Double clutching properly as said, reduces wear on the tranny synchros. Increases wear slightly on clutch linkages, but minimal wear on the clutch if you're doing ti right. Slight decrease in fuel mileage since you have to rev the engine when double clutching down but I also double clutch all my downshifts. A habit from racing. My 3000GT's synchros are getting very difficult to find so preserving them is a good thing.
Yes, it's possible to double clutch up as well, but the only reason to do it would be if the tranny's synchros are shot (time to rebiuld or replace). To double clutch up, instead of blipping the throttle to raise rpms to where they should be when shifting into a lower gear as you do when doubleing down, you need to pause in neutral to allow the rpms to drop to where they need to for the gear you're shifting up into.
Max