Abstract: Objects of unknown identity are identified through comparison with incompletely specified models in incompletely specified databases of a computer-based system. These incomplete models and databases are described by specifying suspected ambiguities in both the categories of classification and a priori frequencies of occurrence of the objects to be identified. Such ambiguities are mathematically represented as fuzzy Dempster-Shafer bodies of evidence. Accumulated pieces of evidence about an unknown object are fused using a Dempster-Shafer-like combination operation. This operation takes the state of prior knowledge in regard to the database--ambiguities in classification categories and in frequencies--into account. The operation provides the correct Bayesian probability estimate of identity (of an unknown target) if all pieces of evidence delivered to the process have been constructed as Bayesian posterior probabilities.