This paper presents a three-class mental task classification for an electroencephalography based brain computer interface. Experiments were conducted with patients with tetraplegia and able bodied controls. In addition, comparisons with different time-windows of data were examined to find the time window with the highest classification accuracy. The three mental tasks used were letter composing, arithmetic and imagery of a Rubik's cube rolling forward; these tasks were associated with three wheelchair commands: left, right and forward, respectively. An eyes closed task was also recorded for the algorithms testing and used as an additional on/off command. The features extraction method was based on the spectrum from a Hilbert-Huang transform and the classification algorithm was based on an artificial neural network with a fuzzy particle swarm optimization with cross-mutated operation. The results show a strong eyes closed detection for both groups with average accuracy at above 90%. The overall result for the combined groups shows an improved average accuracy of 70.6% at 1s, 74.8% at 2s, 77.8% at 3s, 79.6% at 4s and 81.4% at 5s. The accuracy for individual groups were lower for patients with tetraplegia compared to the able-bodied group, however, does improve with increased duration of the time-window.