Information Entropy Based Optimal Scale Selection In Multi-scale Decision Tables

Granular computing is a discipline that studies ways of thinking,methods of solving problems,theory,method,technology and tools of information processing mode based on granular structure.It is a new computing paradigm.Multi-scale data analysis is one of the important research directions in the field of granular computing.Hierarchical data also exists widely in real life.In order to represent and process the data with hierarchical structures,Wu and Leung proposed a multi-scale decision table,and gave the optimal scale selection method.Using these methods,we can select the optimal scale to make decisions while keeping the decisions credible,thereby saving the cost of decisions made by hierarchical data.Most of the existing methods are to study the optimal scale selection method from the perspective of consistence or lattice,and the optimal scale selection method based on information entropy is rarely reported.Therefore,this paper chooses to carry out research on the optimal scale selection method based on information entropy,which has the following contents:(1)For the multi-scale decision table,the definition of the optimal scale based on Shannon conditional entropy and complementary entropy and the method for selecting these two optimal scales are proposed.The confidence of the decision rules of the decision table corresponding to optimal scale based on Shannon conditional entropy is consistent to the confidence of the decision rules of the finest scale.The optimal scale based on complementary conditional entropy is finer than the optimal scale based on Shannon conditional entropy.(2)For the generalized multi-scale decision table,an optimal scale combination selection algorithm based on Shannon conditional entropy and complementary conditional entropy is proposed.The method based on Shannon conditional entropy can obtain the distribution optimal scale combination of consistent and inconsistent generalized multi-scale decision table.The method based on complement conditional entropy can find a new and more optimal scale combination than distribution optimal scale combination.Finally,data experiments are used to verify the effectiveness of the algorithm.