Attribute Reduction Methods Based On Dominance Relations And Concentration Matrix

Attribute reduction is an important issue in rough set theory research.The traditional attribute reduction method based on discernibility matrix can only deal with consistent decision tables,while the improved discernibility matrix can deal with consistent and inconsistent objects respectively.However,not every element in the improved discernibility matrix is useful for the attribute reduction,that is,there are a large number of redundant elements which will cause a low computational efficiency.The concentration discernibility matrix is proposed to reduce the storage cost of attribute reduction to a certain extent and improves the reduction efficiency.And then the concentration Boolean matrix further improves the generation efficiency of the discernibility matrix by Boolean algebra.However,most of the relevant models are based on equivalence relations and cannot extract ordered information.On this basis,the main research contents and contributions of this study are as follows:Firstly,for inconsistent decision tables,the reduction method based on discernibility matrix is further improved.Combined with the idea of variable precision,some inconsistent objects were reasonably added to the set of consistent objects,thereby increasing the amount of consistent information and improving the quality of reduction.The use of condensed Boolean matrix effectively reduces the computational cost of attribute reduction.Secondly,an efficient attribute reduction model based on concentration dominance matrix is established,which extends the method on equivalence relations to dominance relations.The concept of concentration dominance matrix is proposed for the dominance matrix,and the corresponding model of efficient reduction is developed.Thirdly,we further put forward the concept of concentration boolean matrix under dominance relations and establish a corresponding attribute reduction method.For inconsistent decision tables with preference-valued attributes.The concept of concentration Boolean matrix is proposed for the dominant matrix.The concentration Boolean matrix further improves the generation efficiency of the dominance matrix by Boolean algebra,and further improve the efficiency of attribute reduction based on dominance relations.