Entropy, Vol. 21, Pages 73: Negation of Belief Function Based on the Total Uncertainty Measure (Entropy)

The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.