A study of interrelationships between rough set model accuracy and granule cover refinement processes

Abstract

Rough set model accuracy varies when granules change. Refinement is one way to characterize granule evolutions, but it has not been formally defined in rough set theory so far. Topologically, a granule cover W is called a refinement of another granule cover F if there exists some FW∈F such that W⊆FW for each W∈W. In this article, we show that the concept refinement in topology is too abstract to describe the variability of the rough set model along with the change in granules. By abstracting from some important granule refinements, such as reductions and minimal descriptions, we propose two novel granule cover refinements named base-type refinements and base-preserving refinements, which combine both point-set topology and rough set theory. We analyze the accuracy relationships of some typical approximation operators between granule covers and their base-type or base-preserving refinements. We also show that higher accuracy implies finer granule covers for some approximation operators. These are promising results for rough set model accuracy comparisons. Furthermore, the results hint at how to avoid exponentially increased computation complexity on rough set model accuracy comparisons by checking refinement relationships of granule covers directly instead of computing on them using approximation operators.