Study Of Variable Precision Rough Set And Its Applications In Databases

The classical Rough Set theory(RS) developed by Professor Z.Pawlak in 1982 has made a great success in knowledge acquisition in recent years.Unfortunately,it requires accurate classification. In practice,because of possible errors in data measuring,noice data often occur.To deal with inconsistency in decision tables ,Professor W.ziarko developed the Variable Precision Rough Set model(VPRS) in 1990s,which is an extension of the RS.However,the research on VPRS has been a bit stagnant.The main objective of this thesis is to study VPRS under both incomplete information systems and complete information systems.The structure of the paper is as follows. First two chapters are devoted to a brief introdunction of RS theory as well as the motivation and main results of this thesis. In chapter 3, the limitations of three extensions of RS,namely, tolerance relation,non-symmetric similarity relation and limited tolerance relation ,under incomplete information systems are analyzed at first.Then a variable precision extension based on a limited tolerance relation is developed and it is demonstrated that the new extension inherits the merit of the other extended relations and discards their limitation.The research of the 4th chapter mainly focuses on knowledge reduction based on VPRS theory under complete information systems.firstly,it draws up two algorithms: the approximate reduction algorithm and distribution reduction algorithm,analyzes them and points out their strongpoint and shortcoming.Secondly, it introduces an improved algorithm which revises the discernibility relation of similarity sets on the basis of the Discernibility Matrix of distribution reduction.The improved algorithm eliminates the harsh requirements of distribution reduction.To some degree,it overcomes the drawback of possible reduction that the derived decision rules may be in full incompatible with the ones derived from the original system. Finally,theoretical analysis and experimental results are used to prove the improvement of the algorithm.