Study On Rough Sets In Quotient Approximation Spaces

In the era of big data,industries like healthcare,transportation,communications are flooded with data,and the presentation of data information also tends to be diversified.In the face of massive data,the theory and method of generalized rough set can effectively extract useful information and apply it to data processing and analysis,so as to improve the ability of information acquisition.On the basis of covering rough set theory,this paper studies the covering on quotient space and its related operators as well as matrix calculation methods by combining quotient space theory with rough set theory,which establishes the relationship between coarse-grained information space and fine-grained information space,so as to solve the problem of particle description in coarse-grained information space.The ordered pair(V,CR)consisting of the quotient space and the covering on it is called the quotient approximation space.Keeping the good properties of the original approximation space to the quotient approximation space and describing the quotient space accurately as well as calculating it efficiently are of essential importance for the study of coarse-grained information space.Therefore,this paper studies a series of problems in the quotient space.(1)This paper proposes a unique covering definition for the quotient space,which preserves the good properties of the minimum description unit in the original approximation space(referring to the neighborhood and the complementary neighborhood of the element)into the quotient approximation space.(2)In order to give a better description of the quotient space,this paper defines four pairs of approximation operators,which establish the close relationship between the original approximation space and the quotient space from both microscopic and macroscopic points of view,and then the application of the operators is given in practical problems.(3)In order to improve the computational efficiency in the context of big data,this paper presents the matrix representation of four pairs of approximation operators on the quotient space,so that the computer can help to calculate the results quickly and accurately.(4)On the basis of the above research,the definition mode of operators on quotient space are extended to the quotient space of quotient space,and then six pairs of approximation operators are defined to provide a theoretical basis for the study of rough sets in coarser-grained information space.(5)In this paper,we compare the approximation operators involved in the quotient space,and show their relationships through a graph.What's more,some examples for further supplement explanation are also provided in this paper.