Nested structure in parameterized rough reduction

In this paper, by strict mathematical reasoning, we discover the relationship between the parameters and the reducts in parameterized rough reduction. This relationship, named the nested reduction, shows that the reducts act as a nested structure with the monotonically increasing parameter. We present a systematic theoretical framework that provides some basic principles for constructing the nested structure in parameterized rough reduction. Some specific parameterized rough set models in which the nested reduction can be constructed are pointed out by strict mathematical reasoning. Based on the nested reduction, we design several quick algorithms to find a different reduct when one reduct is already given. Here ‘different’ refers to the reducts obtained on the different parameters. All these algorithms are helpful for quickly finding a proper reduct in the parameterized rough set models. The numerical experiments demonstrate the feasibility and the effectiveness of the nested reduction approach.