Research On Invariant Subspace In Rough Set Theory

All current work on calculating approximate sets of a rough set inevitably requires the participation of all elements in the universe.However,it is cumbersome and causes a huge waste of resources when the universe is quite big and the computed set is small enough.By introducing the notion of invariant subspace in rough set theory,we skillfully reduce the range of elements involved in the computations of approximations of a rough set from the whole universe U to a suitable invariant subspace V of U,and then give the modular method within the reduced range.In addition,we present the modular Boolean matrix method,such that the calculation of upper and lower approximations of rough sets can be converted into operations on modular matrices.Moreover,the results in covering approximation space are generalized to fuzzy β covering approximation space to calculate the upper and lower approximations of the crisp sets.In particular,an algorithm for calculating the value of β is proposed to make the involved information has the highest distinction degree.This β is more credible and meaningful than the empirical one.Besides,we take the patient diagnosis of COVID-19 as an example to elaborate the application of this β.Finally,we proposed fuzzy accompanied approximation space(FAAS)and the approximate operator models on two universes and their relationships are investigated from a new perspective.The model may open a new way for the study of rough set and invariant subspace.