@dave462a: There are a few smaller indie ones, but more zombie survival. One I'm thinking of is called "How to Survive," I think. It should have a yellow box art, but it's a digital only game. It's not so much a base, it's a little enclosure to keep zombies out at night and you gather resources.
There are other similar games like "7 Days To Die" and " Deadlight."
I only played How to Survive on the 360 very briefly and I liked it because it was similar to State of Decay. They released 2 sequels, though I don't know if the PS4 has them. The other 2 games I never played, but are similar. I think How To Survive being the best.