In which case I'll guess that you're using Chrome as your browser.
One of the reasons I don't like Chrome is because Google tries to link together everything you do using their products and services. (So, because your using Google's browser and Google's social media site, you get Facebook notifications through Chrome; it wouldn't happen with any other browser).
Reading through this lot suggests that you can either turn off the notifications in Chrome (see the post from Ashley Wall) or within Facebook (see the post from David Richards):
https://en-gb.facebook.com/help/community/question/?id=10203291643932421