Digital BW, The Print

How does an RGB scanner determine Greyscale equivalents? Is there a formula it applies to 
the three components? If so, would the color "fringing" I see on some RGB scans contribute to 
a softening of Greyscale scans? 

The only way I can see to avoid this is for only one of the RGB components to be used, and I 
know that would not be an accurate representation of RGB translated into GS.

Thanks,
Dale Hoffman