Based On Variable Precision Tolerance Relations Extended Rough Set And Its Application In Data Mining Research

Rough set theory initialized by Professor Pawlak in early 1980's has been proved to be an excellent mathematical tool dealing with uncertain and vague description of objects, whose basic idea is to derive classification rules of conception by knowledge reduction with the ability of classification unchanged. It may find the hiding, potential and effective rules, that is knowledge, and relationship from the data without any preliminary or additional information. So rough set can deal with objects more objective and practically. In recent years, as an important part of soft computing, rough set theory and its applications have played an important role, especially in the areas of pattern recognition, machine learning, decision analysis, knowledge discovery and knowledge acquisition and so on. But Classic rough set is not suitable for incomplete decision information systems which this paper just deal with. Firstly, the basic theory of rough set and its extended models are introduced. After their shortcomings are provided, an new extended rough set model based on variable-precision tolerance relation is raised which divides objects based on some statistics information and psychological factors, and then upper and lower set approximations are defined. Secondly, the problem of attribute reduction is discussed. To find all reductions and a minimal reduction has been proved to be NP-Hard. But many heuristic algorithms especially some methods based on discernable matrix have been provided recently. A new method to get discernable matrix is raised which can overcome the inadequate of discernable matrix based on tolerance relation and then an algorithm to get reduced attributes sets is designed which is more simple than those literatures. Thirdly, a knowledge tree is provided, and then its restrict conditions and an algorithm for getting decision rules are discussed which not only lower the computational complexity, but also reduce redundancy rules. All models and algorithms are brought about by seven matlab programs, and the effectiveness of each model or algorithm is proved by one example. At the end of the paper, the application of extended rough set based on variable-precision tolerance relation about assurance and mileage of car is discussed.