I sink a good number of fringe putts, you just have to know when its better to use chip or whatever, but 80% of the time, you are good with the putter if it within 10 yards or so.
I add 2 feet of power for 1 foot or less or fringe. add 1 foot per foot after that. 1.5 if it's a little up hill. If its a steep uphill, chip, pitch, bump and run, flop, hit it even harder with the putter - whatever feel best.
that's for tourney greens, I'm not sure if the fringe changes a bit with green speeds.