The Research And Application Of Attribute Reduction And Decision Rule Generation For Decision Tables Based On Rough Sets Theory

Rough set theory, proposed in early 1982, is a new mathematical tool in dealing with imprecision and uncertainty. The most remarkable characteristic of this theory is that it does not require any additional empirical information of data sets. By analyzing and reasoning the database, this theory can discover the patterns and rules hidden in database. In recent years, rough set theory has been applied to many areas successfully including pattern recognition, machine learning, decision support, predictive modeling. As a new tool of data analysis and processing, rough set theory has been taken more attention by the academic. Many researchers pay attention to the study of the algorithm using rough set approach, such as generation of decision rule algorithm, reduction of attributes algorithm, the algorithm associated the neural networks or GA with rough set and so on. The attributes reduction and decision rule generation are the kernel contents of rough set theory.The problem of synthetic evaluation is an extremely complex problem; it involves the object set of evaluation, the goal (the attribution) of evaluation, the evaluation method. The final result of the evaluation is decided by the above various factors. The commonly used synthetic evaluation method include: principal components analysis method, hierarchy analysis method, incidence matrixes evaluation method, fuzzy synthetic evaluation method and so on. These methods are subjective and fuzzy in weight establishment, which restrict people to appraise the object. As rough set theory has the ability of data analysis and processing, it could classify the object effectively and analyze incomplete information. So it is used in the weight coefficient determination of synthetic evaluation problem, which might avoid the limitation of the former method. At the same time, according to the relationship between the attribution and the result of the evaluation in the study sample, we can data mining the corresponding rules. Thus, the future object will be analyzed and forecast.In this thesis, we study the methods of decision rule generation and attributes reduction of the rough set and the application in the synthetic evaluation problem. On the base of these, the mainly work are done in this paper as follows:(1) An efficient attributes reduction algorithm based on different graph is proposed firstly. Different decision classification is separated at first in this algorithm, so comparing every two objects, we don't need to judge if they belong to the different decision classes each time. The algorithm's efficiency is high and the algorithm can apply to any decision table. The time complexity of the algorithm in the worst case is max (O(|C|2 ), O(|C||U|2 )) . |C| is the amount of the condition attributes; |U| is the amount of the object in the universe. At last, the proof of the algorithm relative to the completion of Pawlak reduction and the smallest attribution reduction are given and the algorithm's validity in the example is confirmed.(2) An algorithm of generation rules based on the membership function is proposed. All the decision rules on decision table without core-valued reduction would be generated by this algorithm. The practical significance of the rules obtained from the decision table is analyzed. Moreover, if we remove the redundant rules in the same classification, we will get the decision rules under each attribute reduction.(3) A synthetic evaluation example of the inhabitant consumption level of Shandong Province is used to discuss the application of the rough set in the synthetic evaluation problem.At the end of this paper, contents of this paper are summarized and the according work will be done in the future.