Positive And Negative Domain Covering Generalized Rough Sets And Rough Knowledge Dissemination

Worldwide,there has been a rapid growth in interest in rough set theory and its applications in recent years.There are lots of high-quality articles on rough sets that have been published in a variety of international journals.Rough set theory is a new mathematical approach to uncertain and vague data analysis.It is,no doubt,one of the most challenging areas of modern computer applications.Rough set theory has led to many interesting applications and extensions.It seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences, especially in research areas such as machine learning,intelligent systems,pattern recognition,knowledge discovery,decision analysis and expert systems.The research contents of this dissertation are positive-negative region covering generalized rough set,rough communication of knowledge,law mining by the function s-rough set and rough set theory applications in the evaluation of academic degree and graduate education and the identification of Chinese medicine habitat.The generalization of rough sets is a hot topic recently.Zakowski prop os ed covering generalized rough set by generalizing the partition to covering.It is a model with promising potential for applications to data mining.An extensive body of research works has been developed.But the covering generalized rough set has some shortcomings.One is that some elements,which are not in the given set,are in upper approximations of Zakowski's covering generalized rough set.Another is that the lower approximation and upper approximation are not dual.For a given crisp set,every element in the universe belongs to it or belongs to its complement.There are no boundaries.If there are some elements,which do not surely belong to the set or its complement,it means that there existed boundaries.So,it is a rough set.Based on the above,a new covering generalized rough set—positive-negative region covering generalized rough set,is proposed. The new rough set avoids the shortcomings of Zakowski's rough set.Its positive operation and negative operation are dual.The main contributions on positive-negative region covering generalized rough sets are as follows;Corresponding to the properties of Pawlak's rough set,the properties of new rough set are discussed.Some properties of Pawlak's lower and upper approximations do not hold for the covering positive and negative approximations.Some examples are given.In Pawlak's rough set theory,the main concepts are the lower and upper approximations.Different partitions of a universe generate different lower and upper approximations.In covering generalized rough set theory,however, different coverings could generate the same covering positive or negative approximations.By defining the equivalence covering,we have the conclusion that different coverings of a universe generate the same covering positive and negative approximations if and only if the covering are equivalence.As for the algebraic structure of positive-negative region covering generalized rough set,we get the axiomizations of the positive and negative approximation operations,and the positive rough sets and the negative rough sets are lattices about(?)_c in a quasi double representative approximation.The above conclusions have provided a solid foundation for the further development of new rough set and its applications in data mining.Pawlak's rough set theory has found many applications for knowledge discovery,data mining and cognitive sciences.Knowledge communication plays a more and more important role today.Based on the knowledge rough recognition and rough communication,rough communication of knowledge is proposed,we have shown the supremum of last result,no matter what transmission order among n Agent is,for a given concept X and the relation between the supremum and common knowledge and between the supremum and possible knowledge.The conditions,which the last result is zero or unchanging,are given. Rough communication of knowledge is a model with promising potential for applications to machine learning,expert systems and decision analysis.It is significance to discuss the best transmission order and the related problems.The S-rough set notion and function S-rough set notion were proposed by Shi kaiquan.Many articles of S-rough set and function S-rough set have published.Using dual function one direction singular rough sets,we give the concept of F-generation law in the system,the generation model of F-generation law and the recognition method of the system law.Dual function one direction singular rough set is a new theory and method in recognizing the turbulent law existing in the system and recognizing the system law.Two applications of rough set theory were tried.One application is in the evaluation of academic degree and graduate education.Using the reduct of attributes and the attribute significance,we analysis the expert evaluations of doctoral dissertations and find the problems in doctoral dissertation evaluating.The suggestion about dissertation evaluating has given. Another application is in identification of Chinese medicine habitat.This is the first time to use the rough set theory to identify the Chinese medicine habitat. The result show the rough set method is easy to operate and the identification is exact.It gives a direction to use the rough set theory in Chinese medicine.The main contributions are as follows;1.Corresponding to the shortcoming of Zakowski's covering generalized rough set,a new covering generalized rough set—positive-negative region covering generalized rough set,is proposed.Get the conclusion that different coverings of a universe generate the same covering positive and negative approximations if and only if the covering are equivalence,And get the axiomizations of the positive and negative approximation operations(Theorem 4.4.2).Prove the positive rough sets and the negative rough sets are lattices about (?)_c in a quasi double representative approximation(Theorem 4.5.1).2.Based on the knowledge rough recognition and rough communication, rough communication of knowledge is proposed.Show the supremum of last transmission results,no matter what transmission order among n Agent is,for a given concept X(Theorem3.3.4).3.Using dual function one direction singular rough sets,the concept of(?)-generation law in the system is given.The generation model of (?)-generation law and the recognition method of the system law are proposed (Theorem 5.3.1-5.3.4).4.Give two examples for rough set theory applications,one is the evaluation of academic degree and graduate education and another is the identification of Chinese medicine habitat.The results are satisfying.