The Information Measure And Application Research On Intuitionistic Evidence Set

The modeling of uncertainty is always an open issue.Currently,the existing uncertainty modeling theories are probability theory,Dempster-Shafer theory,fuzzy theory and so on.As the frontier theory of uncertainty,evidence theory is widely focused and researched for its ability of uncertainty expression.The researches on evidence theory not only promote the development of evidence theory,but also explore the applications in practical problems.The thesis concentrates on intuitionistic evidence sets(IESs),concluding the researches on the mathematically analysis and practically application.The fundamental definition of IES is Intuitionistic Basic Probability Assignment(IBPA).In the thesis,the mathematically analysis consists of two aspects,one of which is that a uncertainty measure and a divergence on IBPA are proposed,and the other one is that the mathematical properties of the proposed uncertainty measure and divergence are analysed and proved.In the thesis,the total uncertainty of an IES is measured by calculating the interval distance between belief interval and interval corresponding to the most uncertainty.By generalizing Belief Jensen-Shannon(BJS)divergence,a novel difference measure on IBPA is proposed.Except for definitions of uncertainty measure and difference modeling,the properties of the measure are mathematically analysed and proved.The most important conclusion is the distribution of the IES corresponding to the maximum uncertainty.In addition,when the IES degenerates to a basic probability assignment(BPA),the distribution corresponding to the maximum uncertainty is the same as the distribution corresponding to the maximum Deng entropy.Practical applications include data classification and medical diagnosis.The critical ideas of classification method are the IESs generation method,the discounting coefficient for revising generated IESs,and grade function for finnal classification.In the practical example,it is illustrated that the accuracy rate of the proposed method is higher than that of the classical BPA method,meanwhile,the proposed method is effective even in few-shot training sets.To deal with medical diagnosis,a diagnosis method based on divergence of IBPAs is proposed.In the practical example,it is suggested that the proposed decision making method is feasible and effective.