Not sure if this is the cause of a new update or the PS4 simply not being able to handle the game. But no game I own has been crashing since the release of Battlefield 4. What gives. Edit: Yes I know the title was misspelled. Typo.
There is a fix. It's general maintenance you should perform on your PS4 once in a while. Rebuild the database. Turn the PS4 off. Hold the power button for 7 seconds until you hear the beep. Plug in the dual shock, hit the PS button, select Rebuild Database from the menu. I was crashing sometimes every time I went to a 96+ fight. Rebuilt the database and played for 3 hours without a crash yesterday. Any time the performance or crashes start to get worse Rebuild the Database.