Attribute Reduction Method For Covering Information System Based On Set Covering Theory

Rough set theory is an effective tool for handling uncertain information and has been widely applied in various fields of artificial intelligence.However,the classification of classical rough set theory based on equivalence relation is too rigorous,which limits its practical application in many fields.Therefore,Classical rough set theory has been widely popularized,among which covering rough set theory is an important generalization direction.Attribute reduction is one of the core contents of rough set theory.The attribute reduction of coverage information systems is currently a research focus.The set coverage problem has a wide range of applications in logistics,location selection,transportation,and other fields.Many scholars have proposed various heuristic algorithms for this problem and have successfully applied them.In recent years,the cross research between set covering theory and rough set theory has attracted a large number of scholars.This article studies and finds a method to transform the attribute reduction problem of covering information systems into a set covering problem,and provides an effective new solution to the attribute reduction problem of covering information systems based on set covering theory.The specific work content of this article is as follows:(1)An effective new solution based on set coverage theory is proposed for attribute reduction in information systems without decision coverage.Firstly,a set covering model for covering information systems is constructed,and the relationship between the set covering problem and the attribute reduction problem for decision free covering information systems is established.Furthermore,it was proved that a minimal cover of the set covering model is a attribute reduction set of the original decision free covering information system,which provides the possibility of using existing efficient set covering theories to solve the attribute reduction problem of decision free covering information systems.Finally,a heuristic algorithm based on set covering problem was used to solve the attribute reduction problem in non decision covering information systems,and the feasibility and effectiveness of this method were verified through examples.(2)Extend work(1)to the coverage decision information system and find an effective new solution based on set coverage theory for the attribute reduction problem of the coverage decision information system.Firstly,the spatial complexity of the attribute reduction algorithm for non decision covering information systems was optimized,and it was proved that the attribute reduction method for non decision covering information systems based on set covering theory is also applicable to the attribute reduction problem of decision covering information systems.Subsequently,the concepts of internal attribute importance and external attribute importance were introduced,and a new solution for attribute reduction in covering decision information systems based on set covering theory was designed.Finally,the feasibility and effectiveness of this method were verified through an example.This article enriches the cross research between set covering theory and rough set theory,brings new theoretical tools and methods for attribute reduction problems in covering information systems,and expands the application background of set covering theory.