Multi-Source Fusion Operations in Subjective Logic

The purpose of multi-source fusion is to combine information from more than two evidence sources, or subjective opinions from multiple actors. For subjective logic, a number of different fusion operators have been proposed, each matching a fusion scenario with different assumptions. However, not all of these operators are associative, and therefore multi-source fusion is not well-defined for these settings. In this paper, we address this challenge, and define multi-source fusion for weighted belief fusion (WBF) and consensus & compromise fusion (CCF). For WBF, we show the definition to be equivalent to the intuitive formulation under the bijective mapping between subjective logic and Dirichlet evidence PDFs. For CCF, since there is no independent generalization, we show that the resulting multi-source fusion produces valid opinions, and explain why our generalization is sound. For completeness, we also provide corrections to previous results for averaging and cumulative belief fusion (ABF and CBF), as well as belief constraint fusion (BCF), which is an extension of Dempster's rule. With our generalizations of fusion operators, fusing information from multiple sources is now well-defined for all different fusion types defined in subjective logic. This enables wider applicability of subjective logic in applications where multiple actors interact.