Partial Ordering of Hyper-powersets and Matrix Representation of Belief Functions within DSmT

In this paper, we examine several issues for ordering or partially ordering elements of hyper-powertsets involved in the recent theory of plausible, uncertain and paradoxical reasoning (DSmT or Dezert-Smarandache Theory) developed by the authors. We will show the benefit of some of these issues to obtain a nice and useful matrix representation of belief functions.