Fin rot in my experience always had black edges. I'd keep him alone until it grows back, and test your water quality since fin rot is most often caused by poor water quality. Test your ammonia, nitrite, and nitrate. If ammonia is anything higher than 0 it's a problem.
If it's bitten off, you'd have to find out who's doing the biting, so I'd watch the other fish to see if anyone's a perpetrator.