The Canonical Decomposition of a Weighted Belief

Any belief function can be decomposed into a confidence and a diffidence components. Each components is uniquely decomposable into simple support functions that represent the impact of the simplest form of evidence, the one that only partially supports a given subset of the frame of discernment. The nature of the inverse of Dempster's rule of combination is detailed. The confidence component translates the impact of 'good reasons to believe'. It is the component classically considered when constructing a belief. The diffidence component translates the impact of 'good reasons not to believe'. K e y w o r d s : uncertainty, belief functions, simple support f unc t i ons , Dempster 's ru le o f combina t ion and decombination.