Discussion On Attribute Reduction Approach Of Covering Rough Sets

Rough set theory proposed by Pawlak is a mathematical tool to deal with fuzzy and imprecise problems,which can be used to find hidden knowledge in data,to reveal potential rules and to make accurate decisions.However,the requirement of equivalence relation in Pawlak rough set model limits the application range and processing effect of rough set theory to a great extent.In order to solve this problem,many generalized rough set models have been proposed in recent years,including relational rough sets,fuzzy rough sets,variable precision rough sets and covering rough sets.The covering rough set theory has become an important part of rough set theory.Attribute reduction is one of the most important contents in the rough set theory.It removes the redundant information of high-dimensional data and is widely used in data mining,pattern recognition,and other fields.The covering rough set mainly focuses on the properties of covering approximate operators.It is a significant and urgent task to improve the efficiency and complexity of attribute reduction based on the covering rough set.In this thesis,we proposed three attribute reduction methods based on the covering rough set theory.The specific research mainly involves the following aspects.In Chapter 1,we firstly describe the research background and present situation involved in this thesis,and then introduce the main research work and the organizational structure of this thesis.In Chapter 2,we firstly introduce the following theories: attribute reduction based on the covering rough set and graph,the relationship between minimum vertex covering of graph and attribute reduction of covering decision information system,and the equivalence between attribute reduction of covering decision information system and solving minimum vertex covering of a hypergraph.Then,we proposed a new attribute reduction algorithm based on graph for covering decision information system.The experimental results show that the proposed algorithm can not only reduce the dimension of data effectively but also run fast and maintain a high classification accuracy.In Chapter 3,we propose a local covering rough set model and the local reduction theory of the covering decision information system.Then we present an algorithm for the local covering approximate set.Finally,we prove the advantages of the proposed algorithm by instance analysis.In Chapter 4,we firstly propose a multi-granularity local covering rough set model and then present the local attribute reduction theory of the multi-granularity covering decision information system.Finally,examples and algorithm analysis verify that the local reduction theory of multi-granularity covering rough sets has certain advantages.