You need to replace the rubber membrane - the trigger has a plastic blade in it which pushes on the rubber, and eventually wears it down - see the link below for a picture/description of the problem. If you don't want to order/wait for new parts in the mail, you can remove the trigger button, put a glob of epoxy in the hole, and that will fix it.
https://www.reddit.com/r/PS4/comments/3446xi/image_is_your_dual_shock_4_trigger_misbehaving/
here is a picture of the problem
http://i.imgur.com/JTnrzM0.jpg