| The extension of rough sets theory and the information processing based on it in incomplete information system are studied systematically in this dissertation, including rough sets model extension, attribute reduction, rule extraction and incomplete data filling. The main content of this dissertation can be generalized as follows:(1) The existing extended rough sets models for incomplete information system are separated into two types by the difference of similarity description method between two objects, and the merits and demerits of this two types are analysed. Then an improved extended rough sets model based on dynamic tolerance relation is proposed on the basis of valued tolerance relation. Firstly, an improved calculating method of tolerance degree is presented. This method gives a comprehensive consideration of the same probability of unknown attributes and the effect of known attributes to unknown attributes. And it is an effective combining of similarity calculating method in connection degree tolerance relation and valued tolerance relation. At present, tolerance degree thresholds haven't been given out an definite calculating method in all the valued extended rough sets models, usually been set subjectively. It's not object, and affect the model's classification result. So secondly, an objective calculating method of tolerance degree threshold is proposed. And the threshold can been adjusted expediently with the dynamic updating of data. Experiments prove that extended rough sets model based on dynamic tolerance relation has better classification result than all existing extended rough sets models.(2) The imperfectness of information may cause new incompatibility to decision information system. While traditional discernibility matrix and it's improvements can't deal with this problem well. So the concept of coordinate discernibility matrix and an attribute reduction algorithm based on it are proposed in this dissertation. The imperfectness of information causes waste of time and space in discernibility matrix algorithm. To solve this problem, an attribute reduction algorithm of approximate quality for large information system is proposed, and the complexity of this algorithm is also been analysed. This algorithm mainly save up the time-space price of discernibility matrix by means of accordant tolerance class. The calculating of it can compress the repeating comparison of missing value in information system. Lastly, the procedure of algorithm is shown through a specific case, and the validity of it is proven by experiment.(3) As an effective rule extraction method, the efficiency of LEM2 algorithm is under improve. To solve this problem, this dissertation proposes an improved rule extraction algorithm. It changes the inner circulation from blind search to heuristic search by decision distribution force matrix. Single condition rules can been extracted directly, and some redundant attribute can been deleted simultaneously. Further more, the end condition of LEM2 algorithm is also been modified to better fit incomplete information system. At last, detailed example illustration and experiment analysis proves the validity of LEM2.(4) Besides attribute reduction and rule extraction, the process of incomplete information also includes data filling. On the basis of ROUSTIDA algorithm, an improved valued tolerance relation based coordinate incomplete data filling approach(IVTRCIDA) is advanced. Firstly, this algorithm improves the calculating of tolerance degree to describe the similarity between objects more precision. Secondly, a data filling method of both positive and negative is given out according to whether two objects have same decision value. This method declines the conflict rate of completed information table, and increases the completing rate. Thirdly, this algorithm declines space complexity by replacing discernibility matrix with tolerance class. Lastly, this algorithm decreases the filling work by random filling to redundant attributes. Experiment shows that this IVTRCIDA algorithm can effectively increase the precision and completing rate and decrease the conflict rate.The innovative points of this dissertation include:(1) An improved calculating method of tolerance degree is presented. This method gives a comprehensive consideration of the same probability of unknown attributes and the impact of known attributes to unknown attributes. Then the dynamic tolerance relation and the extended rough sets model based on it are advanced. This extended model gives out the calculating and dynamic refreshing algorithms. Classification experiment shows that this extended rough sets model has better classification performance than existing models.(2) The imperfectness of information may cause new incompatibility to decision information system. The concept of coordinate discernibility matrix and an attribute reduction algorithm based on it are proposed in this dissertation. The definition of accordant tolerance class is given out. Then an approximate quality attribute reduction algorithm based on it is proposed for large scale information system. This algorithm improves time-space efficiency by compressing the repeating comparison of missing value in information system.(3) An improved rule extraction algorithm based on traditional LEM2 algorithm is proposed. It defines the decision distribution force matrix, and changes the inner circulation from blind search to heuristic search. Then it can extract the rules of singer attribute and delete some redundant attributes directly. So the improved LEM2 algorithm has better efficiency.(4) A coordinate incomplete data filling algorithm based on dynamic tolerance relation is advanced. This method improves how to calculate tolerance degree, gives a data filling method of both positive and negative, replaces discernibility matrix with tolerance class, and decreases the filling work by random filling to redundant attributes.
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