There's a little controversy about the history of our instrument. Some say that the bass is descended from the bass version of the viol, and others the violin family. A French guy even wrote a book "History of the doublebass," putting forth his thesis that the bass is entirely a member of the violin family and always was. There seems to be not enough documentation to really do more than make an educated guess, I think. The essential difference between the violin and viol families is that the violin places the soundbar (bracing) under the bass side foot of the bridge, and a post under the treble side foot. So the bridge and post assembly acts as a fulcrum. Whoever came up with this was the "inventor" of the violin, and a real genius. Anyway, I think it's reasonable to think that the violin, viola and cello developed together as a family, and as a bigger bass instrument was needed, the bass came into use, with probably the first basses being converted bass viols. If you look at Dragonetti's famous bass, you can see from the spread of the F-holes that it had probably 6 strings or more when it was built.... Anyway, because of the ungodly size of the instruments, some makers kept viol features that worked for that big a box -sloping shoulders, flat back, shapes etc. maybe they didn't want to throw out their old moulds... in any case, what makes a violin a violin is first and foremost the bassbar/soundpost arrangement, which the double bass has.
For the OP, I wonder why you'd want such a thing. It wouldn't be easily intonated, and it wouldn't sound like a double bass as we know it, so if you're attracted to the sound of the double bass, you wouldn't really get that from a fretted instrument. If you are interested in the double bass, great, welcome. Take on the instrument as it is for now, it's really not as hard as it might seem, it's just a different level of physical discipline.
Good luck.
Edit: maybe I'm reading too much into your (the original) post. It seems like you might be asking just because you thought you saw one at school, not because you want to have one.... oops