On the uncertainty and ignorance of statistical decision and evidence combination

The classical Bayesian decision theory and the hypothesis testing for processing distributed decision fusion problems have an important shortcoming-lack of flexibility. In other words, they can not discriminate uncertainty and ignorance. The Dempster-Shafer (DS) theory overcomes this shortcoming, but its mathematical basis, the axiomatic definition of evidence is not very rigorous. Therefore, a perfect, reliable, and general method of statistical decision and evidence combination is demanded. In this respect, Thomopoulos presented a generalized evidence processing (GEP) method, based on Bayesian theory and DS theory. This paper presents a new strategy for statistical decision and evidence combination-the double bound testing (DBT). Compared with GEP, DBT not only increases the flexibility of decision, but also presents a sound mathematical basis and an explicit concept.