A property of reductions in Fuzzy Variable Precision Rough Set model

In this paper, we use strict mathematics reasoning to discover the relation between the threshold and reduction in Fuzzy Variable Precision Rough Sets (FVPRS), i.e., the reductions act as a nested structure with the monotonously increasing threshold. By using the nested structure of reductions, we could design algorithms to quickly find different reductions when a reduction is required. Here `different' means the reductions obtained using different thresholds.