Most vessel fenders are inflated plastic balls or cylinders with a line attached.
Rope mats are rarely used any more, even on tug boats.
Tugs generally have large used aircraft tires as fenders, or sometimes closely folded flaps of sheet rubber, attached around the bow, from one side to the other, like a giant piece of terrible tasting ribbon candy.
Regards,
Chris
Navy test range auxiliary vessel "Swiss Ladder-120