Attribute Reduct Of Several Information Systems In Fuzzy Environment

Attribute reduction and decision rule acquisition are important applications of rough set theory and fuzzy rough set theory.Fuzzy rough set theory,which combines rough set theory with fuzzy set theory,can deal with uncertain and fuzzy information.The use of fuzzy tolerance relation in the study of set valued information system and real valued information system can greatly reduce the loss of information.So,in this paper,based on fuzzy tolerance relation,attribute reduction and decision rule acquisition are studied for several information systems,and a new fuzzy rough set model is established.The paper includes the following parts:In Chapter 1,the research background and research status of fuzzy rough set theory and attribute reduction in information systems are introduced,and the organization and innovation of this paper are given.In Chapter 2,some notations and basic concepts for Pawlak rough set model and fuzzy rough set model such as equivalence relation,equivalence class,covering of the universe,partition of the universe,fuzzy set and fuzzy relation are introduced.In Chapter 3,the attribute reduction for the set valued information systems is firstly studied.The similarity degree of two fuzzy relation matrices is defined and utilized to design one heuristic algorithm for computing the attribute reducts.This heuristic algorithm only employs the minimizing operation and comparison operation of the matrices.Then,for the set valued decision information systems,considering that the relative reducts is defined according to the decision values of the objects,the fuzzy matrix defined in the set valued information system is modified and utilized to design the heuristic algorithm for computing the relative attribute reducts.This approach is also applicable to other information systems when the fuzzy relation is employed to describe the similarity degree of objects.In Chapter 4,for real valued information systems with fuzzy decision,based on the proposed concept of supporting set of the decision interval,two types of relative reducts called the relative reduct based on fuzzy tolerance relation and the relative reduct based on maximal tolerance class are defined.For the first type of relative reduct,the computing method based on the discernibility function and heuristic algorithms are given,respectively.For the second type of relative reduct,the computing method based on the discernibility function is given,and the optimal decision rules are obtained by the second type of relative reduct.Finally,the relationship between these two types of reducts is revealed.In Chapter 5,in the fuzzy covering approximation space,the definition of fuzzy ?-neighborhood based on fuzzy tolerance relation is given.By using the fuzzy ?-neighborhood,a new fuzzy rough set model is proposed and the properties of the proposed model are discussed.Finally,based on the new fuzzy rough set model,the relative reduct is defined in set valued information systems.In Chapter 6,we conclude our work and look forward to the future work.