Are Venn Diagrams with two circles in a shape like the number 8 still Venn Diagrams?

I think that they are when dealing with Fuzzy Logic and 3 Set Categories like the example of 3 states of matter (Solid, Liquid, Gas). What do you think?

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- Sep 16th 2010, 11:49 PMVurgVenn Diagrams & Fuzzy Logic
Are Venn Diagrams with two circles in a shape like the number 8 still Venn Diagrams?

I think that they are when dealing with Fuzzy Logic and 3 Set Categories like the example of 3 states of matter (Solid, Liquid, Gas). What do you think? - Sep 17th 2010, 01:49 AMemakarov
The number of circles corresponds to the number of sets being considered. Wikipedia article has examples with two sets as well as more than three sets. Further, according to the article, all circles must have a nonempty intersection by definition of Venn diagrams; this precludes figure-eight shape. Euler diagrams, however, don't have to contain "all 2^n hypothetically possible zones corresponding to some combination of being included or excluded in each of the component sets."