The Relationship Among Attribute Reduction Of A Decision Table

Rough set theory is a kind of theory for data analysis,it is mostly used to deal with uncertain information.Compared with the general rough set theory,i.e.Pawlak rough set,the theories of Variable precision rough set and Multi-granulation rough set have more application in various fields.One of core issues in rough set theory is attribute reduction in information systems,and the idea of three-way decisions is also an important topic in rough set theory.On the basis of Pawlak rough set,Variable precision rough set and Multi-granulation rough set,this paper defines different attribute reductions,which can preserve the positive region,negative region and boundary region,respectively.And then,the relationship among them are further studied.The main contents of this paper are as follows:1.Based on Pawlak rough set,Variable precision rough set and Multi-granulation rough set,three kinds of attribute reductions which can preserve the positive region,negative region and boundary region are defined respectively.The relationship between positive regions(negative regions;boundary regions)in the framework of Pawlak rough set and Multi-granulation rough set is studied.The properties of positive region,negative region and boundary region in the framework of Variable precision rough set are presented.2.A lot of relationship are discussed for these three kinds of rough set theories.Firstly,the relationship of eight kinds of attribute reduction for Pawlak rough set are discussed.Then,three kinds of attribute reduction for Multi-granulation rough set are searched.Finally,three kinds of attribute reduction in Variable precision rough set are studied.