The Method Study Of Belief Fimction Probability Approximation In D-S Evidence Theory

Evidence theory is an uncertain theory, and it has been widely used in dealing with uncertainty in decision- making problems. Belief function in evedience theory is to provide the corresponding reliability for each proposition based on the experience of experts, and then make decisions. Belief function exists reliability in multiple-proposition.When making decisions, we hope to get reliability in the single proposition. Therefore, there are some difficulties in making decisions by using belief function directly. The solution is converting the reliability of multiple proposition to the probability distribution on the single proposition. Then make decisions, that is to say belief function probability approximate s. But the probability approach of belief function is not unique, and how to find the best probability approach is a hot issues. But the information entropy is to measure the uncertainty of information, and it can measure the uncertainty of the approached probability distribution. Therefore, the information entropy of probability approach we obtained is as small as possible for decision- makers. How to obtain the best probability distribution(ie, the minimum entropy) is our main purpose of research.The probability approach of belief function is related to application on making decision and information technology, so it has caused high concern among domestic and foreign scholars and they make corresponding research. Pignistic probability conversion(ie trust Pignistic probability function approximation) which Smets proposed is most widely used. But Pignistic probability function approach is the most conservative estimation of the probability. This paper proposes a new method of probability approach of belief function by researching the properties of information entropy, simultaneously considering the high risk of making decisions caused by the pursuiting entropy minimization. This new method can quickly and efficiently get the best probability approximation by example, and can effectively reduce the high-risk decisions broughted by probability approximation of belief function.First, the paper introduces the background and significance of the probability approach of belief function, sketching its research status and the basic knowledge of evidence theory.Then introduces several probability approach of belief function method in detail and study some properties of information entropy. Combined with the current results of other scholars, integrating of the properties of the information entropy, we propose a new algorithm for probability approach of belief function.Finally, we study the method of probability approach of the interval of belief structure, analysising several properties of probability inteval. Then disguss the links to belief function and provide a method for the study of belief function theory.