Comparative Study Of Grey System And Rough Set

Grey system theory takes the uncertainty system with small samples and poor information as research objects. It mainly draws valuable information out of the partial already known, and its aim is to realize the correct description and effective control of system running and evolution rule. Rough set theory is too a new powerful mathematical method of processing vague and uncertain information. This theory is used to represent incomplete knowledge and set up their models, inducing the decision or classification rules of problems by the reduction of knowledge.Grey system theory and are rough set theory have some similarities and complementarities. The two theories both generalize the classical set theory in order to characterize the imprecise and uncertain information, and for uncertain problems, they hardly need any experiential knowledge, whereas some other theories require experiential knowledge for problem solving. This thesis compares the two theories with each other and finds some complementarities between them: the real data and rules processing by grey system are a supplement of attribute reduction based on rough set, and the attribute reduction based on rough set is too a supplement of grey incidence analysis with massive redundant attributes.Firstly, through the analysis of grey system theory, and the researchment of application of rough set used in attribute reduction, this thesis draws two points in which we can get an integration of the two theories. With two real examples, applications of grey incidence analysis and grey cluster are researched, and feasible analysis of integration of the two theories has been done.Secondly, based on the analysis above, two advanced model have been drew. One is using attribute reduction based on rough set for the preprocess of grey incidence analysis. The other one is that integrating the initial information with the result of grey cluster to form rule sets of policy decision. Additionally, this thesis has drew a general modeling step of the two advanced models, and the suitable condition of the models has been given.Finally, with a example of failure diagnosis of differential piston air compressor, one of the advanced models has been realized, and the new model is called grey incidence analysis model based on attribute reduction. By analyzing the result of the experiment, the advanced model has concluded a consistent result which the traditional analysis model concludes. In the other hand, the application of the advance model could reduce the computation load and increase the precision of the analysis result.