The problem of fusing beliefs in the Dempster-Shafer belief theory has attracted consid-erable 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 lit-erature. We show that it is crucial to consider the nature of the situation at hand and to select the appropriate fusion operator as a function thereof. In this paper we present the cu-mulative 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 assign-ments (bbas). These rules, which can be directly derived from classical statistical theory, produce results that correspond well with human intuition.