not been effective ways to find better approximate descriptions of indefinable granules. Motivated by these discussions, this paper puts forward granule description methods for definable and indefinable granules. First of all, we propose the notions of covering elements and inserting elements of a target granule by which sufficient and necessary conditions of ∧-definable and (∧,¬)-definable granules are constructed. And then, the smallest definable granule containing the target indefinable granule and the largest definable granule included in the target indefinable granule are investigated, which are used to solve the problem of finding better approximate descriptions for indefinable granules. Finally, a comparison is made to show that the existing work on complete sets should be improved for providing feasible solutions to the granule description problem.