The Cumulative Rule for Belief Fusion

Abstract

The problem of combining beliefs in the Dempster-Shafer belief theory has attracted considerable attention over the last two decades. The classical Dempster's Rule has often been criticised, and many alternative rules for belief combination have been proposed in the literature. The consensus operator for combining beliefs has nice properties and produces more intuitive results than Dempster's rule, but has the limitation that it can only be applied to belief distribution functions on binary state spaces. In this paper we present a generalisation of the consensus operator that can be applied to Dirichlet belief functions on state spaces of arbitrary size. This rule, called the cumulative rule of belief combination, can be derived from classical statistical theory, and corresponds well with human intuition.