Research on distribution reduction and maximum distribution reduction by dominance rela-tions
Peng Hong · Computer Engineering and Applications Journal · 2009
The distribution reduction and maximum distribution reduction in inconsistent decision table based on dominance rela-tions is studied.This paper points out that the results about the distribution reduction and maximum distribution reduction in ref-erence [9] is not correct.Firstly,by giving a counterexample,the paper points out errors of the judgment theorems of the distribu-tion reduction and maximum distribution reduction in reference [9],and the cause of these mistakes is analyzed.Secondly,this pa-per points out the methods based on discernibility matrix for calculating the distribution reduction and maximum distribution re-duction in reference[9] is not correct.Therefor,the concept of absolute reduction in inconsistent decision table based on dominance relations is introduced,and it is proved that the absolute reduction is equal to the distribution reduction and maximum distribu-tion reduction.Furthermore,a new maximum distribution reduction is discussed and proved that the new maximum distribution re-duction is equal to the lower approximation reduction.