Some notes on canonical decomposition and separability of a belief function

The separable support function is a subclass of belief function, and it plays an important role in evidence theory. Although many properties of separable support function have been analyzed, the problem that how to judge whether a belief function is separable has not been solved. Through the canonical decomposition, any belief function could be decomposed into a set of generalized simple support functions. A judgment could be made from the decomposition result by checking all the weights, being a little cumbersome. Thus an alternative is provided. Some notes are made on the canonical decomposition, based on which two sufficient conditions to judge a separable support function are established. It is shown that whether a belief function is separable or not is not only decided by the relations between focal elements, but also influenced by the mass distributions among focal elements. Using the proposed conditions, one could directly make a judgment in certain cases from the basic probability assignment. © Springer International Publishing Switzerland 2014.