An advancing investigation on reduct and consistency for decision tables in Variable Precision Rough Set models

Variable Precision Rough Set (VPRS) model is one of the most important extensions of the Classical Rough Set (RS) theory. It employs a majority inclusion relation mechanism in order to make the Classical RS model become more fault tolerant, and therefore the generalization of the model is improved. This paper can be viewed as an extension of previous investigations on attribution reduction problem in VPRS model. In our investigation, we illustrated with examples that the previously proposed reduct definitions may spoil the hidden classification ability of a knowledge system by ignoring certian essential attributes in some circumstances. Consequently, by proposing a new β-consistent notion, we analyze the relationship between the structures of Decision Table (DT) and different definitions of reduct in VPRS model. Then we give a new notion of β-complement reduct that can avoid the defects of reduct notions defined in previous literatures. We also supply the method to obtain the β- complement reduct using a decision table splitting algorithm, and finally demonstrate the feasibility of our approach with sample instances.