Knowledge reduction of dynamic covering decision information systems with varying attribute values

In practical situations, it is time-consuming to conduct knowledge reduction of dynamic covering decision information systems caused by variations of attribute values with the non-incremental approaches. In this paper, motivated by the need for knowledge reduction of dynamic covering decision information systems, we introduce incremental approaches to computing the type-1 and type-2 characteristic matrices for constructing the second and sixth lower and upper approximations of sets in dynamic covering approximation spaces caused by revising attribute attributes. We also employ several examples to explain how to compute the second and sixth lower and upper approximations of sets in dynamic covering approximation spaces. Then we propose the incremental algorithms for computing the second and sixth lower and upper approximations of sets and employ experimental results to illustrate the incremental algorithms are effective to calculate the second and sixth lower and upper approximations of sets in dynamic covering approximation spaces. Finally, we give two examples to show how to conduct knowledge reduction of dynamic covering decision information systems caused by altering attribute values.