Research On Extended Covering Rough Set Models

Rough set theory is a mathematical tool for dealing with uncertain knowledge.It is proposed based on the classification mechanism and used to approximate the inaccurate or uncertain research objects by using of known knowledge.Up to now,it has been successfully applied to many aspects of social life.With the widespread application of rough set theory,the study on extended rough set models has become one of the hot spots in rough set theory.This paper focuses on the study of the extended model of covering rough set and the extended model of fuzzy covering rough set from the perspective of knowledge granule.The paper is organized as follows.In Chapter 1,the research background and research status of rough set theory are introduced,and the framework and innovations of this paper are given.In Chapter 2,the concepts of rough set,fuzzy set,rough fuzzy set,fuzzy rough set,covering and fuzzy covering and other related basic knowledge are introduced.In Chapter 3,the concepts and properties of core in the classical covering approximation space are discussed.Firstly,by considering the membership repeat degree and the common block repeat degree of objects with respect to covering,the concept of core is proposed,and the existence and uniqueness of the core are discussed.Also,the relationships among elementary set,neighborhood and core are studied,and the structure of the covering approximation space is further characterized.Secondly,by using the concepts of core and reduction,the concept of consistent covering is proposed,and the relationship between core and consistent covering as well as the relationships among reduction,core and consistent covering are revealed.Finally,the necessary and sufficient conditions for the covering and the neighborhood family derived from the covering to be equal are given.In Chapter 4,the neighborhood system based covering rough set models in the covering approximation space are discussed.Firstly,the concept of the neighborhood system is defined and its properties are studied.Secondly,by using the neighborhood system,two kinds of neighborhood system based covering rough set models are defined,and the relationships among these two new models and the neighborhood based covering rough set are revealed.Finally,the properties of these models are compared.In Chapter 5,inspired by Pawlak rough set model that the lower and upper approximations were defined by comparing the approximated crisp set with all definable sets in the approximation space,in a fuzzy covering approximation space,the membership degree based fuzzy covering rough set model is defined by comparing the membership degree of one object belonging to the approximated fuzzy set with those of the component fuzzy sets in the fuzzy covering,and the property of the model is discussed in a completed fuzzy covering approximation space.Further,the relationship between the model and Pawlak rough set as well as the relationship between the model and fuzzy rough set are revealed.In Chapter 6,by comparing the membership function of the approximated fuzzy set with those of component fuzzy sets in the fuzzy covering,the membership function based fuzzy covering rough set model is defined in a fuzzy covering approximation space,and the property of the model is discussed.Further,the relationship between the model and the membership degree based fuzzy covering rough set as well as the relationship between the model and Pawlak rough set are revealed.In Chapter 7,by generalizing the membership function based fuzzy covering rough set model defined in fuzzy covering approximation space to fuzzy ?-covering approximation space,the fuzzy ?-covering rough set model is defined,and its properties are given.In Chapter 8,the work in this paper is summarized,and the future work is looked forward based on the research of this paper and the current research trends in this field.