Research On Decision Analysis Method Based On Improved Bayesian Rough Set And Evidence Theory

Abstract:As two important tools for information processing, rough set theory and evidence theory have been widely used in the field of decision analysis, artificial intelligence and so on. By using the rough set theory, the information and the redundant attributes can be reduced, which improves the efficiency of analyzing and processing the information; the information can be synthesized by the evidence theory, which facilitates the decision maker to make the decision. Since the Bayesian rough set based on variable precision rough set, has the characteristics which can be affected by any parameters, so it is applied more widely in the field of artificial intelligence and data mining. Bayesian rough set theory is based on the objective reasoning of knowledge database, and on the basis of fully information using, improving the scientific of decision-making, certain subjectivity can be avoided by combing the evidence theory. Therefore, the research of decision methods combined Bayesian rough set theory and evidence theory has important significance.In this paper, improvements in the some relative theorems regarding Bayesian rough set and evidence theory have been made based on the previous literature. Several decision making methods are proposed with regard to multi-criteria decision making problems and classification problems of decision information table. The main work is as follows:(1)With the limitations of traditional Bayesian rough set in dealing with multiple decision classes, the traditional Bayesian rough set theory is improved and extended to multiple decision classes. The properties of Bayesian rough set model are analyzed and testified. The attribute reduction method is provided by using the lower distribution reduction. Firstly, the division of the information system on the condition attribute set and decision attribute set can be obtained by using the method, and then calculate the Bayesian lower distribution sets of the decision classes under the condition attribute set; Then, on the basis of the above, the discernibility attribute set and discernibility attribute matrix of lower distribution can be calculated; Finally, the discernibility formula of lower distribution can obtained by definition, and the attribute reduction set is received by calculating the minimal disjunctive norm.(2)With the problems of traditional evidence theory during the synthesis process, a method of quantifying the conflict between the evidences is proposed based on evidence conflict and evidence distance. Considering the new method of quantifying conflict, an improved combination rule is constructed, and the comparative examples with other evidence synthesis methods illustrate the effectiveness of the new method.(3)With regard to the discrete MCDM problems, in which the criteria weights are completely unknown, we give the decision-making methods based on Bayesian rough set and evidence theory. Firstly, the Bayesian rough set theory is used to the attribute reduction, and by using information entropy of rough set, the information gain is obtained, through which we can get the criteria’s weights, or the weights of evidences. Then, the dominance degree of the alternative under the criteria is defined, and the weighted matrix of dominance degree is acquired by incorporating the weights of criteria, after that, the characteristic sequence of the alternative under each criterion can be obtained. Finally, we can calculate the basic probability assignment and the overall uncertainty, and then fuse the evidences by using the improved combination rule. The decision can be made by the fusion results.(4)With regard to the classification problems of the complete and incomplete decision information systems, the decision methods are provided. In the complete decision information system, the evidences are obtained based on the support degree and the certainty gain function. Firstly, the redundant condition attributes are reduced. Then, we get the expansion decision information table by incorporating the new object, and calculate the Bayesian lower distribution sets under the reduced attribute sets; The support degree is defined to express the exact classification, and calculate the support degree and the certainty gain function of the Bayesian rough set to rate the support degree of the evidences. Finally, the basic probability assignment is obtained after normalization, and then fuses the evidences by using the improved combination rule. The decision can be made based on the fusion results. In incomplete decision information system, the evidences are obtained based on the limited tolerance relation and support degree. Firstly, by using the method of limited tolerance relation and Bayesian rough set, the lower distribution sets of the decision classes is obtained when each of the condition attributes is deleted.The classified quality is calculated, and the support degrees of condition attributes to decision classes are obtained on the basis of the above. Then the basic probability assignment is obtained after normalization. Finally, the evidences are fused by the improved combination rule, and the new object is classified based on the fusion result.