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Attribute reduction is among the most important areas of research in rough sets. This paper investigates the types of local attribute reduction for decision tables. We propose the concepts of l th decision class lower approximation reduction, l th decision class reduction, and l th decision class β -reduction for decision tables, and provide their corresponding reduction algorithms via discernibility matrices. We also establish the relationship between positive-region reduction and the l th decision class β -reduction, and report a case study using the University of California–Irvine dataset to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Covering rough sets are an important extension of Pawlak rough sets. This paper studies the relations arising from coverings and their topological structures. Every covering induces a reflexive and transitive relation. We represent the approximate pairs proposed by Ma (2015) [20] with different combinations of a relation and its inverse. Based on this representation, we give the relationship among approximate pairs. We also consider the topological structures induced by these lower approximations and establish the relationship among these topologies. The results show that the approximate pairs can be precisely characterized by a relation and its inverse. [ABSTRACT FROM AUTHOR]