Correlation Fuzzy Rough Sets

Nowadays, the society has entered the era of network information, the rapid development of computer network information technology makes data and information in various fields increased dramatically (explosion), the uncertainty in the data and information systems becomes more significant due to the participation of human (complex systems). With the rough set theory put forward by Polish mathematician Z.Pawlak in1982, people gradually found that rough set theory has an advantage to deal with this large and complex data uncertainty. Therefore, many experts and scholars dedicated to the study of rough set theory in recent years. They proposed algorithm of rough set model, general relations of rough set model, rough logic and decision-making, variable precision rough set model, the probability rough set model, fuzzy rough set model and a series of concepts. In this paper, I study the promotion of fuzzy rough set on the basis of the previous work, put forward the concept of two kinds of fuzzy rough sets which are respectively under ordinary binary relation and fuzzy binary relation, give the general relation of fuzzy rough set model, fuzzy rough set model based on fuzzy relation, study on their properties and relationships. This paper also studies the fuzzy relation of fuzzy rough set α, β cut set and related roughness, and obtain some interesting inequality. This paper discusses the general binary relation fuzzy rough sets and topological spaces relationship. The paper is divided into four chapters.The first chapter is the introduction and preliminaries. The chapter introduces the overview of the development of the rough sets and fuzzy sets and research background, given the need of prior knowledge.Chapter two promotes the fuzzy rough set model under the equivalence, puts forward ordinary binary relation fuzzy rough set, discusses the nature of it. In this paper, I also discusse the ordinary binary relation and fuzzy approximation operator characteristics, thereby, obtain two important corollary.The third chapter does the work of further promotion of fuzzy rough set. In this paper I give the definition of the fuzzy relation fuzzy rough set and some properties and discuss the relations between fuzzy rough sets and topological spaces under fuzzy relations.The last chapter studies, under the fuzzy relation, the α, β cut set and related roughness of fuzzy rough set. It also gives a instruction that ρAα,β of fuzzy rough set which is a roughness about two parameters is a promotion of PR(A).