Uncertain Information Modeling Based On Evidence Theory

In the real life,the obtained information is often uncertain,due to the influence of var-ious subjective factors and objective environment.By modeling the uncertain informa-tion,the essential properties of the given information can be effectively extracted,then be analyzed and applied to solve practical problems based on some mathematical tool-s.Basic probability assignment(BPA)function in Dempster-Shafer evidence theory has good performance for handling the uncertainty information,thus it has significant advantages in the expression and modeling of uncertain information.However,how to determine basic probability assignment is still an open issue in practical application.The problem of uncertain information modeling based on Dempster-Shafer evidence theory,namely the problem of how to determine BPA,will be researched in this paper.The existing methods to determine BPA pay more attention to the uncertainty of infor-mation,but do not simultaneously consider the reliability of information sources,which may lead to generate an unreasonable BPA.How to address this issue will be researched in this paper,which aims to promote the development of evidence theory.The main re-search results and the innovation points in this paper are as follows:In this paper,a novel method to determine BPA is proposed based on attribute weight.The attribute weight is generated using the similarity degree among the classes under a certain attribute,which reflects the degree of reliability relatively in the practical ap-plication.Then,the attribute weight is taken as a factor to correct the traditional BPA,and BPA is gained which contains the reliability of the information source.The pro-posed method is based on the gaussian fuzzy number,which can reflect the feature information of training data.Finally,the application examples of the multiple attribute classification and fault diagnosis,are demonstrate the validity and reasonability of the proposed method.In further research,we found that the reliability of information sources is not only af-fected by the similarity among classes,but also affected by the test samples.In order to solve this problem,originating from the idea of the Z-number,a new method to rep-resent BPA along with their associated reliability is proposed in this paper,which is named two-tuples BPA.Two-tuples BPA is an ordered pair,noted as(BBA,R).Its first component BP A is a mass function,and the second component R is a measurement of the reliability of the first component.According to this ordered pair,the reliability of BPA can be measured well at the stage of BPA generation.In addition,the proposed method is an improvement on the method based on attribute weight.The main manifes-tation is that the proposed method further considers the risk distance between the test sample and the overlapping area among classes when measuring the reliability of BPA.This makes the results more reasonable and more credible.