Compositional models for credal sets

We present the composition operator, already known from probability, possibility, evidence and valuation-based systems theories, for credal sets. We prove that the proposed definition preserves all the properties enabling us to design compositional models in a way analogous to those in the above-mentioned theories. A special kind of compositional models, the so-called perfect sequences of credal sets, is studied in more detail and (among others) its relationship to perfect sequences of probability distributions is revealed. The theoretical results are illustrated by numerous simple examples. (C) 2017 Elsevier Inc. All rights reserved.