The Combination of Di erent Pieces of Evidence Using Incidence

Combining multiple sources of informationis a major and diicult task in the management of uncertainty. Dempster's combination rule is one of the attractive approaches. However, many researchers have pointed out that the application domains of the rule are rather limited and it sometimes gives unexpected results. In this paper, we have further explored the nature of combination and achieved the following main results. 1). The condition of combination in Dempster's original combination framework is more strict than that required by Dempster's combination rule in Dempster-Shafer theory of evidence. 2). Some counterintuitive results of using Dempster's combination rule shown in some papers are caused by the overlooking (or ignorance) of diierent independence conditions required by Dempster's original combination framework and Dempster's combination rule. 3). In Dempster's combination rule, combinations are performed at the target information level. This rule itself does not provide a combination mechanism at the original information level so that it is not able to combine the overlapped information. 4). An alternative approach to the combination of diierent pieces of evidence by using incidence calculus is proposed. In this approach diierent pieces of evidence are combined at both the original information level and the target information level rather than only at the target information level. 5). In this approach, we can combine not only independent pieces of evidence but also dependent pieces of evidence. 6). This new approach turns out to be consistent with traditional probability theory. It is more powerful than Dempster's combination rule at combining dependent evidence.