The problem of distributed decision fusion is studied in the case when the probability distributions of the individual detectors are not available. The detector system is available so that a training sample can be generated by sensing objects with known parameters or classification. Earlier solutions to this problem required some knowledge of the error distributions of the detectors, for example, either in a parametric form or in a closed analytical form. Here we present three methods that, given a sufficiently large training sample, yield an approximation to the optimal fusion rule with an arbitrary level of confidence. These methods are based on (i) empirical estimation, (ii) approximate decision rule, and (iii) nearest-neighbor rule. We show that a nearest-neighbor rule provides a computationally viable solution, which approximates a neural network-based one while ensuring fast computation.