I've done this using epoxy. I got mine from system 3 resins -- trial kit costs $25bucks and will last you for years for small uses here and there (https://www.ndic.com/systemthree/trial_kits.asp) -- but I think any good marine epoxy will work.

If you have a spot that's chipped, then put some duct tape on the back of the floor mat and pour the mixed epoxy into the hole from the front and let set.

For small cracks, apply the epoxy/glue to the crack with a small spatula from the back side and then tape together across the length of the break till it sets.

If it's a big crack, then use fiberglass (comes with the trial kit) on the back side of the mat to reinforce the weld.

I've used fillers/colorings with this epoxy, and you can get iron oxide powder to mix in (very litle bit!) that will approximate the color of the mats for tan interior. Also, if any excess is sticking out of the weld when you're done, you can cut it off with a sharp knife before it fully sets, and sand it afterward.