A unified approach to reducts in dominance-based rough set approach

The Dominance-based Rough Set Approach (DRSA), which is an extension of the Rough Set Approach (RSA), analyzes a sorting problem for a given data set. Attribute reduction is one of major topics in RSA as well as DRSA. By attribute reduction, we can find an important attribute set, which is called a reduct. In this paper, we propose a new approach to reducts in DRSA. A few kinds of reducts have been already proposed in DRSA, therefore, we clarify relations among the proposed and previous ones. We prove that they are consolidated into four kinds. Moreover, we show that all kinds of reducts can be enumerated based on two discernibility matrices.