The traditional markings string players use to indicate on which string a particular pitch should be played are Roman numerals. When they are notated above the staff, they indicate which string to play on. When we want to indicate position, we tend to use Roman numerals as well, so we put them in a different place (usually below the staff). When you have two sets of Roman numerals to consider, one above the staff, and one below the staff, things can get confusing. Roman numerals also take up a lot of vertical space on the page, and with all the other information given on pre-printed music (not to mention ledger lines), things can get cluttered. Here's an example of clutter from the Franck Violin Sonata.
The other day I came across the Phantasy for Viola and Pianoforte by Benjamin Dale, and noticed the elegant markings he (or Lionel Tertis, the editor of the piece, or Schott, who published it in 1912) used to indicate which string particular pitches should be played on.
Here's a bit of detail:
These markings made immediate sense to me, and this is the way I plan on marking fingerings from now on. Pitches on the A string are pretty obvious for violists, so there is no reason for using a single line for the A string. Two lines indicate a pitch should be played on the D string, three lines indicate it should be played on the G string, and four lines indicate that the pitch should be played on the C string. The lines are always below the finger number, and they act like icons that lead directly to location without the need of translation (or more numbers).