I'm not sure you can use alias for that, but you could use bash to create a script.
Now I'm no bash scripter, so I wouldn't be able to tell you the exact code for accomplish that, but what you could do is something like (this is just pseudocode, sort of, so don't expect it to work!!!):
get action, input
if action == search
then do apt-cache search input
if action == remove
then do apt-get remove input
if action == install
then do apt-get install input
Keep in mind you can write the script (or even a compiled application) in what ever language you are comfortable with, such as python or ruby for example, it does not have to be bash.
Again, remember my example is just pseudocode.