Design of parallel binary decision fusion systems is often performed under the assumption that the decision integrator (the data fusion center, DFC) possesses perfect knowledge of the local-detector (LD) statistics. In most studies, other statistical parameters are also assumed to be known, namely the a priori probabilities of the hypotheses, and the transition probabilities of the DFC-LD channels. The local observations are assumed to be statistically independent (conditioned on the hypothesis). Under these circumstances, the DFC's sufficient statistic is a weighted sum of the local decisions and the weights depend on the statistical parameters. When these parameters are unknown, we propose to estimate them online, using the discriminant function of the DFC as the performance index. This process can be performed with the help of a teacher that supplies the correct labels of the data, or without supervision, by estimating the correct labels from the data. The label-estimates are generated by the DFC, on the basis of its own past decisions and its assessment of the LD-data reliability.