Research On Attribute Reduct For Multi-Scale Decision Tables Based On Granularity Tree

Rough set theory is an effective tool for dealing with uncertain information,and attribute reduct is one of the important research contents.The attribute reduct algorithm of classical rough set theory can discover decision rules and perform attribute reduct,without requiring prior knowledge.However,this algorithm has certain limitations,such as inability to handle multiscale decision tables and incomplete decision tables.Based on this premise,this study proposes attribute generalization reduct algorithms for multi-scale decision tables and generalized multiscale decision tables based on the rough set theory.Given the above background,this paper pursued two main research objectives:(1)Conducted attribute generalization reduct of multi-scale decision tables from the perspective of granularity tree cut.Firstly,a granularity tree construction method based on hierarchical clustering was proposed according to the characteristics of multi-scale decision tables.Secondly,the global cut space was obtained based on the granularity tree and the concept of cut.Afterward,the consistent global cut spaces were updated using sequential three-way decisions.Finally,optimal global cut and its corresponding attribute generalization reduct were obtained using cost theory.(2)Extended the concept of attribute generalization reduct to generalized multi-scale decision tables to explore scale selection and attribute generalization reduct.Firstly,this paper regarded searching for the optimal scale as an optimization problem and used the idea of sequential threeway decisions to obtain the optimal scale of generalized multi-scale decision tables.Secondly,based on the optimal scale,the generalized multi-scale decision table and the corresponding granularity tree were reconstructed.Further,heuristic algorithms were utilized to find the corresponding attribute generalization reduct.Finally,this study considered incomplete cases and proposed an attribute generalization reduct algorithm for incomplete generalized multi-scale decision tables.In conclusion,the task of attribute generalization reduct in this paper is targeted.Based on the cut concept in the granularity tree,combined with the ideas of sequential three-way decision and cost theory,new algorithms for attribute generalization reduct have been designed for different types of decision tables,and the effectiveness of the proposed algorithms has been verified through experiments.The algorithms proposed in this paper can improve the theoretical framework of multi-scale decision tables and expand the application scope of multi-scale decision tables.