Belief function independence: II. The conditional case

In the companion paper [Int. J. Approx. Reasoning 29 (1) (2002) 47], we have emphasized the distinction between non-interactivity and doxastic independence in the context of the transferable belief model. The first corresponds to decomposition of the belief function, whereas the second is defined as irrelevance preserved under Dempster's rule of combination. We had shown that the two concepts are equivalent in the marginal case. We proceed here with the conditional case. We show how the definitions generalize themselves, and that we still have the equivalence between conditional non-interactivity and conditional doxastic independence. © 2002 Elsevier Science Inc. All rights reserved.