The Matroidal Method In Rough Set

In recent years,rough set with its excellent performance in dealing with uncertain problems,is considered to be an important source of intelligent processing technology,and has attracted many scholars’ interests at home and abroad.As a mathematical tool for dealing with imprecise and uncertain problems,rough set theory has got considerable development in recent years,and is widely used in various fields.In particular,the rough set theory in artificial intelligence and cognitive science has been successfully used in the field,and provides a theoretical framework effectively for knowledge acquisition,machine learning,decision analysis,data mining,and other areas of information processing.At present,rough set research has made some fruitful results,but as a new intelligent processing teconology,there are many aspects to be improved and perfected.Matroid is a mathematical theory,which has a perfect and strong axiom system.It can describe things equivalently from different perspectives and provide a good solution for graph theory,lattice theory as well as many other mathematical fields.Therefore,using rough set to study matroid is good for scholars to observe the structure and fectures of rough set from different perspects.In this paper,we mainly study the matroid method in rough set.First of all,the matroid method in covering-based rough set is researched.On one hand,by building a new type of covering-based rough set and using the matroid method to study this covering-based rough set model;On the other hand,the quantitative analysis for covering-based rough set have been conducted by building matroid approximation operators.Then,we investigate the matroid method based on the generalized rough set,mainly by establishing matroid structure of the generalized rough set and using matrix to represent the approximation operators based on two universes.Specifically,the main results of this study are the following points:(1)A new type of covering rough set model is established.Based on the existing typesof covering-based rough set model,a new type of covering-based rough set is proposed,which is between the second type of covering rough set and the classic rough set.What’s more,we compare it with the second type of covering rough set and the classic rough set,then some of its unique properties are got.(2)Using the lower approximation number to quantify covering-based rough set.By establishing lattice structure of approximation number and the approximate operators of matroid to conduct covering-based rough set quantitatively.The approximation number of covering-based rough set viewed as a quantitative tool,has played an important role for quantitatively covering-based rough set.(3)Using matrix method to represent the approximation operators of rough set based on two universes.In fact,the rough set based on two universes is an extension of rough set on one universe to two different universes.Due to the different universes,the computational difficulty of approximation operators is also increasing.In rough set theory,matrix is a tool of efficient and measurable.Therefore,using matrix method to study the rough set based on two universes is a meaningful work.(4)The matroid structure of generalized rough sets is established.We can construct sets to satisfy the independent set axioms or closed set axioms,then some matroid structures are formed,and we can use the matroid structures to investigate the properties of rough set.It is conducive to use the powerful axiomatic system of matroid to study generalized rough set.