On the negation of a Dempster-Shafer belief structure based on maximum uncertainty allocation

Abstract

Probability theory and Dempster-Shafer theory are two germane theories to represent and handle uncertain information. Recent study suggested a transformation to obtain the negation of a probability distribution based on the maximum entropy. Correspondingly, determining the negation of a belief structure, however, is still an open issue in Dempster-Shafer theory, which is very important in theoretical research and practical applications. In this paper, a negation transformation for belief structures is proposed based on maximum uncertainty allocation, and several important properties satisfied by the transformation have been studied. The proposed negation transformation is more general and could totally compatible with existing transformation for probability distributions.