Cumulative and averaging fusion of beliefs

The problem of fusing 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 fusion have been proposed in the literature. We show that it is crucial to consider the nature of the situation to be modelled and to select the appropriate fusion operator as a function thereof. In this paper, we present the cumulative rule and the averaging rule of belief fusion, which represent generalisations of the subjective logic consensus operator for independent and dependent opinions respectively. The generalised operators are applicable to the combination of general basic belief assignments (bbas). These rules, which can be directly derived from classical statistical theory, produce results that correspond well with human intuition.