Optimal Scale Reduction Of Multi-scale Decision Tables

Data in the real world is often organized at different levels of granularity and has a specific conceptual hierarchy.Multi-scale decision tables represent this type of data in hierarchical form.The current research on multi-scale decision tables includes but is not limited to optimal scale,optimal scale combination,decision rules.However,it is not a real reduction set obtained by optimal scale combination.It still needs to be reduced again.So it might lead to a higher reduction time.In order to further reduce the time complexity of reduction,this paper attempts to combine rough set with multi-scale decision tables,and gives a variety of optimal scale reduction methods.The main innovations are as follows:1)The optimal scale combination is further extended,and several definitions of optimal scale reduction and local optimal scale reduction are given,and the relationship between optimal scale reduction and local optimal scale reduction is discussed.2)In order to quickly obtain the optimal scale reduction under small-scale data,the graph is used to find the optimal scale reduction.Firstly,according to the relationship of the same attribute in the multi-scale decision tables at different scales,the multi-scale identification matrix is constructed.Then,the identification matrix is combined with the graph and the relationship between the graph and reduction is considered.A fast algorithm for optimal scale reduction is given.Finally,the effectiveness of the proposed algorithm is verified by numerical experiments.3)Considering the reduction problem of large scale data,an algorithm for optimal scale reduction based on divisibility is presented.Firstly,based on the relationship between object and decision class,the definitions of intra-class object compactness and inter-class object dispersion are given,respectively.On this basis,the separability of attribute subsets is given and the definition of importance degree is given in combination with weight.An algorithm for optimal scale reduction is given by using significance definition.Finally,experiments show the effectiveness of the proposed method.4)Considering the problem of local reduction,an optimal scale reduction algorithm based on conditional entropy is presented.First of all,the concept of boundary domain conditional information entropy is introduced into multi-scale decision tables.Then,some properties of boundary domain conditional information entropy.Its relationship with multiple optimal scale reduction.It is considered that how to use boundary domain conditional entropy to solve local optimal scale reduction.Finally,the effectiveness of this method is verified by experiments.