Topological Properities Of The Covering Rough Topology Space

At present,the human has entered a new era of big data.With the rapid development of artificial intelligence and information technology,the data and information acquired by human beings in various fields are expanding rapidly,and the relationship between information and data is more complex.Rough set theory and method can effectively deal with these fuzzy and incomplete massive information,and obtain potential,correct and valuable knowledge from it.It has become a new mathematical tool to deal with fuzzy and inaccurate problems,and has been widely concerned by researchers at home and abroad.Rough set theory is an extension of set theory,but the classical rough set theory has great limitations in application,and it is particularly important to study and develop more general theories,so the generalized rough set theory has developed rapidly.Covering rough set theory is a very important branch of generalized rough set theory.In this paper,rough set theory based on cover is studied theoretically and computationally.Under the covering,as the main research object,the classification method of the approximate operator is not clear enough,the definition is complex,and the defects in various properties are also obvious.In this paper,we will focus on the improved methods and applications of the operator generated by the neighborhood,including the condition that when will the operator satisfies the closure property and internal property,and the condition that when will the operator satisfies the stability property.Since the object of rough set research is the collection of data,and topology is the classical mathematical subject of collection research,the study of rough set theory with topology theory will provide important theoretical support for the internal connection,classification,model building and algorithm implementation of the research data.This paper not only defines a new covering rough topological space,but also studies the topological separation and connectivity of the space.Moreover,a new stable operator model is defined,the important topological properties of operators are explored,and a simple and effective matrix calculation method for the new operator model is given.The main results of this paper have rigorous theoretical argumentation and logical reasoning,at the same time,through specific examples and charts to explain and apply the main conclusions.The research foundation of this paper can also be applied to knowledge reduction and big data mining and analysis in the field of intelligent information.