The Approach To Local Rough Sets Based On Set-valued Information Systems

As for a kind of granular computing model,rough set is an important model tool to deal with data.With the maturity of rough set theory,the data analysis based on the rough set theory has been used widely in machine learning,pattern discrimination,data mining and other fields.All walks of life are faced with massive and complex data issues with the era of big data coming.How to select large-scale data effectively and process large-scale data is the main content of this paper.Information systems often have set-valued data because of the diversity of data sources in real life.This paper establishes the local rough set model in set-valued information systems in order to deal with set-valued data effectively.The way of processing set-valued data can narrow down the scope of screening information to local scope,exclude redundant information which has nothing to do with the target concept in the global scope,reduce the calculating time and simplify the calculation steps.In this paper,we establish the local rough set model in set-valued information systems and study the attribute reductions of the local rough set model in this context.As the information renewing constantly,information systems are dynamic change in practical application.And especially,the attribute sets in the information systems change dynamically.Therefore,based on the local tolerance rough sets,this paper presents the incremental mechanisms of dynamic local tolerance rough sets based on the matrix.At the same time,from the perspective of multi-granularity,this paper establishes the local multigranulation tolerance rough sets while taking the same problem from different views into consideration.In order to make the application of multigranulation rough sets more extensive,the local generalized multigranulation variable precision tolerance rough sets model by introducing characteristic function is established.On this foundation,the methods of attribute reduction are studied.This paper mainly includes the following three aspects:(1)The local tolerance rough set model in the set-valued information system is established,and then the related properties and the attribute reduction problem are studied.Furthermore,how to update the lower and upper approximations of local tolerance rough sets quickly and effectively when the attribute sets change dynamically is studied.As a result,how to update dynamically by using the incremental mechanisms of updating local relation matrices is proposed.At the same time,corresponding experiments are given to prove the feasibility of the dynamic updating algorithms.(2)By combining local rough sets with multigranulation rough sets,two kinds of local multigranulation tolerance rough sets which include optimistic and pessimistic cases in the set-valued information system are established,and then the related properties are studied.In addition,the lower approximation algorithms of local optimistic multigranulation tolerance rough sets and global optimistic multigranulation tolerance rough sets are given.Finally,a concrete example is used to verify the effectiveness of the proposed algorithms.(3)The local generalized multigranulation variable precision tolerance rough set model in the set-valued information system is established,and then the related properties are studied.Moreover,the concepts of inner and outer importance of the attribute are defined.At the same time,the local attribute reduction algorithm and the global attribute reduction algorithm of local generalized multigranulation variable precision tolerance rough sets in the set-valued decision information system are given,and the effectiveness of the algorithms is proved by the experiments.