I'm not a heavy Facebook user, but tend to check it on average few times a week. Facebook normally sends a push notification to your phone when somebody posts on your wall, comments on a photo you uploaded, or does something similar concerning yourself. This is all well and good and if I visit Facebook at least once a day, it all works as expected.
However, lately I noticed that if I don't visit Facebook website or their app for a few days, they send a completely random notification. Something like "your friend added a photo", or "your friend liked a page". They are not even people I regularly interact with on Facebook! I looked through notification settings on Facebook website and Android App. There is simply nothing that would explain such random notifications. It seems that it's just Facebook's sneaky way or reminding about itself!
Some people who had similar problem few years ago, suggested disabling "Activity you've missed" option in notification settings, but that option is no longer there...
I find this behavior extremely annoying, especially on a phone. So I had no other option than completely disable all Facebook notifications on Android app level. This can be done by unchecking Show notifications box in Settings > Application Manager > Facebook.
Facebook Android App v18.104.22.168.16
Samsung Galaxy Note 3