Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.