Perhaps I am not clear on what type of notifications the original poster is talking about. But I would think that when on the vty connection using terminal no monitor should stop notification messages. And on the console using no logging console should stop the messages. If that does not solve the issue then please provide clarification about what these notifications are.
actually, if you just want to get rid of these particular interface messages, you could use the interface command:
no logging event link-status
If the interface up/down notifications are the only notifications that the original poster is concerned with then the suggestion from @Georg Pauwen is a good solution. If they are just examples of the kind of notifications but other notification messages should also not show up then I believe that my suggestions about stopping syslog messages for the vty/console session would be the better solution.