In this work, we study the uncertainty aspects in bio-metric identification and authentication systems. The uncertainty lies in two aspects, i.e., the probability mass function (p.m.f.) of users' biometric information and the observation channel. For the p.m.f. of users' biometrics, it is assumed that the users are from different groups and the distribution of each group is determined by the state. For the observation channel, it is assumed that there is a set of channels and the actual observation channel is from this set.