A note on the approximation of Shenoy's expectation operator using probabilistic transforms

Abstract

ABSTRACTRecently, a new way of computing an expected value in the Dempster–Shafer theory of evidence was introduced by Prakash P. Shenoy. Up to now, when they needed the expected value of a utility function in D-S theory, the authors usually did it indirectly: first, they found a probability measure corresponding to the considered belief function, and then computed the classical probabilistic expectation using this probability measure. To the best of our knowledge, Shenoy's operator of expectation is the first approach that takes into account all the information included in the respective belief function. Its only drawback is its exponential computational complexity. This is why, in this paper, we compare five different approaches defining probabilistic representatives of belief function from the point of view, which of them yields the best approximations of Shenoy's expected values of utility functions.