fadeOut() is a core jQuery method, not a Superfish option. Also, Superfish does not support animations for closing the submenus, as I've never been able to get that working in a completely non-buggy way - likely due to my own incompetence.
Part of the reason I haven't persevered to get that option working is because I personally like the responsiveness of the sudden closing of the submenus, whereas the opening animation serves a good purpose as it draws the eye to an important event. If you search this group you will find other people's efforts to add closing animations, some look to me like they would run into the bugs that I did during my experimentation, while others look more promising, although I haven't tested them. Joel Birch.