Fuzzy Venn diagram regions labeled in ternary

Question

I have a couple of questions about the Venn diagrams object :

1. Words from the binary alphabet with n letters label each region of an order-n Venn diagram. Is there any more profound connection between binary representations and say the way Venn diagrams should be laid out with respect to neighbors (Hamming distance between labels, say)?

2. What are the consequences if we consider 'fuzzy' sets, say a type of set with a inclusion metric that is ternary (0,out),(1,inbetween),(2,in) , and we label the 'regions' of some kind of Venn diagram using words of n letters from the ternary alphabet?

Answer 1

You might want to explore this article, which goes some way to addressing your questions and gives some references to follow up.

Lewis Carroll explores diagrams and methods in Symbolic Logic and the Game of Logic, but this is a less relevant and rather old fashioned treatment.

Answer 2

Randolph diagram might be an alternative to Venn diagrams.
Randolph's paper on jstor