Most of the decision fusion systems proposed hitherto in the literature for multiple data source (sensor) environments operate on the basis of pre-defined fusion logic, be they crisp (deterministic), probabilistic, or fuzzy in nature, with no specific learning phase. The fusion systems that are trainable, i.e., ones that have a learning phase, mostly operate in the features-in-decision-out mode, which essentially reduces the fusion process functionally to a pattern classification task in the joint feature space. In this study, a trainable decisions-in-decision-out fusion system is described which estimates a fuzzy membership distribution spread across the different decision choices based on the performance of the different decision processors (sensors) corresponding to each training sample (object) which is associated with a specific ground truth (true decision). Based on a multi-decision space histogram analysis of the performance of the different processors over the entire training data set, a look-up table associating each cell of the histogram with a specific true decision is generated which forms the basis for the operational phase. In the operational phase, for each set of decision inputs, a pointer to the look-up table learnt previously is generated from which a fused decision is derived. This methodology, although primarily designed for fusing crisp decisions from the multiple decision sources, can be adapted for fusion of fuzzy decisions as well if such are the inputs from these sources. Examples, which illustrate the benefits and limitations of the crisp and fuzzy versions of the trainable fusion systems, are also included.