Untreated and treated example.
This Hummel hooded top in our example is a major fuzz up. Made from 100% (new cheap, rubbish!) Polyester. Before I did the whole top I took this shot of a treated and untreated area. What I use is a heat gun to burn off the broken filaments. This may sound as if this would destroy the item totally. Indeed it is a kill or cure method and the difference between success or a write off is MILLISECONDS! Have you ever tried running your finger through a candle flame? If you move your finger at about 10cm/sec you don't feel anything. But you'll be without hair on your finger. It's the same principal here.
Special clothes shavers like the Remington Fuzzaway or a plain electric shaver are OK for small areas. Don't bother using a razor you end up breaking more fibres than you cut off. This 1500 watt heat gun produces an airflow about 500 °C. Commonly used for removing paint it's just the job. If you can use something like this. It's best swept across the surface of the item to de-fuzz at a distance of about 8cm. At a speed of about 40cm/sec. Anything less and you'll shrivel the area. It's fast and leaves the area more resistant to further damage by the way of sealing the ends of the filaments in a very small round blob. You must practice the use of a tool like this before going for it. Practice on the inside of the pocket or something first. The closer you can take your timing to the point just before shrivelling occurs the better and more resilient your work will be. But it's a very fine line between success and failure.

If you need more information. A good place to ask is in the rec.crafts.textiles.misc newsgroup.