In Cutting Edge Software, users can control which notifications appear in their Notifications screen. To do so, simply click the Notifications bell in the top right on the screen, and on the new screen click the "Control Panel" button:

In the popup that opens, you can choose to check or uncheck from a list of options. Checking a box prevents any new notifications of that type from being generated for your site not per provider :

It is important to note that checking one of the options will not hide any existing notifications of that category, it will simply prevent new ones from being generated until such time as a user re-checks the relevant box. Unchecking a box will also not re-generate any notifications that were prevented while the box was checked.