Belief eXtropy: Measure uncertainty from negation

Abstract

As the duality and complement of the Shannon entropy, the eXtropy is proposed in this years. The eXtropy also can be explained from the perspective of negation, which can be seen as an entropy with one-step negation operation of elements. The Dempster-Shafer theory (DST), as the generalization of probability theory (PT), it can express the more uncertain information than the Bayesian distribution. It contains the uncertainty of the event probability expressed in the Bayesian distribution and the uncertainty of the Bayesian distribution. Based on above, this article proposes a new belief entropy in DST called SU entropy, which is the first belief entropy to use the elements rather than mass functions. And then, a new negation of non-specificity part in DST is proposed, which is the first time to research the negation of non-specificity alone. Finally, a new belief eXtropy was proposed. It is different from the traditional eXtropy thinking, but from the perspective of elements' negation. After verification, it has a satisfying performance in measurement uncertainty in DST. At the end of the paper, we discuss how to understand eXtropy from the perspective of negation, and the future research direction for the new belief eXtropy.