First, to receive alert from an artist you must be subscribed to that artist. Next, you can change the types of alerts you receive from each artist by checking (or unchecking) the types of alert that you want to receive from that artists.
Note: if you uncheck all of the subscription options for an artist he/she/they will still remain in your listing. If you wish to delete the artist from your subscription list you must visit Manage Subscriptions.
First, select Subscriptions from the fans navigation menu. Next, select Manage Subscription and you from here you can delete the artist subscription that you no longer desire to follow.