Comparative Research of Different Attribute Reduction Definitions
To study the relationships of the attribute reduction definitions based on Hu's discernibility matrix,information entropy,distribution,maximum distribution,approximate and positive region,we construct the Hu's simplified discernibility matrix at first.Secondly,simplified discernibility matrix based on positive region is also constructed,and the corresponding attribute reduction definition is proposed.At the same time,it is proved that the attribute reduction definition of simplified discernibility matrix based on positive region is equal to that based on positive region.Thirdly,by using Hu's simplified discernibility matrix,it is proved that if B satisfies φ≠mij∈M■mij∩B≠φ,where M is Hu's discernibility matrix,then B must satisfy H(D|B)=H(D|C).By exploiting simplified discernibility matrix based on positive region and simplified discernibility matrix based on approximate reduction,it is also proved that if B is approximate consistent set,then B must satisfy POSB(D)=POSC(D).According to the existed research results,the relationships of these six different definitions about attribute reduction are obtained.