Research On The Rough Set Models Based On The Fuzzy Covering

Since Ma extended fuzzy covering to fuzzyβ-covering,fuzzyβ-covering usher in a vigorous development,and even its own branch of fuzzy covering is more and more.Fuzzy minimum description,lattice,matrix,etc.make it associated with many mathematical knowledge.With the knowledge of attribute reduction proposed by Yang et al.,many reduction propositions about four types of fuzzyβ-covering approximation space are proposed in this paper based on this theory.This theoretical achievement can reduce some unnecessary operations in the application of rough set model based on fuzzy covering to some extent,thus improving the efficiency of operation.In Chapter 1,the research background and significance of rough set models based on fuzzy covering are introduced,and some necessary theoretical knowledge is given to understand this paper,and the structure of this paper is also given.In Chapter 2,in the fuzzyβ-covering approximation space（U,Cμ）,based on Ma,Yang et al.’s four fuzzyβ-covering approximations,two fuzzyβ-covering Cμ₁ and Cμ₂,eight propositions and four inferences corresponding to attribute reduction under four rough set models are given successively,and their proofs are given.Then through the comparison of two examples,on the one hand,it is shown that the reduction results will be simplified and the amount of calculation will be reduced,on the other hand,the reason why the necessity is not established is discussed.In Chapter 3,in fuzzy information system FIS（28）（U,AT）,the sufficient conditions of two fuzzy information systems and the approximate equality of fuzzyβ-covering height are obtained based on the fuzzyβ-covering approximation theory and the concept of attribute reduction,and an example is given.Secondly,based on the definition of the high-low fuzzy covering of the fuzzy information system itself and the problem of attribute reduction,the necessary conditions for the equality of the two fuzzy information systems are given.In Chapter 4,firstly,in the fuzzyβ-covering approximation space（U,Cμ）,Yang et al.obtained a new rough set model by combining the concept of fuzzy minimum description.On this basis,we obtain the sufficient conditions for the approximate equality of two fuzzyβ-covering descriptions,and illustrate them with examples.Secondly,in the L-fuzzyβ-covering approximation space（U,C°）,the sufficient conditions are obtained.In Chapter 5,in the approximation space（U,C）of L-fuzzy covering,according to the three rough set models obtained by Yang et al.,this chapter mainly obtains the sufficient conditions for two L-fuzzy covering to produce the upper and lower approximation of the same L-fuzzy covering under three definitions.In Chapter 6,this paper is summarized,and the prospect of research on fuzzy covering rough set model is given.