Consider you have 4 "treated" and 4 "control" samples. Using the two dyes "A" and "B", you can perform 4 dual-color hybridisations, each one comparing a treated sample to a control sample (on the same array).You are actually free to decide which of these samples should be labelled with which dye. A simple approach was to choose "A" for all treated and "B" for all control samples. Theoretically, this is absolutely ok. However, the detection sensitivity is not linear and depends on the dye and the intensity. Therefore, for instance, an equal dye-ratio at a larger intensity may give a different resullt that the same equal dye-ratio at a lower intensity. This eventually means that the ratios you are measureing are biased (the bias is intensity-dependend, possibly probe-sequence dependent and the amount of bias is unknown). This bias can be corrected when the both dyes are used for each kind of sample: once "treated" is labelled with "A" and hybiridized against a "control" labelled with "B", and onnce a "treated" is labelled with "B" and hybridized against a "control" labelled with "A". Bith, the first and the second hybridisation are biased, but just to opposite directions. Taking the average will (mostly) eliminate this dye-specific bias.

With the 4/4 samples you could go an label each of the 4 treated and also each of the four controls in either dye (A and B). A simple design was to average always a pair of hybridizations where the very same samples were used twice (once labelled in A and once in B). However, this doubles your number of arrays/hybridizations (gaining a little more precision by lowering the technical variance; this might not always be required or reasonable).

Another approach is to label half of the treated samples in A and the other half in B (the same wih the controls) and combine them to get 4 dual-color hybridizations. In this design, the bias is statistically cancelled out.

However the experiment is finally designed, at the end you (should) have the equal numbers of samples of each group labelled with either dye, so the experiment can be devided into two identical/similar subgroups where only the dyes are "swapped" (exchanged between the groups "treated"/"control").