Comparison study on different core attributes.

How to find the core attributes is important for attribute reduction based on rough set. However, there are few literatures discussing this topic, and most existing works are mainly based on Skowron’s discernibility matrix. Till now, there are main three kinds of core attributes: core of the skowron’s discernibility matrix (denoted by Core1(C)), core of the positive region (denoted by Core2(C)), and core of the information entropy (denoted by Core3(C)). Some researchers have been pointed out that these three kinds of cores are not equivalent to each other. Based on the above three kinds of core attributes, we at first propose three kinds of simplified discernibility matrices and their corresponding cores, which are denoted by SDCore1(C), SDCore2(C) and SDCore3(C), respectively. Then it is proved that Core1(C) = SDCore1(C), Core2(C) = SDCore2(C), and Core3(C) = SDCore3(C). Finally, based on three proposed simplified discernibility matrices and their corresponding cores, it is proved that Core2(C) $${\subseteq}$$ Core3(C) $${\subseteq}$$ Core1(C). [ABSTRACT FROM AUTHOR]