Research Of Fuzzy Rough Approximation Based On Bisimulation

Nowadays,with the rapid development of the internet,people's life is be-coming more and more intelligent and convenient.At the same time,a lot of data will be generated.If we classify data from the perspective of attributes and relationships of objects being described,they can be classified into three categories:attribute data,relational data and data with attributes and relation-ships.As a mathematical tool for data analysis and processing,rough set theory can effectively mine potential knowledge and information from attribute data.But rough set theory has some shortcomings in dealing with relational data.To solve this problem,a kind of relational structure describing relational data emerges as the times require.The relational structure consists of a universe and a set of relations.By bisimulation technology which describes "multi-step" in-formation,rough set theory is applied to relational structure and used to process relational data.In this paper,a class of fuzzy relational structure is taken as the starting point,and the fuzzy rough approximation is studied by using bisimulation tech-nology.The main research contents and innovations are as follows:1.The concept of a kind of multivariate fuzzy relational structure is put forward,and a mathematical model for fuzzy relation data is established.As an abstrac-tion of relational data system in the real world,relational structure can represent relational data to a certain extent.But we have noticed that relational structure describes relational data through some common relations,while ordinary rela-tions can only describe precise or strict relational data.That is to say,ordinary relations restrict the application of relational structure.Therefore,in order to meet the requirements of some relational data with fuzzy information,this pa-per extends the relational structure to the multivariate fuzzy relational structure on complete residual lattice.A multivariate fuzzy relational structure consists of a universe U and a set of fuzzy relations(?i)i?I,in which ?i,i?I,is a finite dimensional L-relation.Fuzzy relational data can be described by ?i,i?I.The fuzzy rough approximation is studied in the multivariate fuzzy relation struc-ture.Binary fuzzy relational structure is also discussed,and the fuzzy rough approximation is studied in this structure.At this point,the complete residue lattice L=[0,1]and the ?i,i?I,is ordinary binary fuzzy relations.2.The fuzzy relational structure is studied by bisimulation technology to provide theoretical support for complex data processing.This paper mainly studies the fuzzy relational structure whose set of fuzzy relations is finite.These fuzzy relations can be regarded as the knowledge about the fuzzy relational structure that has been acquired.But the knowledge is too scattered and need to be processed to make them more convenient and useful.Therefore,bisim-ulation describing "multi-step" information is introduced into fuzzy relational structures and the knowledge scattered in these fuzzy relations is collected by using the bisimulation.Taking bisimulation as the indistinguishable relation of the structure of fuzzy relation,this paper constructs the upper approxima-tion and the lower approximation of the study object,and discusses their re-lated properties.There are two methods to construct bisimulation in fuzzy en-vironment:one is to define bisimulation by general binary relation,the other is to define bisimulation by fuzzy relation(fuzzy bisimulation).In this paper,fuzzy rough approximation based on bisimulation and fuzzy rough approxima-tion based on fuzzy bisimulation are studied in fuzzy relational structures.3.Taking fuzzy relations as information granules,the concept of fuzzy rough relation is proposed,which provides theoretical support for dealing with fuzzy relation information.In the classical rough set theory,any subset A of the universe U is called a concept of the universe U.Any family of concepts in the universe U is called knowledge about U.The so-called information granules in the universe are the concepts in the universe.Given the approximation space(U,R),where R represents the binary relation on the universe U,we can define the upper approximation and the lower approximation of concept A with R as the indiscernibility relation.Similarly,in fuzzy relational structures,we construct the upper and lower approximations of any concept A in the universe of U by us-ing bisimulation relations as indistinguishable relations.In addition,this paper expands the application scope of information granule,and proposes the fuzzy rough relation from the angle of fuzzy relation.In other words,a fuzzy relation is understood as a concept or information granule,and upper approximation and lower approximation of fuzzy relations are constructed.Further,this paper studies the basic properties of the fuzzy rough relation based on bisimulation on universe U,and discusses the basic properties of the fuzzy rough relation based on bisimulation on two universe.